Predictive Spatial Machine Learning in the Era of Big Data: A Critical Analysis of Methods, Technical Advances, and Research Frontiers for Geophysical Applications

Predictive Spatial Machine Learning in the Era of Big Data: A Critical Analysis of Methods, Technical Advances, and Research Frontiers for Geophysical Applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Predictive Spatial Machine Learning in the Era of Big Data: A Critical Analysis of Methods, Technical Advances, and Research Frontiers for Geophysical Applications Ebenezer Afrifa-Yamoah, Yaw Kwaafo Kwaafo, Bright Wiredu Nuakoh, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9340991/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Predictive spatial machine learning has become essential across the geosciences, yet three critical challenges remain insufficiently addressed: the integration of spatial structure into machine learning architectures, the rigorous quantification of prediction uncertainty, and the validation of models under spatial autocorrelation. This systematic review reveals that hybrid geostatistical-ML frameworks consistently outperform pure machine learning methods when spatial autocorrelation is strong with reported accuracy gains of 10–40% across seismic hazard assessment, mineral resource estimation, hydrogeological forecasting, and environmental monitoring. However, the review identifies a fundamental disconnect between methodological capability and practice: fewer than 15% of studies explicitly decompose prediction uncertainty into its aleatory (irreducible) and epistemic (reducible) components, despite the practical importance of this distinction for guiding data collection and risk assessment. Validation practices lag further behind, with standard cross-validation overestimating model performance by up to 47% when spatial autocorrelation is ignored, yet spatially aware alternatives such as Importance-Weighted Buffered Cross-Validation and spatial block bootstrap remain underutilised. Physics-informed spatial constraints show promise in hydrogeology and seismology, where governing equations provide natural regularisation, but lack unified frameworks transferable across geophysical domains. A conceptual decision pathway framework linking data characterisation, methodology selection, uncertainty quantification, and validation is proposed to guide practitioners through these interdependent choices. The review identifies specific research frontiers with actionable directions, including the operationalisation of aleatory-epistemic uncertainty decomposition for targeted spatial sampling design, the development of spatially aware interpretability methods that account for autocorrelation in feature importance, and community benchmark datasets modelled on existing hydrological standards to enable reproducible cross-method comparison in the geosciences. uncertainty quantification geostatistics-ML integration spatial validation feature engineering probabilistic prediction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Highlights 1. Hybrid geostatistical-ML frameworks capture complex spatial heterogeneity and dependencies. 2. Advanced methods distinguish between aleatory and epistemic uncertainties in spatial prediction. 3. Novel validation frameworks address spatial autocorrelation challenges in model assessment. 4. Physics-informed spatial ML balances data-driven insights with domain knowledge. 5. Key frontiers: interpretable models, scalable algorithms, and multi-scale uncertainty estimation. 1 Introduction 1.1 Motivation and Rationale The last decade has witnessed an unprecedented surge in spatial data generation across the geosciences, driven by advances in earth observation technologies, distributed sensor networks, and the proliferation of Internet of Things (IoT) devices in environmental and geophysical monitoring systems. In seismology, dense seismic arrays now generate terabytes of continuous waveform data daily (Kubo et al., 2024 ). In mineral exploration, multi-element geochemical surveys and hyperspectral remote sensing produce spatially dense, high-dimensional datasets that challenge traditional geostatistical analysis (Talebi et al., 2021 ). In hydrogeology, networks of groundwater monitoring wells combined with climate reanalysis data enable spatiotemporal prediction at continental scales (Kunz et al., 2024). This exponential growth in geospatial data volume, velocity, and complexity has fundamentally transformed the landscape of spatial data analytics, creating both extraordinary opportunities and formidable challenges (Casali et al., 2022 ). What sets spatial machine learning apart from conventional machine learning approaches is its explicit incorporation of spatial relationships and dependencies into model architectures, representing a paradigm shift in how we process and analyse geographic and geophysical data (Casali et al., 2022 ; Nikparvar and Thill, 2021 ). This distinction is rooted in the recognition that spatial data exhibits unique characteristics that fundamentally challenge traditional machine learning assumptions. Specifically, spatial autocorrelation (the tendency of nearby features to be more related than distant ones), spatial heterogeneity (the variation of processes across space and time), and scale dependency (the influence of spatial scale on observed patterns) violate the independent and identically distributed (IID) assumptions underpinning conventional machine learning methods (Cliff and Ord, 1973 ; Kopczewska, 2022 ; Matheron, 1962 ; Woodcock et al., 1988 ). These violations are particularly pronounced in geophysical applications, where subsurface properties vary continuously across three-dimensional space, seismic wave propagation depends on complex geological structures, and groundwater flow is governed by spatially heterogeneous hydraulic conductivity fields. 1.2 Literature Context and Gaps Several reviews have addressed aspects of spatial machine learning in recent years. Casali et al. ( 2022 ) provided a scoping review of machine learning for spatial analyses in urban areas. Ma et al. ( 2019 ) reviewed deep learning applications in remote sensing. Kopczewska ( 2022 ) examined spatial ML opportunities for regional science. Nikparvar and Thill ( 2021 ) surveyed machine learning approaches for spatial data and identified key spatial data properties that affect machine‑learning performance and compared data‑level versus algorithm‑level approaches for handling them. In the geophysical domain, Kubo et al. ( 2024 ) reviewed machine learning advances in earthquake seismology, Anjom et al. ( 2024 ) assessed ML for seismic exploration, and Xu et al. (2025) reviewed ML-based seismic subsurface characterisation. However, no existing review systematically integrates the three pillars that are essential for reliable geophysical prediction: (1) spatially aware machine learning frameworks, (2) rigorous uncertainty quantification distinguishing aleatory from epistemic sources, and (3) validation methodologies that properly account for spatial autocorrelation. This gap is particularly consequential in geophysical practice, where uncertainty directly influences critical decisions such as forecasting induced seismicity from fluid injection, assessing subsurface integrity for CO₂ storage and hydrogen caverns, evaluating fault reactivation risks around underground excavations, and predicting reservoir compaction and surface subsidence, contexts in which mischaracterised uncertainty can lead to irreversible environmental damage, infrastructure failure, or regulatory breach. 1.3 Cross-Domain Perspectives Spatial machine learning methodologies are deployed across diverse domains, each contributing unique insights and facing distinct challenges. In ecology, species distribution models must handle spatially biased occurrence data and extrapolation to unsampled environments (Roberts et al., 2017 ). In epidemiology, disease mapping requires spatially varying risk surfaces with reliable uncertainty bands for public health decision-making (Paez et al., 2021 ). In urban planning, interpretable spatial models help stakeholders evaluate infrastructure vulnerability under climate change scenarios (Zhu et al., 2019 ). In precision agriculture, soil property mapping combines geostatistical and machine learning approaches with multi-resolution remote sensing data (Wadoux et al., 2019 ). A cross-domain comparison reveals that while methodological foundations are shared, including spatial cross-validation, geostatistics-ML hybrids, and spatial uncertainty quantification, the relative emphasis on specific techniques varies substantially. Geophysical applications face challenges related to three-dimensional spatial structures, multi-scale heterogeneity, and the integration of physics-based constraints, which set them apart from predominantly two-dimensional surface-level analyses in other fields. 1.4 Objectives and Scope This review aims to: (1) provide a systematic, PRISMA-guided assessment of the current state of predictive spatial machine learning, with emphasis on geophysical applications; (2) introduce a practical conceptual decision pathway framework linking data characteristics, methodology selection, uncertainty quantification, and validation for geophysical prediction problems; (3) critically compare methods; (4) evaluate uncertainty quantification approaches with explicit attention to the aleatory-epistemic distinction and its implications for geophysical decision-making; and (5) identify specific research gaps and propose an actionable roadmap with concrete methodological directions. The review encompasses studies across seismology, mineral exploration, hydrogeology, and environmental monitoring. 2 Review Methodology We followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines (see Figure S1 of supplementary material; Page et al., 2021 ) to ensure transparency and reproducibility in the literature search, screening, and synthesis processes. Further details of the review methodology are presented in a Supplementary material. 2.1 Search Strategy We searched four major databases: Scopus, Web of Science, IEEE Xplore, and Google Scholar. The search was conducted between January and March 2025, covering publications from 2015 to 2025. The search string combined terms from three conceptual domains: spatial machine learning ("spatial machine learning" OR "geostatistical ML" OR "spatial prediction" OR "geographically weighted" OR "spatial deep learning"), uncertainty quantification ("uncertainty quantification" OR "prediction uncertainty" OR "aleatory" OR "epistemic" OR "probabilistic prediction" OR "conformal prediction"), and geophysical applications ("geophysics" OR "seismic" OR "mineral exploration" OR "hydrogeology" OR "subsurface" OR "environmental monitoring" OR "geological modeling"). Additional records were identified through reference list screening of included studies, relevant preprints, and conference proceedings from key venues including AGU, EGU, and the Geostatistics Congress. 2.2 Inclusion and Exclusion Criteria Studies were included if they: (a) developed or applied machine learning methods with explicit spatial modelling components for prediction tasks; (b) addressed uncertainty quantification or spatial validation; (c) were published in peer-reviewed journals or established conference proceedings; and (d) were available in English. Studies were excluded if they: (a) applied standard machine learning without spatial considerations; (b) focused exclusively on image classification without spatial prediction; (c) were editorials, commentaries, or non-peer-reviewed opinion pieces; or (d) duplicated content from the same research group without methodological advancement. 2.3 Study Selection and Screening The initial database search identified 847 records, with an additional 123 records from other sources. After removing 328 duplicates, 642 unique records were screened by title and abstract. Of these, 389 were excluded as they did not meet the spatial ML criteria or were outside the geophysical scope. The remaining 253 full-text articles were assessed for eligibility, with 131 excluded for lacking uncertainty quantification components, spatial prediction focus, or methodological novelty. The final review synthesises 122 studies, categorised into four thematic areas: geostatistical-ML hybrid frameworks (n = 34), uncertainty quantification methods (n = 28), spatial validation and feature engineering (n = 31), and geophysical domain applications (n = 29). The PRISMA flow diagram documenting this process is provided in the supplementary material as Figure S1 . 2.4 Conceptual Framework To organise the review and provide a novel analytical contribution, we developed a five-layer conceptual decision pathway framework for predictive spatial machine learning in geophysical applications (Fig. 1 ). The framework links: Layer 1 (Spatial Data Characterisation) covering data types, spatial properties, geophysical context, and integration requirements; Layer 2 (Methodology Selection) addressing ML framework choice, spatial feature engineering, and uncertainty quantification approach; Layer 3 (Validation and Assessment) encompassing spatially aware validation and model interpretation; Layer 4 (Geophysical Application Domains) spanning seismic hazard, mineral exploration, hydrogeology, environmental monitoring, and subsurface characterisation; and Layer 5 (Decision outputs) highlighting important deliverables to support decision-making processes. An iterative feedback loop connects application outcomes back to data collection and methodology refinement. This framework serves as the organising principle for the review and is intended as a practical guide for researchers and practitioners selecting appropriate methods for specific geophysical prediction problems. 3 Spatial Data Foundations for Geophysical Analysis This section synthesises the spatial data landscape relevant to predictive modelling in the geosciences, consolidating data types, resolution challenges, multi-source integration approaches, and exploratory analysis considerations into a focused treatment that provides the necessary background without duplicating material available in standard GIS references (Fig. 2 ). 3.1 Data Types and Resolution Challenges Spatial and geospatial databases serve as the foundation of geographic information systems (GIS), playing a pivotal role in geophysical applications from environmental science to mineral resource management. The fundamental distinction lies between vector formats, encoding spatial information through points, lines, and polygons, and raster formats, organising data in grid structures where each cell contains attribute values. In geophysical contexts, vector data commonly represents drill-hole locations, seismic station networks, and fault traces, while raster data captures continuous fields such as elevation models, satellite imagery, and gridded geophysical survey data (Liu et al., 2020 ; Feng and Koch, 2024 ). Beyond these fundamental types, geophysical databases increasingly incorporate object-oriented structures that combine geometric and non-geometric attributes for complex subsurface objects (Bei et al., 2010 ; Duckham et al., 2024 ), time-series spatial databases that facilitate analysis of dynamic phenomena such as groundwater level fluctuations and seismic catalogues (Pelekis et al., 2004 ), and multimedia spatial databases integrating spatial data with remote sensing imagery and geophysical logs (Li et al., 2016 ). Resolution fundamentally influences prediction accuracy and uncertainty. Higher resolution data captures more spatial variation but introduces noise and computational burden, while lower resolution data may miss critical patterns, leading to the modifiable areal unit problem (MAUP). In geophysics, this tension is particularly acute: seismic data may have metre-scale resolution along profiles but kilometre-scale spacing between lines, creating highly anisotropic sampling patterns that challenge standard spatial prediction methods (Heuvelink et al., 2021 ; Atkinson and Graham, 2006 ). Table 1 Spatial Data Types, Resolutions, and ML Preprocessing Requirements Across Geophysical Domains Geophysical Domain Primary Data Sources & Types Typical Spatial Resolution Temporal Characteristics Key ML Preprocessing Challenges Recommended Preprocessing Key References Seismology (hazard & risk) Continuous waveforms (SAC, miniSEED); strong-motion records; station metadata (vector points); fault maps (vector lines/polygons); VS30 site classification grids (raster) Station spacing: 5–50 km (regional), < 1 km (dense arrays); DAS: metre-scale; VS30 grids: 250m-1km Continuous (Hz-kHz sampling); event catalogues span decades; non-stationary seismicity rates Irregular network geometry; signal-to-noise separation; 3D wave propagation effects; anisotropic spatial coverage; catalogue completeness varies regionally Denoising (PhaseNet); STA/LTA event detection; spectral feature extraction; coordinate encoding; spatial declustering of catalogues Kubo et al. ( 2024 ); Anjom et al. ( 2024 ); Reichstein et al. ( 2019 ); Camps-Valls et al. ( 2020 ) Mineral Exploration (resource evaluation) Drill-hole assays (point data at depth); geochemical soil/rock samples; hyperspectral remote sensing (raster); geophysical surveys: magnetics, gravity, EM (raster/profile) Core: cm-scale along hole; drill spacing: 25-200m; geochemical: 50-500m grid; airborne surveys: 50-400m line spacing Static geological properties; exploration campaigns span years; sequential infill drilling changes data density Preferential sampling (holes target mineralisation); support change (core to block); 3D geological domains; compositional data constraints; informative censoring (below detection) Compositing to regular lengths; spatial declustering; domain separation; log-ratio transforms for compositions; imputation of below-detection values Fouedjio et al. ( 2017 ); Talebi et al. ( 2021 ); Fouedjio & Talebi ( 2022 ); Erdogan Erten et al. ( 2022 ); Talebi et al. ( 2019 , 2020 ) Hydrogeology (groundwater) Well logs (lithology, geophysics); pump test data; piezometric time series; recharge estimates; DEM-derived variables (raster); climate reanalysis grids Wells: point-scale, spacing 1–50 km; climate grids: 0.1–0.5 deg.; DEMs: 30-90m Continuous monitoring (hourly-daily); strong seasonal and multi-year trends; climate-driven non-stationarity Very sparse and irregular networks; aquifer heterogeneity poorly constrained; mixing of confined/unconfined systems; temporal gaps in monitoring records Gap filling via interpolation or physics-based models; temporal aggregation; static feature derivation (aquifer type, soil, land use); normalisation of pumping effects Wu et al. ( 2025 ); Dai et al. ( 2025 ); Kunz et al. (2024); Wohling et al. ( 2025 ); Sun ( 2018 ) Environmental Monitoring (soil, air, water quality) Soil samples (point); air quality stations (point with time series); satellite-derived indices (raster: NDVI, LST); land-use/land-cover maps (classified raster/polygon) Soil: 50m-5km grids; air stations: 10-50km; satellites: 10m (Sentinel) to 1km (MODIS) Satellite: daily-16 day revisit; soil campaigns: periodic; air quality: continuous hourly Multi-resolution fusion (MAUP); measurement support differences; spatial-temporal misalignment; mixed land-use pixels; cloud contamination in optical RS Resampling/downscaling; spatiotemporal co-registration; cloud masking; compositing (median, max NDVI); feature stacking of multi-source covariates Kasraei et al. ( 2021 ); Hsu et al. ( 2020 ); Hengl et al. ( 2018 ); Wadoux et al. ( 2019 ); Behrens et al. ( 2018 ); Heuvelink et al. ( 2021 ) Subsurface Characterisation (3D geological modelling) Seismic reflection volumes (3D raster); well logs (1D profiles at points); core photos; training images (geological analogues); conceptual geological models Seismic: 12.5-50m inline/crossline, ms vertical; wells: 0.15m log sampling, km-scale spacing Geological properties are static but knowledge evolves with infill data; 4D seismic for reservoir monitoring Vast dimensional mismatch between seismic coverage and sparse well control; ill-posed inversion; non-unique solutions; geological realism constraints; training image selection Seismic attribute extraction; well-to-seismic tie; upscaling of well data to seismic resolution; training image curation; conditioning to hard data Bai & Tahmasebi ( 2020a , 2020b ); Avalos & Ortiz ( 2020 ); Xu et al. (2025); Fouedjio et al. ( 2021 ); Fouedjio & Arya ( 2024 ) Note : Abbreviations: DAS = Distributed Acoustic Sensing; VS30 = time-averaged shear-wave velocity in the upper 30 m; STA/LTA = Short-Term Average / Long-Term Average; MAUP = Modifiable Areal Unit Problem; RS = Remote Sensing; EM = Electromagnetic. 3.2 Multi-Source Data Integration The complexity of spatial data integration in geophysical applications stems from the heterogeneous nature of data sources, formats, and structures, necessitating sophisticated approaches for effective harmonisation (Garosi et al., 2022 ; Mohammadi et al., 2006 ). Several strategies have emerged to address resolution-related challenges. Traditional approaches include careful application of resampling techniques such as upscaling or downscaling. More advanced methods employ multi-resolution analysis using wavelets or Gaussian pyramid decomposition, alongside hierarchical Bayesian frameworks that account for different scales of variation (Banerjee et al., 2019 ; Afrifa-Yamoah and Osei, 2025 ). Change of support techniques and data fusion methods, including Bayesian maximum entropy and area-to-point kriging, facilitate the integration of multi-resolution data (Wang et al., 2013 ). Recent advances in machine learning have transformed multi-resolution geospatial data handling. Convolutional Neural Networks demonstrate effectiveness in super-resolution tasks for satellite imagery (Pouliot et al., 2018 ). Deep learning architectures, including autoencoders and Generative Adversarial Networks, excel at fusing multi-resolution remote sensing data while preserving fine details (Chen et al., 2017 ; Ghamisi et al., 2019 ; Qin et al., 2022 ). In subsurface characterisation, deep generative models now provide geological priors that encode non-Gaussian, non-stationary, and multi-scale patterns directly from training examples (Xu et al., 2025). These developments underscore the importance of balancing technical sophistication with practical implementation considerations across varying observational scales. 3.3 Exploratory Spatial Analysis Exploratory Data Analysis (EDA) serves as a cornerstone in the spatial prediction workflow, providing systematic approaches to understanding complex datasets through summarisation and visualisation (Tukey, 1977 ). The methodological framework for spatial prediction EDA encompasses spatial correlation techniques such as geographically weighted regression (GWR) and spatial econometrics (Georganos et al., 2019 ; Oshan et al., 2019 ; Wu et al., 2023 ), variogram analysis for evaluating spatial continuity (Goovaerts, 1997 ), machine learning-driven outlier detection (Xu et al., 2019 ), and local indicators of spatial association (LISA) for cluster identification (Anselin, 1995 ; Chen, 2024 ). While established techniques such as variogram analysis and spatial autocorrelation measures including Moran's I and Geary's C remain foundational (Anselin, 1995 ; Cliff and Ord, 1981; Cressie, 1993 ), contemporary developments address critical challenges in spatial analytics including non-stationarity, multi-scale analysis, and big data processing. Oshan et al. ( 2019 ) introduced local spatial heterogeneity measures extending beyond traditional global statistics. Artificial intelligence applications in automated feature extraction have opened new frontiers in spatial data analysis (Li and Hsu, 2020 ), while integration with cloud computing has expanded the scope of spatial EDA capabilities (Yang et al., 2017 ). These evolving approaches are reshaping spatial analysis, enhancing both accuracy and interpretability of spatial predictions across geophysical applications. 4 Predictive Spatial Machine Learning Frameworks The evolution of spatial machine learning frameworks reflects the growing complexity of geospatial data analysis and the need for scalable solutions that respect the unique characteristics of spatial data. Modern frameworks address challenges in processing vast amounts of spatial data from ground observations and airborne data collections (Sabek and Mokbel, 2021 ). Key research domains encompass event detection, variable estimation, long-term forecasting, and relationship mining, with emphasis on integrating physical laws into ML models for enhanced predictive accuracy (Karpatne et al., 2019 ). This section critically analyses the major framework categories, evaluating their assumptions, strengths, and limitations for geophysical applications. 4.1 Integration of Geostatistics and Machine Learning Recent advances in spatial modelling have demonstrated powerful synergies between geostatistical techniques and ML approaches, particularly in capturing complex geological heterogeneity. A pioneering hybrid approach combining cross-correlation simulation (CCSIM) with convolutional neural networks (CNNs) addresses fundamental limitations in subsurface modelling, achieving perfect conditioning data accuracy in 2D scenarios and enhanced structural preservation in 3D models (Bai and Tahmasebi, 2020a ). Another framework integrating geostatistical conditional simulation with supervised learning effectively utilises both labelled and unlabelled spatial data, demonstrating superior prediction performance by leveraging spatial autocorrelation principles (Fouedjio and Talebi, 2022 ). The integration of ML models with kriging through stacked ensemble super learner models has shown improved accuracy for non-stationary and non-Gaussian data (Erdogan Erten et al., 2022 ). The combination of Kriging-Land-use Regression with Random Forest and XGBoost significantly improved BTEX concentration predictions, with R-squared values reaching 0.79 compared to 0.37–0.52 for traditional land-use regression alone (Breiman, 2001 ; Chen and Guestrin, 2016 ; Hsu et al., 2020 ). The geostatistics-informed machine learning (GIML) approach has accelerated spatial interpolation by orders of magnitude while maintaining accuracy by integrating Ordinary Kriging principles into deep neural networks, though it remains limited to stationary variogram assumptions (Bai and Tahmasebi, 2020b ). The Hybrid Regression Kriging method incorporates nonlinear ML mapping, achieving over 10% reduction in estimation error compared to standard regression kriging (Li et al., 2020 ), and the neural network-generalised least squares (NN-GLS) algorithm integrates neural networks with Gaussian process modelling for complex non-linear spatial patterns, though its O(n-cubed) computational scaling for the GP component limits applicability to very large datasets (Zhan and Datta, 2024 ). Further innovations include recursive convolutional neural networks applied to multiple-point statistics simulation, effectively capturing structural characteristics across two-dimensional and three-dimensional geological domains (Avalos and Ortiz, 2020 ). More recently, the locally varying geostatistical machine learning approach has addressed the persistent challenge of spatial non-stationarity by combining local regression functions with conditional simulation, allowing model parameters to adapt across geographic space. This framework demonstrates substantial improvements over global models in non-stationary geological and environmental settings, though it requires sufficient local data density and careful bandwidth selection (Fouedjio and Arya, 2024 ). Table 2 provides a comprehensive comparative synthesis of these nine hybrid frameworks, detailing their geostatistical and ML components, spatial assumptions, reported performance gains, limitations, demonstrated geophysical applications, and key references. A critical observation across these methods is that while performance gains are consistently reported, direct cross-method comparison remains difficult due to the absence of common benchmark datasets, an important gap addressed in the research roadmap (Section 7.5 ). Table 2 Comparative Synthesis of Hybrid Geostatistical-ML Frameworks Method Geostatistical Component ML Component Spatial Assumption Reported Performance Gain Key Limitation Demonstrated Application Key Reference CCSIM + CNN Cross-correlation simulation (MPS) Convolutional neural network for pattern learning Training image-based multi-point continuity 100% hard data reproduction in 2D; improved 3D structural connectivity Requires representative training images; computational cost of CNN training Subsurface geological modelling; reservoir characterisation Bai & Tahmasebi ( 2020a ) Kriging-LUR + RF/XGBoost Kriging-based land-use regression for spatial trend Random Forest or XGBoost for nonlinear residuals Second-order stationarity of residuals R-squared up to 0.79 vs 0.37–0.52 for traditional LUR alone Two-stage bias propagation; stationarity assumption may not hold BTEX air pollutant concentration mapping Hsu et al. ( 2020 ) GIML (OK + DNN) Ordinary Kriging principles embedded in network Deep neural network learning variogram parameters Stationary variogram structure Orders of magnitude faster than traditional OK with comparable accuracy Limited to ordinary kriging assumptions; requires sufficient training data Large-scale spatial interpolation Bai & Tahmasebi ( 2020b ) NN-GLS Gaussian process for spatially correlated errors Neural network for mean function Gaussian process with specified covariance Superior prediction in non-linear spatial patterns vs GP or NN alone Scalability: O(n^3) for GP component; Gaussian assumption Environmental spatial prediction with complex nonlinearity Zhan & Datta ( 2024 ) Hybrid Regression Kriging Kriging of regression residuals Nonlinear ML mapping (RF, SVM, ANN) Residual stationarity after ML trend removal > 10% reduction in estimation error vs standard regression kriging Two-stage approach introduces bias; residuals may retain non-stationarity Continuous spatial variable estimation; digital soil mapping Li et al. ( 2020 ) Stacked Ensemble SL + Kriging Kriging as one of multiple base learners Super learner stacking multiple ML algorithms Flexible: inherits assumptions of each base learner Improved accuracy for non-stationary, non-Gaussian distributions High complexity; interpretability challenges; overfitting risk with many learners Geological attribute estimation with heterogeneous data Erdogan Erten et al. ( 2022 ) RCNN + MPS Multiple-point statistics simulation Recursive CNN for pattern extraction from training images Training image-based higher-order statistics Superior reproduction of statistical and spatial properties in 2D and 3D Quality depends on training image selection; high computational cost for 3D Geostatistical modelling; enhanced MPS simulation Avalos & Ortiz ( 2020 ) Geostat. Semi-supervised Learning Conditional simulation preserving spatial structure Supervised learner augmented with simulated labels Spatial autocorrelation for simulation Superior to fully supervised methods when labelled data is scarce Simulation computational overhead: quality depends on variogram model Geospatial classification with limited labels Fouedjio & Talebi ( 2022 ) Locally Varying Geostat-ML Local regression functions + conditional simulation Spatially adaptive ML with local parameter estimation Non-stationary: locally varying parameters and spatial structure Substantial improvement over global models in non-stationary settings Higher complexity; requires sufficient local data; bandwidth selection Mining (non-stationary ore grades); environmental (spatially varying processes) Fouedjio & Arya ( 2024 ) Note : Performance gains are reported relative to each method's stated baseline. Direct cross-method comparison requires common benchmark datasets, which remains an open research need (see Table 6 , Research Roadmap). SL = Super Learner; MPS = Multiple-Point Statistics; OK = Ordinary Kriging; LUR = Land-Use Regression 4.2 Spatially Aware Deep Learning Architectures Deep learning applications in earth sciences present both transformative opportunities and significant challenges. Contemporary neural network architectures, particularly CNNs and RNNs, demonstrate superior capability in capturing complex spatiotemporal dependencies compared to traditional approaches (Reichstein et al., 2019 ). Integration of attention-based networks, geometric deep learning, and Bayesian probabilistic interpretations enables more complex environmental process modelling. These advances particularly benefit seasonal forecasting and extreme event prediction while maintaining physical consistency through hybrid modelling approaches that incorporate domain knowledge. In seismological applications, ML has been applied across the full processing workflow: event detection and classification, arrival time picking, focal mechanism analysis, ground motion prediction, and crustal deformation analysis (Kubo et al., 2024 ). ML-based ground motion prediction equations (GMPEs) now incorporate spatial site effects and path characteristics through neural networks, tree-based models, and kernel methods, often outperforming traditional empirical GMPEs (Anjom et al., 2024 ). For subsurface characterisation, deep generative models provide geological priors that encode non-Gaussian, non-stationary patterns while allowing conditioning to observations, offering flexible alternatives to classical variogram-based and multiple-point statistical methods (Xu et al., 2025). In hydrogeology, graph-based deep learning frameworks model complex spatial dependencies between monitoring wells by characterising multiple types of spatial relationships, including physical proximity, hydrological connectivity, and similarity in recharge patterns (Wu et al., 2025 ; Dai et al., 2025 ). The focus on physical consistency and interpretability alongside computational advancement marks a crucial step toward more reliable and scientifically grounded geophysical modelling. 4.3 Spatial Feature Engineering Spatial feature engineering has significantly enhanced ML capabilities in geographic analysis. The Euclidean distance fields in ML (EDM) framework demonstrates this advancement by integrating distance fields with environmental covariates, outperforming traditional spatial prediction methods (Behrens et al., 2018 ). The incorporation of spatial lag and eigenvector spatial filtering (ESF) features into random forest models has significantly reduced prediction errors and spatial autocorrelation in residuals (Liu et al., 2022 ). The spatial random forests (SRF) algorithm extends traditional random forests by incorporating local spatial-spectral information, demonstrating superior performance in geological mapping and geochemical prediction (Fig. 3 ; Talebi et al., 2021 ). These advancements address critical spatial properties including dependence, heterogeneity, and scale effects across applications from land cover classification to geological domain delineation (Zarger and Lal, 2023 ; Talebi et al., 2020 ). 4.4 Locally Varying Spatial Machine Learning Locally varying machine learning frameworks have emerged as promising solutions to address spatial heterogeneity in geographic analysis. Geographically Weighted Regression (GWR) laid the foundational groundwork by pioneering location-specific parameter estimation (Thapa and Estoque, 2012 ). Recent innovations include the Explainable Geospatial Machine Learning (XGeoML) framework, combining spatial weighting with SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME) for interpretable, superior performance over traditional GWR (Liu, 2024 ). The geostatistical ML methodology introduced by Fouedjio and Arya ( 2024 ) tackles spatial autocorrelation and non-stationarity through local regression functions and conditional simulation (Fig. 4 ). Domain-specific applications include the Geographically Neural Network-Weighted Logistic Regression (GNNWLR) for mineral prospectivity mapping (Wang et al., 2024 ), the Geographically Weighted Machine Learning (GWML) framework for environmental applications (Yang et al., 2022 ), and Spatial Regression Graph Convolutional Neural Networks (SRGCNNs) that handle non-Euclidean spatial multivariate data (Zhu et al., 2021 ). The geographically weighted SRGCNN variant particularly excels in addressing spatial heterogeneity with limited data availability, bridging graph deep learning and spatial regression analytics. 4.5 Spatial Model Validation and Performance Assessment Advances in spatial model validation address the fundamental challenges of spatial autocorrelation and covariate shift. Spatial autocorrelation can lead to substantial performance differences of up to 47% between spatial and non-spatial validation approaches (Schratz et al., 2019 ), making spatially aware validation essential for reliable model assessment. The Importance-Weighted Buffered Cross-Validation (IBCV) framework offers a robust solution by combining spatial buffering with density ratio weighting, providing more accurate performance estimates than traditional cross-validation when both autocorrelation and covariate shift are present (Wang et al., 2023 ). The leave-group-out cross-validation (LGOCV) method handles complex spatiotemporal dependencies effectively for extrapolation tasks, with explicit temporal grouping capability, and is implemented in the ‘mlr3spatiotempcv’ R package (Adin et al., 2024 ). Spatial bagging workflows incorporating effective sample size concepts achieve comparable performance with significantly smaller samples, integrating naturally with existing bagging frameworks (Ozbayrak et al., 2024). Forward feature selection combined with spatial cross-validation, implemented in the ‘CAST’ R package, helps mitigate overfitting by excluding highly autocorrelated but non-predictive features. This approach, combined with the ‘sperrorest’ package for spatial bootstrap-based accuracy assessment (Brenning, 2012 ), can reveal performance differences of up to 47% between spatial and non-spatial validation approaches, as demonstrated by Schratz et al. ( 2019 ) in forest disease prediction. Fair train-test split methods use semi-variogram models and modified rejection sampling to create more representative validation sets for clustered sampling designs (Salazar et al., 2022 ). Table 3 provides a comprehensive comparison of these seven validation approaches, detailing the spatial biases each address, their computational requirements, temporal dependency handling, available software implementations, and empirical evidence supporting their use. These advances collectively address critical evaluation challenges in geospatial datasets, where standard k-fold cross-validation remains inappropriate due to spatial autocorrelation and should be used only as a non-spatial benchmark (Rolf, 2023 ). Table 3 Comparison of Spatial Validation Approaches Validation Method Spatial Bias Addressed Mechanism Comp. Cost Handling of Temporal Dependence Implementation Availability Empirical Evidence Key Reference IBCV (Importance-Weighted Buffered CV) Spatial autocorrelation + covariate shift jointly Spatial buffer zones exclude nearby data; density ratio weights correct distribution mismatch Moderate-High Not explicitly, can combine with temporal blocking Custom R/Python code; not yet in standard packages More accurate than standard spatial CV when both autocorrelation and covariate shift present Wang et al. ( 2023 ) LGOCV (Leave-Group-Out CV) Complex spatiotemporal dependencies Groups observations by spatial/temporal blocks; holds out entire groups Moderate Explicitly handles via temporal grouping R: mlr3spatiotempcv ; Python: custom implementation Superior for extrapolation tasks; effective with structured dependencies Adin et al. ( 2024 ) Spatial Block Bootstrap Spatial autocorrelation in uncertainty estimates Resamples spatial blocks rather than individual observations, preserving local correlation Low-Moderate Can use spatiotemporal blocks R: sperrorest ; conceptually simple to implement Produces realistic confidence intervals; effective sample size concept Brenning ( 2012 ); Russ & Brenning (2010) Forward Feature Selection + Spatial CV Predictor autocorrelation leading to overfitting Sequential variable addition evaluated via spatial cross-validation folds High (iterative) Temporal variables can be evaluated separately R: CAST package; Python: custom pipelines Prevents selection of spatially autocorrelated but non-predictive features; up to 47% performance difference vs non-spatial Meyer et al. ( 2019 ); Schratz et al. ( 2019 ) Spatial Fair Train-Test Split Non-representative training/test partitions due to spatial clustering Semi-variogram range determines buffer; modified rejection sampling for balanced splits Moderate Not explicitly temporal R/Python: custom; conceptual framework transferable More representative validation sets for clustered sampling designs Salazar et al. ( 2022 ) Spatial Bagging Spatial autocorrelation inflating effective sample size Bootstrap with effective sample size adjustment based on spatial autocorrelation range Low-Moderate Can incorporate temporal structure R: custom; integrates with existing bagging frameworks Comparable accuracy to full samples using significantly fewer observations Ozbayrak et al. (2024) Standard k-fold CV (baseline) None Random partitioning ignoring spatial structure Low None All ML frameworks (sklearn, caret, mlr3, tidymodels) Overestimates performance by up to 47% when spatial autocorrelation present; appropriate only as non-spatial benchmark Schratz et al. ( 2019 ) Note : Computational cost is relative to standard k-fold CV. All spatial methods add overhead but prevent optimistic bias. The 47% performance difference ( Schratz et al., 2019 ) was observed for spatial prediction of disease in forests, demonstrating that the bias from ignoring spatial autocorrelation can be substantial. Implementation packages listed are as of 2025. 5 Uncertainty Quantification in Spatial Prediction Spatial predictive modelling has traditionally focused on point predictions, yet these inherently contain uncertainty requiring quantification (Bauer, 1958 ). Probability distributions offer richer information content than point predictions alone, enabling better-informed decision-making under uncertainty. The theoretical foundation of predictive uncertainty combines Bayesian statistics, decision theory, and machine learning approaches (Tyralis and Papacharalampous, 2024 ). Understanding uncertainty is crucial in geophysical applications where decisions carry significant risks. In domains such as mineral exploration, reservoir management, groundwater protection, natural hazard mitigation, and carbon storage, geophysical predictions directly influence investments, safety, and environmental outcomes. These predictions are inherently uncertain due to limited data coverage, indirect measurements, and complex subsurface processes. 5.1 Taxonomy of Spatial Uncertainty Spatial uncertainty manifests primarily through aleatory and epistemic uncertainty, each representing distinct aspects of predictive modelling challenges (Fig. 5 ; Monarch, 2021 ; Hullermeier and Waegeman, 2021). Aleatory uncertainty represents inherent variability in natural phenomena, encompassing both homoscedastic uncertainty with constant prediction residual variation and heteroscedastic uncertainty with spatially varying noise patterns. This statistical uncertainty persists even with perfect modelling and represents a fundamental precision limit that cannot be reduced through additional sampling. In geophysical contexts, aleatory uncertainty includes natural variability in seismic ground motion at a given site, intrinsic geological heterogeneity at scales below measurement resolution, and stochastic variation in groundwater recharge processes. Epistemic uncertainty stems from incomplete knowledge, manifesting through measurement errors, missing data, and model parameter uncertainty (Hullermeier and Waegeman, 2021). Unlike aleatory uncertainty, epistemic uncertainty can be reduced through additional data collection or improved model structures. In geophysics, this includes uncertainty from limited drill-hole coverage in mineral deposits, sparse seismic station networks in regions of interest, and simplified representations of complex hydrogeological boundary conditions. The distinction is practically important: areas with high epistemic uncertainty are candidates for additional data collection, while areas dominated by aleatory uncertainty require probabilistic treatment regardless of sampling density (Gal and Ghahramani, 2016 ; Kendall and Gal, 2017 ). 5.2 Methods for Aleatory Uncertainty Estimation Quantile regression (QR) algorithms have emerged as powerful tools for approximating predictive probability distributions to address aleatory uncertainty. Originally introduced by Koenker and Bassett (1978), QR models the inherent randomness by estimating different conditional quantiles of the response variable. For each quantile, a linear relationship between observed and predicted values is assumed, with parameters determined by minimising a piecewise linear loss function that asymmetrically penalises over- and under-prediction (Kasraei et al., 2021 ). Quantile regression forests (QRF), introduced by Meinshausen ( 2006 ), extend random forests for uncertainty quantification and have been widely applied in spatial prediction (Papacharalampous et al., 2024 ). While QR effectively characterises aleatory uncertainty, it does not explicitly address epistemic uncertainty; comprehensive uncertainty quantification requires combining QR with approaches that represent model-form and parameter uncertainty. 5.3 Methods for Epistemic Uncertainty Estimation Spatial bootstrapping provides a powerful framework for estimating epistemic uncertainty by generating multiple realisations of the spatial data structure. Unlike traditional bootstrapping, spatial bootstrap methods preserve spatial autocorrelation during resampling, maintaining the integrity of spatial relationships (Brenning, 2012 ). Spatial block bootstrap methods are particularly effective at quantifying epistemic uncertainties in regions with sparse observations (Russ and Brenning, 2010). For spatial machine learning, ensemble-based approaches have gained prominence: Meyer et al. ( 2018 ) showed that spatial random effects models can effectively separate aleatory variability from epistemic uncertainty, while Hengl et al. ( 2018 ) demonstrated that machine learning methods with spatial components can characterise epistemic uncertainty through uncertainty maps revealing areas of deficient model knowledge. 5.4 Integrated Uncertainty Quantification Frameworks Several frameworks address both aleatory and epistemic uncertainty simultaneously, as comprehensively compared in Table 4 and conceptually presented as a framework in Fig. 6 (Butvinik 2022 ). Bayesian neural networks provide a principled approach by placing distributions over network weights, yielding predictions with uncertainty estimates that decompose into data noise (aleatory) and model uncertainty (epistemic) components (Kendall and Gal, 2017 ). Monte Carlo (MC) Dropout offers a computationally cheaper approximation to full Bayesian inference by using dropout at test time to generate multiple stochastic forward passes, typically 50–100 passes, producing mean predictions with variance estimates (Gal and Ghahramani, 2016 ). The Uncertainty Estimation based on Local Errors and Clustering (UNEEC) method considers multiple uncertainty sources through residual analysis, clustering residuals spatially to capture location-varying uncertainty patterns (Rahmati et al., 2019 ). Kriging variance, derived directly from the variogram model and data configuration, provides inherent spatial uncertainty estimates at no additional computational cost beyond the prediction itself, though it assumes Gaussian distributions. Implementation is widely available through established packages including ‘gstat’ and ‘geoR’ in R, and ‘pykrige’ and ‘GSTools’ in Python (Goovaerts, 1997 ; Fouedjio and Klump, 2019 ). Geostatistical conditional simulation extends this by generating multiple equiprobable realisations that reproduce both the data values and the spatial variability structure, providing full uncertainty envelopes essential for mineral resource evaluation and three-dimensional geological domain boundary assessment, though it requires 50–100 or more realisations for reliable uncertainty characterisation (Fouedjio et al., 2021 ; Fouedjio and Talebi, 2022 ). Conformal prediction has emerged as a promising distribution-free approach that provides guaranteed marginal coverage prediction intervals, requiring only a post-hoc calibration step on held-out data. Recent extensions address exchangeability violations inherent in spatial data, though geophysical applications remain limited to date and represent an active research frontier (Tyralis and Papacharalampous, 2024 ). Ensemble variance decomposition offers another practical pathway by decomposing total prediction variance into model disagreement (epistemic) and within-model noise (aleatory) components, building on established ensemble methods such as random forests and gradient boosting (Hengl et al., 2018 ; Meyer et al., 2018 ). Our systematic analysis found that fewer than 15% of the 122 reviewed studies explicitly decompose prediction uncertainty into aleatory and epistemic sources, highlighting a significant gap between conceptual recognition and operational implementation. Table 4 Comparison of Uncertainty Quantification Methods for Spatial Prediction UQ Method Uncertainty Type Spatial Awareness Output Form Comp. Cost Software / Implementation Demonstrated Geophysical Application Key Reference Quantile Regression (QR) Aleatory Indirect: via spatial covariates in feature set Conditional quantiles (e.g. Q10, Q50, Q90); prediction intervals Low: single model per quantile R: quantreg ; Python: statsmodels , sklearn Digital soil mapping; uncertainty in soil property prediction Koenker & Bassett (1978); Kasraei et al. ( 2021 ) Quantile Regression Forest (QRF) Aleatory (heteroscedastic) Indirect: captures spatial variation through features; can include coordinates Full conditional distribution approximation; any quantile extractable Moderate: retains all tree predictions rather than just means R: quantregForest ; Python: sklearn-quantile Precipitation uncertainty; environmental monitoring Meinshausen ( 2006 ); Papacharalampous et al. ( 2024 ) Spatial Block Bootstrap Epistemic Direct: preserves spatial autocorrelation by resampling spatial blocks Confidence intervals for model parameters and predictions Moderate: requires multiple model fits on resampled blocks R: sperrorest ; custom blocking by variogram range Remote sensing accuracy assessment; precision agriculture Brenning ( 2012 ); Russ & Brenning (2010) Bayesian Neural Networks (BNN) Both (decomposable) Architecture-dependent; spatial layers can be incorporated Posterior predictive distribution; decomposable into aleatoric + epistemic High: MCMC or variational inference over weight distributions Python: TensorFlow Probability , Pyro , BayesFlow Subsurface property prediction; CO2 leakage detection Kendall & Gal ( 2017 ); He et al. ( 2024 ) MC Dropout Epistemic (approximate Bayesian) Architecture-dependent; approximates BNN via dropout at test time Mean prediction + variance from multiple stochastic forward passes Moderate: N forward passes (typically 50–100) Any framework with dropout: PyTorch , TensorFlow , Keras Deep learning for Earth system science applications Gal & Ghahramani ( 2016 ) UNEEC Both Local: clusters residuals spatially to capture location-varying uncertainty Prediction intervals based on local error distribution Moderate: requires clustering + residual analysis Custom implementation (R/Python) Groundwater nitrate pollution modelling Rahmati et al. ( 2019 ) Kriging Variance Both (under Gaussian assumption) Inherent: directly derived from variogram model and data configuration Kriging variance (conditional variance); conditional simulation envelopes Low-Moderate: computed alongside predictions at no extra model cost R: gstat , geoR ; Python: pykrige , GSTools Mineral resource estimation; grade control; soil mapping Goovaerts ( 1997 ); Fouedjio & Klump ( 2019 ) Conformal Prediction Both (distribution-free) With spatial calibration: recent extensions address exchangeability violations Guaranteed coverage prediction intervals (marginal coverage) Low: post-hoc calibration step on held-out data R: conformalInference ; Python: MAPIE , conformal-prediction Emerging in spatial contexts; limited geophysical applications to date Tyralis & Papacharalampous ( 2024 ) Geostatistical Conditional Simulation Both Full spatial model: reproduces spatial variability and honours conditioning data Multiple equiprobable realisations; full uncertainty envelope High: multiple realisations required (typically 50–200+); variogram fitting R: gstat ; Python: GSTools ; GSLIB; SGeMS Mineral resource classification; 3D geological domain boundaries; reservoir modelling Fouedjio et al. ( 2021 ); Fouedjio & Talebi ( 2022 ) Ensemble Variance Decomposition Both (decomposable) Can incorporate spatial effects via spatially structured base learners Decomposition of total variance into model disagreement (epistemic) and within-model noise (aleatory) Moderate-High: requires training multiple diverse models Custom; builds on ranger , xgboost , etc. Environmental prediction; digital soil mapping Hengl et al. ( 2018 ); Meyer et al. ( 2018 ) Note : Uncertainty Type: Aleatory = irreducible data noise; Epistemic = reducible model/knowledge uncertainty; Both = method captures or decomposes both sources. Computational cost is relative to a single point-prediction model. Software listings are non-exhaustive and current as of 2025. Conformal prediction for spatial data remains an active research frontier with limited geophysical validation to date. 5.5 Uncertainty-Aware Feature Selection Uncertainty fundamentally shapes feature selection in spatial ML applications. Aleatory uncertainty can mask true feature importance, particularly in heteroscedastic spatial datasets where noise varies geographically. Epistemic uncertainty affects how consistently features are selected across model specifications (Fouedjio et al., 2021 ). Probabilistic feature selection methods incorporating uncertainty quantification offer more stable variable rankings, improved generalisability, and transparent reliability assessments (Kalousis et al., 2007 ; Gheyas and Smith, 2010 ). In spatial contexts, autocorrelation structures can artificially inflate feature significance if uncertainty is ignored (Darst et al., 2018 ). Uncertainty-aware feature selection has proven critical in applications from environmental modelling to remote sensing classification, where neglecting uncertainty leads to overconfident predictions and potentially misleading spatial patterns (Degenhardt et al., 2019 ; Calle and Urrea, 2011 ; Krawczyk, 2016 ). 6 Applications in Geophysical Sciences This section synthesises how the SML frameworks, uncertainty quantification methods, and validation approaches reviewed in Sections 4 and 5 are deployed across major geophysical application domains. Rather than merely cataloguing applications, we identify which methodological combinations have proven most effective, where transferable patterns emerge, and where domain-specific solutions remain necessary. 6.1 Seismic Hazard Assessment and Ground Motion Prediction ML has transformed seismological applications across the full processing chain, from event detection to ground motion prediction (Kubo et al., 2024 ). Ground motion prediction equations (GMPEs), traditionally constructed through regression of past records, are increasingly augmented or replaced by ML approaches that capture nonlinear site-path-source interactions. Neural networks, random forests, and gradient boosting models have been applied to predict ground motion intensities, often outperforming empirical equations for specific regional datasets (Anjom et al., 2024 ). Spatial autocorrelation in seismic hazard maps presents validation challenges: standard cross-validation overestimates predictive performance because nearby stations experience correlated ground motions, making spatially blocked validation essential. Uncertainty quantification in seismic hazard assessment requires separating site-specific aleatory variability (inherent randomness in ground motion at a given site) from epistemic uncertainty arising from limited ground motion recordings. Physics-informed approaches that embed seismological constraints, such as attenuation relationships and site amplification models, into neural network architectures have shown promise in maintaining physical consistency while capturing complex nonlinear patterns (Reichstein et al., 2019 ). Future directions include developing spatially varying residual models that account for regional differences in ground motion variability and integrating real-time seismic monitoring data with ML-based rapid hazard assessment systems. 6.2 Natural Resource Evaluation and Geological Modelling Mineral exploration and resource modelling represent some of the most mature applications of spatial machine learning in the geosciences. Geostatistical clustering for ore body domaining, incorporating spatial dependency metrics, has improved domain delineation accuracy (Fouedjio et al., 2017 ). The integration of geostatistical conditional simulation with supervised learning enables effective utilisation of both labelled and unlabelled spatial data in geological classification (Fouedjio and Talebi, 2022 ). Hybrid approaches combining CCSIM with CNNs address limitations in subsurface modelling by improving hard data reproduction and geological feature connectivity (Bai and Tahmasebi, 2020a ). Stochastic modelling of mineral exploration targets using spatial random forests provides both prediction and associated uncertainty crucial for exploration decision-making (Talebi et al., 2019 , 2021 , 2022 ). Uncertainty quantification is particularly critical in mineral resource classification, where the distinction between Measured, Indicated, and Inferred resource categories directly depends on prediction confidence. Geostatistical implicit modelling frameworks provide uncertainty quantification of three-dimensional geological domain boundaries essential for resource reporting (Fouedjio et al., 2021 ). The locally varying geostatistical machine learning approach addresses spatial non-stationarity in geological domains through local regression functions and conditional simulation (Fouedjio and Arya, 2024 ). Spatial random forests that incorporate local spatial-spectral information demonstrate superior performance for geological mapping compared to conventional random forests (Talebi et al., 2021 ). 6.3 Hydrogeological Forecasting Hydrogeological applications of spatial machine learning have expanded rapidly, driven by the need for reliable groundwater level prediction and quality assessment. Graph-based deep learning frameworks model complex spatial dependencies between monitoring wells by characterising multiple relationship types, including physical proximity, hydrological connectivity, and environmental similarity (Wu et al., 2025 ). Physics-based, conceptual, and machine learning models are increasingly compared through Bayesian Model Averaging, which provides multi-model uncertainty estimates that account for structural model uncertainty (Wohling et al., 2025 ). Deep learning has been incorporated into hydrogeological modelling for time series analysis, spatial data analysis, and inverse modelling, with LSTM networks showing much promise for temporal prediction (Dai et al., 2025 ). Uncertainty quantification in hydrogeological prediction faces unique challenges. Groundwater systems are characterised by high spatial heterogeneity, limited observability, and incomplete information regarding aquifer properties (Kunz et al., 2024). The sparse and irregular distribution of monitoring wells means that epistemic uncertainty dominates in many regions, making uncertainty maps particularly valuable for guiding additional data collection. Physics-informed constraints, particularly water balance equations and Darcy's law, provide opportunities for hybrid models that respect hydraulic principles while learning complex nonlinear patterns from data (Sun, 2018 ). 6.4 Environmental and Geochemical Monitoring Environmental monitoring applications benefit from the full suite of spatial ML methods. Digital soil mapping combines machine learning with geostatistical approaches for soil property prediction with uncertainty estimation (Kasraei et al., 2021 ; Wadoux et al., 2019 ; Hengl et al., 2018 ). Air quality prediction using Kriging-Land-use Regression with machine learning has significantly improved pollutant concentration predictions (Hsu et al., 2020 ). Geochemical anomaly detection for mineral exploration uses spatial random forests and spatial-spectral clustering to identify geologically meaningful patterns (Talebi et al., 2020 , 2021 ). Multi-resolution remote sensing data integration through deep learning architectures enables monitoring across varying spatial and temporal scales (Chen et al., 2017 ; Ghamisi et al., 2019 ). 6.5 Cross-Domain Synthesis Table 5 Cross-Domain Application Synthesis Application Domain Most Effective ML Framework(s) Preferred UQ Approach Validation Strategy Dominant Challenge Maturity Level Key References Seismic Hazard Assessment Neural networks (MLP, CNN) for GMPEs; gradient boosting (XGBoost) for intensity; RNN/LSTM for waveform forecasting Between-event / within-event residual decomposition; Bayesian site effect models; physics-guided NN uncertainty Spatial block CV by region/cluster; temporal holdout for earthquake sequences; leave-one-station-out Maintaining physical consistency (attenuation, site effects); real-time processing demands; sparse data in low-seismicity regions High for GMPE; Emerging for real-time prediction Kubo et al. ( 2024 ); Anjom et al. ( 2024 ); Reichstein et al. ( 2019 ) Mineral Resource Evaluation Hybrid geostat-ML (kriging + RF, SL); spatial random forests; geostat. semi-supervised learning; locally varying geostat-ML Geostatistical conditional simulation (grade uncertainty); QRF for continuous variables; geostat. implicit modelling for domain boundaries Spatial CV with domain-aware folds; leave-domain-out; conditioning to hard data validation 3D spatial heterogeneity; preferential sampling bias; support-change (core-to-block); geological domain definition High: most mature geophysical application of hybrid geostat-ML Fouedjio et al. ( 2017 , 2021 ); Fouedjio & Talebi ( 2022 ); Talebi et al. ( 2021 ); Bai & Tahmasebi ( 2020a ) Hydrogeological Forecasting Graph neural networks (TGCN); LSTM/N-HiTS for temporal; Bayesian model averaging of physics-based + ML models Bayesian model averaging (multi-model UQ); quantile prediction from graph networks; conformal intervals for GWL Temporal CV with spatial holdout; rolling-window validation; split-sample temporal test Sparse and irregular monitoring networks; temporal non-stationarity; subsurface heterogeneity poorly constrained; static feature uncertainty Moderate: growing rapidly; benchmark datasets lacking Wu et al. ( 2025 ); Kunz et al. (2024); Dai et al. ( 2025 ); Wohling et al. ( 2025 ); Sun ( 2018 ) Environmental Monitoring (soil, air, water) Kriging-ML hybrids (regression kriging + RF/XGBoost); ensemble RF with spatial features; EDM framework QR and QRF for continuous variables; spatial bootstrap for accuracy assessment; UNEEC for local error estimation IBCV for distribution shift; spatial bagging with effective sample size; forward feature selection + spatial CV Multi-resolution data fusion (MAUP); measurement support differences; spatial-temporal misalignment of data sources High for soil mapping; Moderate for air quality; Emerging for integrated environmental systems Kasraei et al. ( 2021 ); Hsu et al. ( 2020 ); Hengl et al. ( 2018 ); Wadoux et al. ( 2019 ); Behrens et al. ( 2018 ) Subsurface Characterisation (3D geological) CNN + MPS (CCSIM, RCNN); deep generative models (VAE, GAN); physics-guided ML for seismic inversion Full geostatistical simulation (multiple realisations); BNN for inversion uncertainty; ensemble disagreement Conditioning to hard data (well control); blind-well validation; comparison with physics-based forward models Training data scarcity; 3D computational cost; non-unique inversion solutions; geological realism enforcement Emerging: rapid progress but limited operational deployment Bai & Tahmasebi ( 2020a , b ); Avalos & Ortiz ( 2020 ); Xu et al. (2025); Fouedjio et al. ( 2021 ) Note : Maturity levels reflect the authors' assessment based on the volume and quality of published studies, availability of benchmark datasets, and degree of operational deployment. High = well-established with operational use; Moderate = active research with growing applications; Emerging = promising early results with limited deployment. GMPE = Ground Motion Prediction Equation; GWL = Groundwater Level. Several patterns emerge across domains, as synthesised in Table 5 with maturity assessments. First, hybrid geostatistical-ML approaches consistently outperform pure ML methods when spatial autocorrelation is strong, which is the norm in geophysical applications. Mineral exploration and environmental monitoring represent the most mature application domains, with well-established operational workflows, while subsurface characterisation and hydrogeological forecasting are developing rapidly but lack the standardised benchmark datasets needed for systematic method comparison. Second, uncertainty quantification remains underdeveloped relative to point prediction: most studies focus on predictive accuracy metrics rather than calibration of uncertainty estimates. Our systematic analysis found that fewer than 15% of the 122 reviewed studies explicitly decompose prediction uncertainty into aleatory and epistemic sources, despite the practical importance of this distinction for guiding data collection decisions. Third, validation methodologies lag behind modelling advances, with many studies still relying on random cross-validation despite documented biases of up to 47% from spatial autocorrelation (Schratz et al., 2019 ). Fourth, physics-informed constraints are most advanced in hydrogeology and seismology, where governing equations (Darcy's law, wave equations) are well established, but remain largely unexplored in geological mapping and environmental monitoring. Fifth, software implementations are unevenly distributed across methods: spatial validation packages such as CAST, sperrorest, and mlr3spatiotempcv have matured in R, while Python implementations remain more fragmented, particularly for integrated spatial UQ workflows. These findings collectively inform the structured research roadmap presented in Section 7.5 . 7 Research Frontiers and Actionable Directions The field of spatial machine learning and uncertainty quantification stands at a crucial juncture where traditional geostatistical approaches converge with modern machine learning capabilities. The cross-domain synthesis in Section 6 reveals persistent gaps alongside emerging opportunities. This section identifies specific research frontiers and provides a structured roadmap with concrete methodological directions. 7.1 Physics-Informed Spatial Machine Learning The fusion of physics-informed constraints with machine learning architectures represents a critical frontier. Current approaches, while promising, often struggle to maintain physical consistency while leveraging data-driven insights. In hydrology, Daw et al. ( 2017 ) pioneered physics-guided neural networks enforcing mass conservation in lake temperature modelling. Beucler et al. ( 2021 ) developed parameterisations preserving energy conservation while accelerating climate simulations. Willard et al. ( 2020 ) showed how physics-constrained deep learning improves satellite imagery retrieval by incorporating radiative transfer principles. Sun ( 2018 ) integrated physical flow equations with neural networks for hydraulic modelling. Specific research needs include developing physics-constrained loss functions for geophysical inversions, creating benchmark datasets pairing simulations with observations, and establishing evaluation protocols for physical consistency. 7.2 Multi-Scale Uncertainty Quantification Current approaches often assume spatial stationarity or simplified dependency structures, limiting applicability in complex geophysical scenarios (Wang et al., 2023 ). Key research directions include methods for propagating uncertainty across spatial scales in hierarchical geological models, adaptive uncertainty estimation frameworks that adjust to local data density, and real-time uncertainty updating for monitoring systems. In climate impact assessments, Zscheischler et al. ( 2018 ) showed that compound extreme events require sophisticated spatial uncertainty models capturing complex dependencies. For precision agriculture, Wadoux et al. ( 2019 ) highlighted how spatially-aware uncertainty quantification improves resource allocation. For landslide susceptibility, Lombardo et al. (2018) illustrated the value of multi-scale uncertainty models. 7.3 Interpretable Spatial Intelligence While explainable AI has advanced in general machine learning, spatial contexts present unique challenges due to complex dependencies and multi-scale interactions (Liu, 2024 ; Xing and Sieber, 2023 ). Future research needs specialised interpretation methods accounting for spatial autocorrelation, scale dependencies, and temporal dynamics. The challenge is maintaining prediction accuracy while enhancing model transparency, particularly where decisions carry significant consequences (Fouedjio and Arya, 2024 ). Specific needs include spatially aware SHAP variants that account for spatial autocorrelation in feature importance, methods to verify that local explanations are spatially consistent, and frameworks linking interpretability to physical plausibility. 7.4 Scalable Spatial Computing Scaling spatial ML to handle increasingly large datasets remains significant. Specific needs include GPU-optimised spatial algorithms for three-dimensional geophysical data, streaming spatial ML for real-time sensor network processing, federated learning approaches for distributed geophysical monitoring where data cannot be centralised, and efficient data structures for spatial information that maintain query performance at scale. Maxwell et al. ( 2018 ) demonstrated optimised architectures for large-scale land cover classification. Boeing ( 2019 ) highlighted that scalable algorithms are essential for city-scale sensor networks. Camps-Valls et al. ( 2021 ) showed that computationally efficient emulators can accelerate climate projections while preserving spatial patterns. 7.5 Research Roadmap Based on the systematic analysis conducted throughout this review, we propose a structured research roadmap (Table 6 ) that identifies nine specific gaps across five research frontiers, each with proposed methodological approaches, target geophysical applications, expected impacts, timelines, and enabling factors. This roadmap is intended to provide actionable guidance for the research community rather than general aspirational statements. Each gap is grounded in evidence identified through our systematic review: for instance, the finding that fewer than 15% of reviewed studies operationalise the aleatory-epistemic decomposition directly motivates the near-term priority of developing spatially explicit uncertainty decomposition maps. Several enabling factors underpin these priorities. Near-term goals (1–3 years) are those where methodological foundations already exist and primarily require integration and validation: existing SHAP/LIME frameworks can be extended with spatial blocking, and established R packages such as CAST and ‘sperrorest’ provide infrastructure for unified spatial-temporal validation. Critically, the community benchmark datasets modelled on successful precedents like CAMELS in surface hydrology (which provides standardised, spatially aligned static features supporting large-scale model comparison) could be hosted on existing geophysical data repositories such as GDR and PANGAEA. Medium-term goals (3–5 years) require new theoretical development, particularly hierarchical Bayesian inference for multi-scale uncertainty propagation and GPU-native spatial kernels building on libraries such as GPyTorch and KeOps. The single long-term goal, federated learning for distributed geophysical monitoring, depends on institutional changes beyond individual research groups, including inter-agency data sharing agreements and privacy frameworks. The advancement of all these priorities requires interdisciplinary collaboration between statisticians, computer scientists, and domain experts from earth sciences. Table 6 Structured Research Roadmap for Spatial Machine Learning in Geophysics Research Frontier Specific Gap Identified (with evidence) Proposed Methodological Approach Primary Target Application Expected Impact Timeline Enabling Factors / Dependencies Physics-Informed ML No unified framework for embedding geophysical conservation laws (mass, energy, momentum) into spatial ML loss functions. Current physics-informed NNs (Daw et al., 2017 ; Beucler et al., 2021 ) address individual constraints but lack generalisable spatial formulation. Differentiable physics layers with spatial attention mechanisms; conservation-law penalty terms in spatially structured loss functions; physics-constrained normalising flows for geological simulation Seismic hazard (attenuation models); groundwater flow (Darcy's law); reservoir simulation (material balance) Physically consistent predictions that extrapolate reliably beyond training domain; reduced epistemic uncertainty from physics constraints Near-term (1–3 year) Requires collaboration between ML researchers and domain physicists; existing JAX/PyTorch differentiable physics libraries provide foundation Physics-Informed ML Lack of community benchmark datasets pairing physics-based simulations with spatially distributed field observations. Current studies use proprietary or site-specific datasets preventing reproducible comparison. Community-driven open benchmark datasets with: (a) known physical constraints, (b) realistic spatial heterogeneity, (c) multiple fidelity levels (simulation + field data), (d) defined evaluation protocols Cross-domain validation and method comparison Reproducible comparison of spatial ML methods; accelerated method development; reduced duplication of effort Near-term (1–3 year) Institutional support for data sharing; existing models from CAMELS (hydrology) provide templates; geophysical data repositories (GDR, PANGAEA) can host Multi-Scale UQ Uncertainty propagation across spatial scales is rarely addressed. Most UQ methods operate at a single scale; hierarchical geological models require uncertainty characterisation from core-scale to deposit-scale. Hierarchical Bayesian frameworks with scale-dependent priors; nested variogram models with scale-specific nugget estimation; multi-resolution conditional simulation Mineral resource classification (core to block to panel); regional groundwater modelling (well to aquifer) Reliable uncertainty estimates at decision-relevant scales; appropriate resource classification confidence Medium-term (3–5 year) Requires multi-scale datasets (rare); computational advances in hierarchical Bayesian inference; change-of-support theory from geostatistics Multi-Scale UQ Aleatory-epistemic decomposition is conceptually recognised (Hullermeier & Waegeman, 2021) but rarely operationalised in spatial prediction. Fewer than 15% of reviewed studies explicitly separate these sources. Spatially explicit decomposition maps: ensemble variance (epistemic) vs. within-model noise (aleatory); adaptive sampling designs guided by epistemic uncertainty maps All geophysical domains; particularly valuable for exploration targeting and monitoring network design Targeted data collection in high-epistemic regions; quantified irreducible uncertainty for risk assessment; optimal sensor/well placement Near-term (1–3 year) Ensemble methods already available; requires validation against ground truth; connects to optimal experimental design theory Interpretable ML SHAP and LIME do not account for spatial autocorrelation, leading to inflated importance of spatially correlated but non-causal features. No spatial XAI methods currently exist. Spatially weighted permutation importance; conditional SHAP with spatial blocking; spatial partial dependence profiles that account for neighbourhood effects Environmental monitoring (identifying pollution drivers); geological mapping (understanding lithological controls) Trustworthy feature importance in spatial contexts; spatially consistent explanations that domain experts can validate Near-term (1–3 year) Extensions of existing SHAP/LIME frameworks; spatial blocking infrastructure from validation literature; R/Python packages can be extended Interpretable ML No framework links ML model interpretation to physical plausibility. A model can achieve high accuracy with physically implausible feature relationships. Physics-consistency scoring: evaluate whether learned feature-response relationships align with known physical mechanisms; constrained SHAP with physical monotonicity Geological modelling (e.g., grade-depth relationships); hydrogeology (recharge-level relationships) Models that are both accurate and physically defensible; increased stakeholder trust in ML predictions Medium-term (3–5 year) Requires domain knowledge formalisation; connects to physics-informed ML frontier; interdisciplinary collaboration essential Validation Standard CV overestimates performance by up to 47% (Schratz et al., 2019 ) yet remains the default in many studies. No unified framework handles spatial + temporal + scale dependencies simultaneously. Unified spatiotemporal CV framework with automatic blocking based on empirical variogram/correlogram analysis; integrated treatment of spatial, temporal, and cross-scale dependencies All spatial prediction tasks; mandatory for any operational deployment Realistic performance assessment; prevention of optimistic bias in reported accuracy; reproducible model evaluation Near-term (1–3 year) Building on existing CAST , sperrorest , mlr3spatiotempcv packages; automatic variogram estimation for blocking; needs consensus guidelines from the community Scalability 3D spatial ML is limited by memory and computation: geostatistical simulation for a 10M-cell geological model requires days on conventional hardware. GPU-native spatial kernels using CUDA/ROCm; sparse approximations for large covariance matrices; streaming algorithms for incremental learning; model distillation for deployment 3D subsurface characterisation; real-time seismic monitoring; large-scale environmental mapping Feasibility of spatial ML at operational scales; real-time uncertainty estimation for monitoring systems Medium-term (3–5 year) GPU hardware advances; sparse GP approximations (inducing points); existing work on scalable GPs (GPyTorch, KeOps) provides foundation Scalability Federated learning is unexplored for distributed geophysical monitoring networks where raw data cannot be centralised due to privacy, sovereignty, or bandwidth constraints. Privacy-preserving spatial federated learning: local model training at each monitoring site with aggregation of spatial parameters; federated variogram estimation Multi-site mining operations; international groundwater monitoring; multi-agency environmental networks ML deployment across organisational boundaries; leveraging distributed data without centralisation Long-term (5 + yr) Federated learning frameworks maturing (Flower, PySyft); geophysical challenge is preserving spatial structure across federated nodes; requires inter-institutional agreements Note : Timelines are indicative and assume active research effort. Near-term priorities are those where methodological foundations exist and primarily require integration and validation. Medium-term priorities require new theoretical development. Long-term priorities depend on infrastructure and institutional changes beyond individual research groups. The 15% figure for aleatory-epistemic decomposition is based on the authors' systematic coding of the 122 included studies. 8 Conclusions This review has provided a systematic, PRISMA-guided assessment of predictive SML in the big data era, with a specific focus on geophysical applications. Through the analysis of 122 studies, we have critically examined the evolution from traditional geostatistical approaches to advanced hybrid methodologies that address the unique challenges of spatial data, including spatial autocorrelation, non-stationarity, scale dependency, and three-dimensional heterogeneity. The conceptual decision pathway framework introduced in this work provides a structured approach for practitioners to navigate from data characterisation through methodology selection, uncertainty quantification, and validation to geophysical application. Our cross-domain synthesis across seismology, mineral exploration, hydrogeology, and environmental monitoring reveals both transferable patterns and domain-specific requirements. Hybrid geostatistical-ML frameworks consistently outperform pure ML approaches when spatial autocorrelation is strong, yet uncertainty quantification remains underdeveloped relative to point prediction accuracy. The six synthesis tables presented throughout this review provide quantitative comparisons that enable direct method selection based on specific application requirements, spatial assumptions, and computational constraints. The structured research roadmap identifies concrete near-term priorities including spatially aware interpretability methods, operationalised aleatory-epistemic decomposition, and unified spatial-temporal validation frameworks, alongside medium-term goals such as hierarchical multi-scale uncertainty propagation and GPU-native spatial computing. The advancement of these priorities requires the interdisciplinary collaboration between spatial statisticians, machine learning researchers, and geoscience domain experts that this review aims to foster. By bridging the gap between methodological innovation and geophysical application, SML can fulfil its potential to provide meaningful insights and reliable predictions for critical decisions in resource management, hazard assessment, and environmental stewardship. Declarations Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data Availability Statement No new data was generated for this work. The PRISMA screening records and data extraction tables are available from the corresponding author upon reasonable request. 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Journal of Data Acquisition and Processing , Vol. 38 (2) . https://doi.org/10.5281/zenodo.776658 Zhan W, Datta A (2024) Neural networks for geospatial data. J Am Stat Assoc 1–21. https://doi.org/10.1080/01621459.2024.2356293 Zhu D, Liu Y, Yao X, Fischer MM (2021) Spatial regression graph convolutional neural networks: A deep learning paradigm for spatial multivariate distributions. GeoInformatica. https://doi.org/10.1007/s10707-021-00454-x Zhu Z, Zhou Y, Seto KC, Stokes EC, Deng C, Pickett ST, Taubenböck H (2019) Understanding an urbanizing planet: Strategic directions for remote sensing. Remote Sens Environ 228:164–182. https://doi.org/10.1016/j.rse.2019.04.020 Zscheischler J, Westra S, Van Den Hurk BJ, Seneviratne SI, Ward PJ, Pitman A, Zhang X (2018) Future climate risk from compound events. Nat Clim Change 8:469–477. https://doi.org/10.1038/s41558-018-0156-3 Supplementary Files supplementarysearch.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 08 May, 2026 Reviewers invited by journal 07 May, 2026 Editor invited by journal 30 Apr, 2026 First submitted to journal 21 Apr, 2026 Editor assigned by journal 17 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9340991","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":636454912,"identity":"31775851-2cc7-4ea7-9a35-31301b550359","order_by":0,"name":"Ebenezer Afrifa-Yamoah","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0003-1741-9249","institution":"Edith Cowan University - Joondalup Campus: Edith Cowan University","correspondingAuthor":true,"prefix":"","firstName":"Ebenezer","middleName":"","lastName":"Afrifa-Yamoah","suffix":""},{"id":636454913,"identity":"6263e3aa-cc39-4355-820b-4cd2aed40cfc","order_by":1,"name":"Yaw Kwaafo Kwaafo","email":"","orcid":"","institution":"Edith Cowan University - Joondalup Campus: Edith Cowan University","correspondingAuthor":false,"prefix":"","firstName":"Yaw","middleName":"Kwaafo","lastName":"Kwaafo","suffix":""},{"id":636454914,"identity":"11ee90d2-0407-4201-b870-98ed813cc8f5","order_by":2,"name":"Bright Wiredu Nuakoh","email":"","orcid":"","institution":"AIMS Rwanda: African Institute for Mathematical Sciences Rwanada","correspondingAuthor":false,"prefix":"","firstName":"Bright","middleName":"Wiredu","lastName":"Nuakoh","suffix":""},{"id":636454915,"identity":"5146fac0-29f6-4913-af76-2116ed40da6e","order_by":3,"name":"Wei Hong Tan","email":"","orcid":"","institution":"Rio Tinto Ltd","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"Hong","lastName":"Tan","suffix":""},{"id":636454916,"identity":"6a2adffa-d0e4-4bee-83d4-7a720288eb3b","order_by":4,"name":"Francky Fouedjio","email":"","orcid":"","institution":"Rio Tinto Ltd","correspondingAuthor":false,"prefix":"","firstName":"Francky","middleName":"","lastName":"Fouedjio","suffix":""},{"id":636454917,"identity":"10eae8ed-31dc-4127-8323-375e7ce31781","order_by":5,"name":"Emet Arya","email":"","orcid":"","institution":"Rio Tinto Ltd","correspondingAuthor":false,"prefix":"","firstName":"Emet","middleName":"","lastName":"Arya","suffix":""}],"badges":[],"createdAt":"2026-04-07 07:16:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9340991/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9340991/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109433904,"identity":"2370ca5d-9928-4836-a605-52e1bbcda8ad","added_by":"auto","created_at":"2026-05-18 05:49:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":323561,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConceptual decision pathway framework for predictive spatial machine learning in geophysical applications.\u003c/strong\u003e This framework provides the organising principle for the review and serves as a practical guide for researchers and practitioners selecting appropriate methods for specific geophysical prediction problems. The framework comprises five layers connected by a forward workflow with two feedback mechanisms.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/0a00ca4cb3df398c36d832f8.png"},{"id":109759967,"identity":"92d307d5-5069-452d-b00c-c341a843a643","added_by":"auto","created_at":"2026-05-22 07:28:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":248618,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpatial data taxonomy for geophysical applications.\u003c/strong\u003e This figure presents the hierarchical organisation of spatial data relevant to predictive machine learning in the geosciences, showing the flow from data sources through data types, spatial properties, application domains, and modelling outputs.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/5b007a3a4e837bbe55e2417c.png"},{"id":109799553,"identity":"d28a8f56-8ee3-457d-83e4-779268f0e741","added_by":"auto","created_at":"2026-05-22 15:31:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":182075,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparing Spatial and Non-Spatial Decision Trees in Remote Sensing Classification\u003c/strong\u003e. We highlight the contrasts between Spatial Random Forest (SRF) and traditional Random Forest (RF) approaches for geospatial analysis. The left panel illustrates\u003cstrong\u003e \u003c/strong\u003ethe SRF methodology, where spatial decision trees incorporate contextual information from\u003cstrong\u003e \u003c/strong\u003emultiple surrounding pixels for classification decisions, as shown by the multi-cell grid patterns at decision nodes. The right panel depicts the classical RF approach, which considers only individual pixel values in isolation, represented by single-cell decision points. The bottom images demonstrate the practical impact of these approaches when classifying stratigraphic units in remote sensing data: the SRF results (bottom left) exhibit greater geological realism and spatial coherence, while the RF results (bottom right) appear noisier and less consistent with natural geological patterns. This comparison highlights the advantage of incorporating spatial context in machine learning algorithms when analyzing inherently spatial phenomena.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/7b6ec34a526be0e2efcb002b.png"},{"id":109433906,"identity":"747047aa-c905-4e36-95ce-232bdd19c1a1","added_by":"auto","created_at":"2026-05-18 05:49:19","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":91302,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpatially adaptive ML with local models across geographic regions. \u003c/strong\u003eIt illustrates a spatially adaptive machine learning approach where localized machine learning models are fitted to different geographic regions based on their spatial coordinates. Four distinct regional models are identified by red ellipses, each labelled as ML(xᵢ, yᵢ) where (xᵢ, yᵢ) represents the center coordinates of each local region. The scatter points represent data samples coloured according to a \"feature variation\" scale (20-80), highlighting the heterogeneity of environmental or socioeconomic factors across space. This framework accounts for spatial non-stationarity by allowing model parameters to vary across different geographic contexts, effectively capturing local relationships that might be missed by global models.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/709012b42bedea6667c206c6.png"},{"id":109759665,"identity":"0de0879f-225d-41c5-b445-2dc6014a485b","added_by":"auto","created_at":"2026-05-22 07:27:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":136275,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTaxonomy of uncertainty types in spatial prediction models.\u003c/strong\u003e We present a conceptual framework of uncertainty types in predictive modeling. Predictive Uncertainty (PU) is shown as the combination of Aleatoric Uncertainty (AU) and Epistemic Uncertainty (EU).\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/16b944fdca841cb94eefbfc5.png"},{"id":109759333,"identity":"410f0dd5-fd68-41e5-918c-b02a29393281","added_by":"auto","created_at":"2026-05-22 07:26:40","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":289668,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComprehensive Framework for Uncertainty Quantification in Computational and Machine Learning Models. \u003c/strong\u003eButvinik (2022) discusses a two-part taxonomy of uncertainty quantification methods. Panel A illustrates the general computational modeling uncertainty approaches, dividing them into Forward Uncertainty Propagation (with Probabilistic and Non-Probabilistic branches) and Inverse Uncertainty methods (categorized as Frequentist, Bayesian, Modular, and Full approaches). The probabilistic methods are highlighted as more rigorous and consistent with decision analysis theory. Panel B focuses specifically on uncertainty quantification in machine learning, organizing methods into two primary paradigms: Frequentist (centred on standard error of parameter estimates) and Bayesian Inference. The Bayesian approach is further subdivided into Traditional Machine Learning methods (including Gaussian Process Regression and physics-informed variants) and Deep Learning techniques (featuring Bayesian Neural Networks and their physics-informed counterparts). This hierarchical organization demonstrates how uncertainty quantification spans from classical statistical approaches to advanced hybrid methods that incorporate domain knowledge into machine learning frameworks.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/772c7c26bb0a9a58e59e23f0.png"},{"id":109433911,"identity":"a98c63f4-a1d4-443e-b261-e9cc584e4c28","added_by":"auto","created_at":"2026-05-18 05:49:19","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":132225,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEmerging Research Frontiers in Spatial Machine Learning.\u003c/strong\u003e We illustrate key research directions that are shaping the future of spatial machine learning. At the center is the core domain of Spatial ML, with five critical research frontiers radiating outward: (1) Integration of Physics-Informed Constraints, which embeds domain knowledge into learning algorithms; (2) Advanced Uncertainty Quantification techniques that address spatial variability and model limitations; (3) Interpretable Spatial Machine Learning approaches that enhance model transparency and explainability; (4) Spatially-aware Validation Frameworks that properly account for spatial dependencies in model evaluation; and (5) Scalability and Computational Efficiency methods to handle increasing data volumes and complexity. These interconnected research areas represent the cutting edge of spatial machine learning development, addressing fundamental challenges that must be overcome to advance the field and broaden its applications.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/fc0dcb3ac7aefd59c93c7fb7.png"},{"id":109433908,"identity":"4b595691-f50f-4e5e-a8ce-a63249cd533e","added_by":"auto","created_at":"2026-05-18 05:49:19","extension":"docx","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":325362,"visible":true,"origin":"","legend":"","description":"","filename":"supplementarysearch.docx","url":"https://assets-eu.researchsquare.com/files/rs-9340991/v1/c00fbdc2729ce4677da88b7e.docx"}],"financialInterests":"","formattedTitle":"Predictive Spatial Machine Learning in the Era of Big Data: A Critical Analysis of Methods, Technical Advances, and Research Frontiers for Geophysical Applications","fulltext":[{"header":"Highlights","content":"\u003cp\u003e1. Hybrid geostatistical-ML frameworks capture complex spatial heterogeneity and dependencies.\u003c/p\u003e\u003cp\u003e2. Advanced methods distinguish between aleatory and epistemic uncertainties in spatial prediction.\u003c/p\u003e\u003cp\u003e3. Novel validation frameworks address spatial autocorrelation challenges in model assessment.\u003c/p\u003e\u003cp\u003e4. Physics-informed spatial ML balances data-driven insights with domain knowledge.\u003c/p\u003e\u003cp\u003e5. Key frontiers: interpretable models, scalable algorithms, and multi-scale uncertainty estimation.\u003c/p\u003e"},{"header":"1 Introduction","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Motivation and Rationale\u003c/h2\u003e \u003cp\u003eThe last decade has witnessed an unprecedented surge in spatial data generation across the geosciences, driven by advances in earth observation technologies, distributed sensor networks, and the proliferation of Internet of Things (IoT) devices in environmental and geophysical monitoring systems. In seismology, dense seismic arrays now generate terabytes of continuous waveform data daily (Kubo et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In mineral exploration, multi-element geochemical surveys and hyperspectral remote sensing produce spatially dense, high-dimensional datasets that challenge traditional geostatistical analysis (Talebi et al., \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In hydrogeology, networks of groundwater monitoring wells combined with climate reanalysis data enable spatiotemporal prediction at continental scales (Kunz et al., 2024). This exponential growth in geospatial data volume, velocity, and complexity has fundamentally transformed the landscape of spatial data analytics, creating both extraordinary opportunities and formidable challenges (Casali et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWhat sets spatial machine learning apart from conventional machine learning approaches is its explicit incorporation of spatial relationships and dependencies into model architectures, representing a paradigm shift in how we process and analyse geographic and geophysical data (Casali et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Nikparvar and Thill, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This distinction is rooted in the recognition that spatial data exhibits unique characteristics that fundamentally challenge traditional machine learning assumptions. Specifically, spatial autocorrelation (the tendency of nearby features to be more related than distant ones), spatial heterogeneity (the variation of processes across space and time), and scale dependency (the influence of spatial scale on observed patterns) violate the independent and identically distributed (IID) assumptions underpinning conventional machine learning methods (Cliff and Ord, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1973\u003c/span\u003e; Kopczewska, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Matheron, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e1962\u003c/span\u003e; Woodcock et al., \u003cspan citationid=\"CR108\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). These violations are particularly pronounced in geophysical applications, where subsurface properties vary continuously across three-dimensional space, seismic wave propagation depends on complex geological structures, and groundwater flow is governed by spatially heterogeneous hydraulic conductivity fields.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2 Literature Context and Gaps\u003c/h2\u003e \u003cp\u003eSeveral reviews have addressed aspects of spatial machine learning in recent years. Casali et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) provided a scoping review of machine learning for spatial analyses in urban areas. Ma et al. (\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) reviewed deep learning applications in remote sensing. Kopczewska (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) examined spatial ML opportunities for regional science. Nikparvar and Thill (\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) surveyed machine learning approaches for spatial data and identified key spatial data properties that affect machine‑learning performance and compared data‑level versus algorithm‑level approaches for handling them. In the geophysical domain, Kubo et al. (\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) reviewed machine learning advances in earthquake seismology, Anjom et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) assessed ML for seismic exploration, and Xu et al. (2025) reviewed ML-based seismic subsurface characterisation. However, no existing review systematically integrates the three pillars that are essential for reliable geophysical prediction: (1) spatially aware machine learning frameworks, (2) rigorous uncertainty quantification distinguishing aleatory from epistemic sources, and (3) validation methodologies that properly account for spatial autocorrelation. This gap is particularly consequential in geophysical practice, where uncertainty directly influences critical decisions such as forecasting induced seismicity from fluid injection, assessing subsurface integrity for CO₂ storage and hydrogen caverns, evaluating fault reactivation risks around underground excavations, and predicting reservoir compaction and surface subsidence, contexts in which mischaracterised uncertainty can lead to irreversible environmental damage, infrastructure failure, or regulatory breach.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.3 Cross-Domain Perspectives\u003c/h2\u003e \u003cp\u003eSpatial machine learning methodologies are deployed across diverse domains, each contributing unique insights and facing distinct challenges. In ecology, species distribution models must handle spatially biased occurrence data and extrapolation to unsampled environments (Roberts et al., \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). In epidemiology, disease mapping requires spatially varying risk surfaces with reliable uncertainty bands for public health decision-making (Paez et al., \u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In urban planning, interpretable spatial models help stakeholders evaluate infrastructure vulnerability under climate change scenarios (Zhu et al., \u003cspan citationid=\"CR118\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In precision agriculture, soil property mapping combines geostatistical and machine learning approaches with multi-resolution remote sensing data (Wadoux et al., \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). A cross-domain comparison reveals that while methodological foundations are shared, including spatial cross-validation, geostatistics-ML hybrids, and spatial uncertainty quantification, the relative emphasis on specific techniques varies substantially. Geophysical applications face challenges related to three-dimensional spatial structures, multi-scale heterogeneity, and the integration of physics-based constraints, which set them apart from predominantly two-dimensional surface-level analyses in other fields.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e1.4 Objectives and Scope\u003c/h2\u003e \u003cp\u003eThis review aims to: (1) provide a systematic, PRISMA-guided assessment of the current state of predictive spatial machine learning, with emphasis on geophysical applications; (2) introduce a practical conceptual decision pathway framework linking data characteristics, methodology selection, uncertainty quantification, and validation for geophysical prediction problems; (3) critically compare methods; (4) evaluate uncertainty quantification approaches with explicit attention to the aleatory-epistemic distinction and its implications for geophysical decision-making; and (5) identify specific research gaps and propose an actionable roadmap with concrete methodological directions. The review encompasses studies across seismology, mineral exploration, hydrogeology, and environmental monitoring.\u003c/p\u003e \u003c/div\u003e"},{"header":"2 Review Methodology","content":"\u003cp\u003eWe followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines (see Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e of supplementary material; Page et al., \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) to ensure transparency and reproducibility in the literature search, screening, and synthesis processes. Further details of the review methodology are presented in a Supplementary material.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Search Strategy\u003c/h2\u003e \u003cp\u003eWe searched four major databases: Scopus, Web of Science, IEEE Xplore, and Google Scholar. The search was conducted between January and March 2025, covering publications from 2015 to 2025. The search string combined terms from three conceptual domains: spatial machine learning (\"spatial machine learning\" OR \"geostatistical ML\" OR \"spatial prediction\" OR \"geographically weighted\" OR \"spatial deep learning\"), uncertainty quantification (\"uncertainty quantification\" OR \"prediction uncertainty\" OR \"aleatory\" OR \"epistemic\" OR \"probabilistic prediction\" OR \"conformal prediction\"), and geophysical applications (\"geophysics\" OR \"seismic\" OR \"mineral exploration\" OR \"hydrogeology\" OR \"subsurface\" OR \"environmental monitoring\" OR \"geological modeling\"). Additional records were identified through reference list screening of included studies, relevant preprints, and conference proceedings from key venues including AGU, EGU, and the Geostatistics Congress.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Inclusion and Exclusion Criteria\u003c/h2\u003e \u003cp\u003eStudies were included if they: (a) developed or applied machine learning methods with explicit spatial modelling components for prediction tasks; (b) addressed uncertainty quantification or spatial validation; (c) were published in peer-reviewed journals or established conference proceedings; and (d) were available in English. Studies were excluded if they: (a) applied standard machine learning without spatial considerations; (b) focused exclusively on image classification without spatial prediction; (c) were editorials, commentaries, or non-peer-reviewed opinion pieces; or (d) duplicated content from the same research group without methodological advancement.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Study Selection and Screening\u003c/h2\u003e \u003cp\u003eThe initial database search identified 847 records, with an additional 123 records from other sources. After removing 328 duplicates, 642 unique records were screened by title and abstract. Of these, 389 were excluded as they did not meet the spatial ML criteria or were outside the geophysical scope. The remaining 253 full-text articles were assessed for eligibility, with 131 excluded for lacking uncertainty quantification components, spatial prediction focus, or methodological novelty. The final review synthesises 122 studies, categorised into four thematic areas: geostatistical-ML hybrid frameworks (n\u0026thinsp;=\u0026thinsp;34), uncertainty quantification methods (n\u0026thinsp;=\u0026thinsp;28), spatial validation and feature engineering (n\u0026thinsp;=\u0026thinsp;31), and geophysical domain applications (n\u0026thinsp;=\u0026thinsp;29). The PRISMA flow diagram documenting this process is provided in the supplementary material as Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Conceptual Framework\u003c/h2\u003e \u003cp\u003eTo organise the review and provide a novel analytical contribution, we developed a five-layer conceptual decision pathway framework for predictive spatial machine learning in geophysical applications (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The framework links: Layer 1 (Spatial Data Characterisation) covering data types, spatial properties, geophysical context, and integration requirements; Layer 2 (Methodology Selection) addressing ML framework choice, spatial feature engineering, and uncertainty quantification approach; Layer 3 (Validation and Assessment) encompassing spatially aware validation and model interpretation; Layer 4 (Geophysical Application Domains) spanning seismic hazard, mineral exploration, hydrogeology, environmental monitoring, and subsurface characterisation; and Layer 5 (Decision outputs) highlighting important deliverables to support decision-making processes. An iterative feedback loop connects application outcomes back to data collection and methodology refinement. This framework serves as the organising principle for the review and is intended as a practical guide for researchers and practitioners selecting appropriate methods for specific geophysical prediction problems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3 Spatial Data Foundations for Geophysical Analysis","content":"\u003cp\u003eThis section synthesises the spatial data landscape relevant to predictive modelling in the geosciences, consolidating data types, resolution challenges, multi-source integration approaches, and exploratory analysis considerations into a focused treatment that provides the necessary background without duplicating material available in standard GIS references (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Data Types and Resolution Challenges\u003c/h2\u003e \u003cp\u003eSpatial and geospatial databases serve as the foundation of geographic information systems (GIS), playing a pivotal role in geophysical applications from environmental science to mineral resource management. The fundamental distinction lies between vector formats, encoding spatial information through points, lines, and polygons, and raster formats, organising data in grid structures where each cell contains attribute values. In geophysical contexts, vector data commonly represents drill-hole locations, seismic station networks, and fault traces, while raster data captures continuous fields such as elevation models, satellite imagery, and gridded geophysical survey data (Liu et al., \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Feng and Koch, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBeyond these fundamental types, geophysical databases increasingly incorporate object-oriented structures that combine geometric and non-geometric attributes for complex subsurface objects (Bei et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Duckham et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), time-series spatial databases that facilitate analysis of dynamic phenomena such as groundwater level fluctuations and seismic catalogues (Pelekis et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), and multimedia spatial databases integrating spatial data with remote sensing imagery and geophysical logs (Li et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eResolution fundamentally influences prediction accuracy and uncertainty. Higher resolution data captures more spatial variation but introduces noise and computational burden, while lower resolution data may miss critical patterns, leading to the modifiable areal unit problem (MAUP). In geophysics, this tension is particularly acute: seismic data may have metre-scale resolution along profiles but kilometre-scale spacing between lines, creating highly anisotropic sampling patterns that challenge standard spatial prediction methods (Heuvelink et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Atkinson and Graham, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSpatial Data Types, Resolutions, and ML Preprocessing Requirements Across Geophysical Domains\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeophysical Domain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePrimary Data Sources \u0026amp; Types\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTypical Spatial Resolution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTemporal Characteristics\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eKey ML Preprocessing Challenges\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRecommended Preprocessing\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKey References\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSeismology\u003c/b\u003e (hazard \u0026amp; risk)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContinuous waveforms (SAC, miniSEED); strong-motion records; station metadata (vector points); fault maps (vector lines/polygons); VS30 site classification grids (raster)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStation spacing: 5\u0026ndash;50 km (regional), \u0026lt;\u0026thinsp;1 km (dense arrays); DAS: metre-scale; VS30 grids: 250m-1km\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eContinuous (Hz-kHz sampling); event catalogues span decades; non-stationary seismicity rates\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eIrregular network geometry; signal-to-noise separation; 3D wave propagation effects; anisotropic spatial coverage; catalogue completeness varies regionally\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDenoising (PhaseNet); STA/LTA event detection; spectral feature extraction; coordinate encoding; spatial declustering of catalogues\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKubo et al. (\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); Anjom et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); Reichstein et al. (\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2019\u003c/span\u003e); Camps-Valls et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMineral Exploration\u003c/b\u003e (resource evaluation)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDrill-hole assays (point data at depth); geochemical soil/rock samples; hyperspectral remote sensing (raster); geophysical surveys: magnetics, gravity, EM (raster/profile)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCore: cm-scale along hole; drill spacing: 25-200m; geochemical: 50-500m grid; airborne surveys: 50-400m line spacing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStatic geological properties; exploration campaigns span years; sequential infill drilling changes data density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePreferential sampling (holes target mineralisation); support change (core to block); 3D geological domains; compositional data constraints; informative censoring (below detection)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCompositing to regular lengths; spatial declustering; domain separation; log-ratio transforms for compositions; imputation of below-detection values\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFouedjio et al. (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2017\u003c/span\u003e); Talebi et al. (\u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Fouedjio \u0026amp; Talebi (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Erdogan Erten et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Talebi et al. (\u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eHydrogeology\u003c/b\u003e (groundwater)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWell logs (lithology, geophysics); pump test data; piezometric time series; recharge estimates; DEM-derived variables (raster); climate reanalysis grids\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWells: point-scale, spacing 1\u0026ndash;50 km; climate grids: 0.1\u0026ndash;0.5 deg.; DEMs: 30-90m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eContinuous monitoring (hourly-daily); strong seasonal and multi-year trends; climate-driven non-stationarity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVery sparse and irregular networks; aquifer heterogeneity poorly constrained; mixing of confined/unconfined systems; temporal gaps in monitoring records\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGap filling via interpolation or physics-based models; temporal aggregation; static feature derivation (aquifer type, soil, land use); normalisation of pumping effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWu et al. (\u003cspan citationid=\"CR110\" class=\"CitationRef\"\u003e2025\u003c/span\u003e); Dai et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e); Kunz et al. (2024); Wohling et al. (\u003cspan citationid=\"CR107\" class=\"CitationRef\"\u003e2025\u003c/span\u003e); Sun (\u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eEnvironmental Monitoring\u003c/b\u003e (soil, air, water quality)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSoil samples (point); air quality stations (point with time series); satellite-derived indices (raster: NDVI, LST); land-use/land-cover maps (classified raster/polygon)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSoil: 50m-5km grids; air stations: 10-50km; satellites: 10m (Sentinel) to 1km (MODIS)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSatellite: daily-16 day revisit; soil campaigns: periodic; air quality: continuous hourly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMulti-resolution fusion (MAUP); measurement support differences; spatial-temporal misalignment; mixed land-use pixels; cloud contamination in optical RS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eResampling/downscaling; spatiotemporal co-registration; cloud masking; compositing (median, max NDVI); feature stacking of multi-source covariates\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKasraei et al. (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Hsu et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e); Hengl et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e); Wadoux et al. (\u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2019\u003c/span\u003e); Behrens et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e); Heuvelink et al. (\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSubsurface Characterisation\u003c/b\u003e (3D geological modelling)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSeismic reflection volumes (3D raster); well logs (1D profiles at points); core photos; training images (geological analogues); conceptual geological models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSeismic: 12.5-50m inline/crossline, ms vertical; wells: 0.15m log sampling, km-scale spacing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeological properties are static but knowledge evolves with infill data; 4D seismic for reservoir monitoring\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVast dimensional mismatch between seismic coverage and sparse well control; ill-posed inversion; non-unique solutions; geological realism constraints; training image selection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSeismic attribute extraction; well-to-seismic tie; upscaling of well data to seismic resolution; training image curation; conditioning to hard data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBai \u0026amp; Tahmasebi (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020b\u003c/span\u003e); Avalos \u0026amp; Ortiz (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e); Xu et al. (2025); Fouedjio et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Fouedjio \u0026amp; Arya (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cem\u003eAbbreviations: DAS\u0026thinsp;=\u0026thinsp;Distributed Acoustic Sensing; VS30\u0026thinsp;=\u0026thinsp;time-averaged shear-wave velocity in the upper 30 m; STA/LTA\u0026thinsp;=\u0026thinsp;Short-Term Average / Long-Term Average; MAUP\u0026thinsp;=\u0026thinsp;Modifiable Areal Unit Problem; RS\u0026thinsp;=\u0026thinsp;Remote Sensing; EM\u0026thinsp;=\u0026thinsp;Electromagnetic.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Multi-Source Data Integration\u003c/h2\u003e \u003cp\u003eThe complexity of spatial data integration in geophysical applications stems from the heterogeneous nature of data sources, formats, and structures, necessitating sophisticated approaches for effective harmonisation (Garosi et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Mohammadi et al., \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Several strategies have emerged to address resolution-related challenges. Traditional approaches include careful application of resampling techniques such as upscaling or downscaling. More advanced methods employ multi-resolution analysis using wavelets or Gaussian pyramid decomposition, alongside hierarchical Bayesian frameworks that account for different scales of variation (Banerjee et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Afrifa-Yamoah and Osei, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Change of support techniques and data fusion methods, including Bayesian maximum entropy and area-to-point kriging, facilitate the integration of multi-resolution data (Wang et al., \u003cspan citationid=\"CR103\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRecent advances in machine learning have transformed multi-resolution geospatial data handling. Convolutional Neural Networks demonstrate effectiveness in super-resolution tasks for satellite imagery (Pouliot et al., \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Deep learning architectures, including autoencoders and Generative Adversarial Networks, excel at fusing multi-resolution remote sensing data while preserving fine details (Chen et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ghamisi et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Qin et al., \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). In subsurface characterisation, deep generative models now provide geological priors that encode non-Gaussian, non-stationary, and multi-scale patterns directly from training examples (Xu et al., 2025). These developments underscore the importance of balancing technical sophistication with practical implementation considerations across varying observational scales.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Exploratory Spatial Analysis\u003c/h2\u003e \u003cp\u003eExploratory Data Analysis (EDA) serves as a cornerstone in the spatial prediction workflow, providing systematic approaches to understanding complex datasets through summarisation and visualisation (Tukey, \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e1977\u003c/span\u003e). The methodological framework for spatial prediction EDA encompasses spatial correlation techniques such as geographically weighted regression (GWR) and spatial econometrics (Georganos et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Oshan et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wu et al., \u003cspan citationid=\"CR109\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), variogram analysis for evaluating spatial continuity (Goovaerts, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), machine learning-driven outlier detection (Xu et al., \u003cspan citationid=\"CR112\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and local indicators of spatial association (LISA) for cluster identification (Anselin, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Chen, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWhile established techniques such as variogram analysis and spatial autocorrelation measures including Moran's I and Geary's C remain foundational (Anselin, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Cliff and Ord, 1981; Cressie, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1993\u003c/span\u003e), contemporary developments address critical challenges in spatial analytics including non-stationarity, multi-scale analysis, and big data processing. Oshan et al. (\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) introduced local spatial heterogeneity measures extending beyond traditional global statistics. Artificial intelligence applications in automated feature extraction have opened new frontiers in spatial data analysis (Li and Hsu, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), while integration with cloud computing has expanded the scope of spatial EDA capabilities (Yang et al., \u003cspan citationid=\"CR113\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). These evolving approaches are reshaping spatial analysis, enhancing both accuracy and interpretability of spatial predictions across geophysical applications.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Predictive Spatial Machine Learning Frameworks","content":"\u003cp\u003eThe evolution of spatial machine learning frameworks reflects the growing complexity of geospatial data analysis and the need for scalable solutions that respect the unique characteristics of spatial data. Modern frameworks address challenges in processing vast amounts of spatial data from ground observations and airborne data collections (Sabek and Mokbel, \u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Key research domains encompass event detection, variable estimation, long-term forecasting, and relationship mining, with emphasis on integrating physical laws into ML models for enhanced predictive accuracy (Karpatne et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This section critically analyses the major framework categories, evaluating their assumptions, strengths, and limitations for geophysical applications.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Integration of Geostatistics and Machine Learning\u003c/h2\u003e \u003cp\u003eRecent advances in spatial modelling have demonstrated powerful synergies between geostatistical techniques and ML approaches, particularly in capturing complex geological heterogeneity. A pioneering hybrid approach combining cross-correlation simulation (CCSIM) with convolutional neural networks (CNNs) addresses fundamental limitations in subsurface modelling, achieving perfect conditioning data accuracy in 2D scenarios and enhanced structural preservation in 3D models (Bai and Tahmasebi, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e). Another framework integrating geostatistical conditional simulation with supervised learning effectively utilises both labelled and unlabelled spatial data, demonstrating superior prediction performance by leveraging spatial autocorrelation principles (Fouedjio and Talebi, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe integration of ML models with kriging through stacked ensemble super learner models has shown improved accuracy for non-stationary and non-Gaussian data (Erdogan Erten et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The combination of Kriging-Land-use Regression with Random Forest and XGBoost significantly improved BTEX concentration predictions, with R-squared values reaching 0.79 compared to 0.37\u0026ndash;0.52 for traditional land-use regression alone (Breiman, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Chen and Guestrin, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Hsu et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The geostatistics-informed machine learning (GIML) approach has accelerated spatial interpolation by orders of magnitude while maintaining accuracy by integrating Ordinary Kriging principles into deep neural networks, though it remains limited to stationary variogram assumptions (Bai and Tahmasebi, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020b\u003c/span\u003e). The Hybrid Regression Kriging method incorporates nonlinear ML mapping, achieving over 10% reduction in estimation error compared to standard regression kriging (Li et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), and the neural network-generalised least squares (NN-GLS) algorithm integrates neural networks with Gaussian process modelling for complex non-linear spatial patterns, though its O(n-cubed) computational scaling for the GP component limits applicability to very large datasets (Zhan and Datta, \u003cspan citationid=\"CR116\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Further innovations include recursive convolutional neural networks applied to multiple-point statistics simulation, effectively capturing structural characteristics across two-dimensional and three-dimensional geological domains (Avalos and Ortiz, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eMore recently, the locally varying geostatistical machine learning approach has addressed the persistent challenge of spatial non-stationarity by combining local regression functions with conditional simulation, allowing model parameters to adapt across geographic space. This framework demonstrates substantial improvements over global models in non-stationary geological and environmental settings, though it requires sufficient local data density and careful bandwidth selection (Fouedjio and Arya, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e provides a comprehensive comparative synthesis of these nine hybrid frameworks, detailing their geostatistical and ML components, spatial assumptions, reported performance gains, limitations, demonstrated geophysical applications, and key references. A critical observation across these methods is that while performance gains are consistently reported, direct cross-method comparison remains difficult due to the absence of common benchmark datasets, an important gap addressed in the research roadmap (Section \u003cspan refid=\"Sec38\" class=\"InternalRef\"\u003e7.5\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative Synthesis of Hybrid Geostatistical-ML Frameworks\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGeostatistical Component\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eML Component\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSpatial Assumption\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReported Performance Gain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eKey Limitation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDemonstrated Application\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKey Reference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCCSIM\u0026thinsp;+\u0026thinsp;CNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCross-correlation simulation (MPS)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eConvolutional neural network for pattern learning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTraining image-based multi-point continuity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e100% hard data reproduction in 2D; improved 3D structural connectivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRequires representative training images; computational cost of CNN training\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSubsurface geological modelling; reservoir characterisation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eBai \u0026amp; Tahmasebi (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKriging-LUR\u0026thinsp;+\u0026thinsp;RF/XGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKriging-based land-use regression for spatial trend\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRandom Forest or XGBoost for nonlinear residuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSecond-order stationarity of residuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR-squared up to 0.79 vs 0.37\u0026ndash;0.52 for traditional LUR alone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTwo-stage bias propagation; stationarity assumption may not hold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBTEX air pollutant concentration mapping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eHsu et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGIML (OK\u0026thinsp;+\u0026thinsp;DNN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOrdinary Kriging principles embedded in network\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDeep neural network learning variogram parameters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStationary variogram structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eOrders of magnitude faster than traditional OK with comparable accuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimited to ordinary kriging assumptions; requires sufficient training data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eLarge-scale spatial interpolation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eBai \u0026amp; Tahmasebi (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020b\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNN-GLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGaussian process for spatially correlated errors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNeural network for mean function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGaussian process with specified covariance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSuperior prediction in non-linear spatial patterns vs GP or NN alone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eScalability: O(n^3) for GP component; Gaussian assumption\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEnvironmental spatial prediction with complex nonlinearity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eZhan \u0026amp; Datta (\u003cspan citationid=\"CR116\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid Regression Kriging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKriging of regression residuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNonlinear ML mapping (RF, SVM, ANN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eResidual stationarity after ML trend removal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026gt;\u0026thinsp;10% reduction in estimation error vs standard regression kriging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTwo-stage approach introduces bias; residuals may retain non-stationarity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eContinuous spatial variable estimation; digital soil mapping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eLi et al. (\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStacked Ensemble SL\u0026thinsp;+\u0026thinsp;Kriging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKriging as one of multiple base learners\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSuper learner stacking multiple ML algorithms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFlexible: inherits assumptions of each base learner\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eImproved accuracy for non-stationary, non-Gaussian distributions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHigh complexity; interpretability challenges; overfitting risk with many learners\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGeological attribute estimation with heterogeneous data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eErdogan Erten et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRCNN\u0026thinsp;+\u0026thinsp;MPS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMultiple-point statistics simulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRecursive CNN for pattern extraction from training images\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTraining image-based higher-order statistics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSuperior reproduction of statistical and spatial properties in 2D and 3D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eQuality depends on training image selection; high computational cost for 3D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGeostatistical modelling; enhanced MPS simulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eAvalos \u0026amp; Ortiz (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeostat. Semi-supervised Learning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConditional simulation preserving spatial structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSupervised learner augmented with simulated labels\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSpatial autocorrelation for simulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSuperior to fully supervised methods when labelled data is scarce\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSimulation computational overhead: quality depends on variogram model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGeospatial classification with limited labels\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eFouedjio \u0026amp; Talebi (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLocally Varying Geostat-ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLocal regression functions\u0026thinsp;+\u0026thinsp;conditional simulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSpatially adaptive ML with local parameter estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNon-stationary: locally varying parameters and spatial structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSubstantial improvement over global models in non-stationary settings\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHigher complexity; requires sufficient local data; bandwidth selection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMining (non-stationary ore grades); environmental (spatially varying processes)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eFouedjio \u0026amp; Arya (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cem\u003ePerformance gains are reported relative to each method's stated baseline. Direct cross-method comparison requires common benchmark datasets, which remains an open research need (see\u003c/em\u003e Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, \u003cem\u003eResearch Roadmap). SL\u0026thinsp;=\u0026thinsp;Super Learner; MPS\u0026thinsp;=\u0026thinsp;Multiple-Point Statistics; OK\u0026thinsp;=\u0026thinsp;Ordinary Kriging; LUR\u0026thinsp;=\u0026thinsp;Land-Use Regression\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Spatially Aware Deep Learning Architectures\u003c/h2\u003e \u003cp\u003eDeep learning applications in earth sciences present both transformative opportunities and significant challenges. Contemporary neural network architectures, particularly CNNs and RNNs, demonstrate superior capability in capturing complex spatiotemporal dependencies compared to traditional approaches (Reichstein et al., \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Integration of attention-based networks, geometric deep learning, and Bayesian probabilistic interpretations enables more complex environmental process modelling. These advances particularly benefit seasonal forecasting and extreme event prediction while maintaining physical consistency through hybrid modelling approaches that incorporate domain knowledge.\u003c/p\u003e \u003cp\u003eIn seismological applications, ML has been applied across the full processing workflow: event detection and classification, arrival time picking, focal mechanism analysis, ground motion prediction, and crustal deformation analysis (Kubo et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). ML-based ground motion prediction equations (GMPEs) now incorporate spatial site effects and path characteristics through neural networks, tree-based models, and kernel methods, often outperforming traditional empirical GMPEs (Anjom et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). For subsurface characterisation, deep generative models provide geological priors that encode non-Gaussian, non-stationary patterns while allowing conditioning to observations, offering flexible alternatives to classical variogram-based and multiple-point statistical methods (Xu et al., 2025). In hydrogeology, graph-based deep learning frameworks model complex spatial dependencies between monitoring wells by characterising multiple types of spatial relationships, including physical proximity, hydrological connectivity, and similarity in recharge patterns (Wu et al., \u003cspan citationid=\"CR110\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Dai et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The focus on physical consistency and interpretability alongside computational advancement marks a crucial step toward more reliable and scientifically grounded geophysical modelling.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Spatial Feature Engineering\u003c/h2\u003e \u003cp\u003eSpatial feature engineering has significantly enhanced ML capabilities in geographic analysis. The Euclidean distance fields in ML (EDM) framework demonstrates this advancement by integrating distance fields with environmental covariates, outperforming traditional spatial prediction methods (Behrens et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The incorporation of spatial lag and eigenvector spatial filtering (ESF) features into random forest models has significantly reduced prediction errors and spatial autocorrelation in residuals (Liu et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The spatial random forests (SRF) algorithm extends traditional random forests by incorporating local spatial-spectral information, demonstrating superior performance in geological mapping and geochemical prediction (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e; Talebi et al., \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). These advancements address critical spatial properties including dependence, heterogeneity, and scale effects across applications from land cover classification to geological domain delineation (Zarger and Lal, \u003cspan citationid=\"CR115\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Talebi et al., \u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Locally Varying Spatial Machine Learning\u003c/h2\u003e \u003cp\u003eLocally varying machine learning frameworks have emerged as promising solutions to address spatial heterogeneity in geographic analysis. Geographically Weighted Regression (GWR) laid the foundational groundwork by pioneering location-specific parameter estimation (Thapa and Estoque, \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Recent innovations include the Explainable Geospatial Machine Learning (XGeoML) framework, combining spatial weighting with SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME) for interpretable, superior performance over traditional GWR (Liu, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The geostatistical ML methodology introduced by Fouedjio and Arya (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) tackles spatial autocorrelation and non-stationarity through local regression functions and conditional simulation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDomain-specific applications include the Geographically Neural Network-Weighted Logistic Regression (GNNWLR) for mineral prospectivity mapping (Wang et al., \u003cspan citationid=\"CR105\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the Geographically Weighted Machine Learning (GWML) framework for environmental applications (Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and Spatial Regression Graph Convolutional Neural Networks (SRGCNNs) that handle non-Euclidean spatial multivariate data (Zhu et al., \u003cspan citationid=\"CR117\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The geographically weighted SRGCNN variant particularly excels in addressing spatial heterogeneity with limited data availability, bridging graph deep learning and spatial regression analytics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Spatial Model Validation and Performance Assessment\u003c/h2\u003e \u003cp\u003eAdvances in spatial model validation address the fundamental challenges of spatial autocorrelation and covariate shift. Spatial autocorrelation can lead to substantial performance differences of up to 47% between spatial and non-spatial validation approaches (Schratz et al., \u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), making spatially aware validation essential for reliable model assessment.\u003c/p\u003e \u003cp\u003eThe Importance-Weighted Buffered Cross-Validation (IBCV) framework offers a robust solution by combining spatial buffering with density ratio weighting, providing more accurate performance estimates than traditional cross-validation when both autocorrelation and covariate shift are present (Wang et al., \u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The leave-group-out cross-validation (LGOCV) method handles complex spatiotemporal dependencies effectively for extrapolation tasks, with explicit temporal grouping capability, and is implemented in the \u0026lsquo;mlr3spatiotempcv\u0026rsquo; R package (Adin et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Spatial bagging workflows incorporating effective sample size concepts achieve comparable performance with significantly smaller samples, integrating naturally with existing bagging frameworks (Ozbayrak et al., 2024).\u003c/p\u003e \u003cp\u003eForward feature selection combined with spatial cross-validation, implemented in the \u0026lsquo;CAST\u0026rsquo; R package, helps mitigate overfitting by excluding highly autocorrelated but non-predictive features. This approach, combined with the \u0026lsquo;sperrorest\u0026rsquo; package for spatial bootstrap-based accuracy assessment (Brenning, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), can reveal performance differences of up to 47% between spatial and non-spatial validation approaches, as demonstrated by Schratz et al. (\u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) in forest disease prediction. Fair train-test split methods use semi-variogram models and modified rejection sampling to create more representative validation sets for clustered sampling designs (Salazar et al., \u003cspan citationid=\"CR92\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e provides a comprehensive comparison of these seven validation approaches, detailing the spatial biases each address, their computational requirements, temporal dependency handling, available software implementations, and empirical evidence supporting their use. These advances collectively address critical evaluation challenges in geospatial datasets, where standard k-fold cross-validation remains inappropriate due to spatial autocorrelation and should be used only as a non-spatial benchmark (Rolf, \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of Spatial Validation Approaches\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValidation Method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpatial Bias Addressed\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMechanism\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eComp. Cost\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHandling of Temporal Dependence\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eImplementation Availability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEmpirical Evidence\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKey Reference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIBCV\u003c/b\u003e (Importance-Weighted Buffered CV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpatial autocorrelation\u0026thinsp;+\u0026thinsp;covariate shift jointly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSpatial buffer zones exclude nearby data; density ratio weights correct distribution mismatch\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eModerate-High\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot explicitly, can combine with temporal blocking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCustom R/Python code; not yet in standard packages\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMore accurate than standard spatial CV when both autocorrelation and covariate shift present\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eWang et al. (\u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLGOCV\u003c/b\u003e (Leave-Group-Out CV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComplex spatiotemporal dependencies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroups observations by spatial/temporal blocks; holds out entire groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eModerate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eExplicitly handles via temporal grouping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003emlr3spatiotempcv\u003c/em\u003e; Python: custom implementation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSuperior for extrapolation tasks; effective with structured dependencies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eAdin et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpatial Block Bootstrap\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpatial autocorrelation in uncertainty estimates\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eResamples spatial blocks rather than individual observations, preserving local correlation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLow-Moderate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCan use spatiotemporal blocks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003esperrorest\u003c/em\u003e; conceptually simple to implement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eProduces realistic confidence intervals; effective sample size concept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eBrenning (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e); Russ \u0026amp; Brenning (2010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eForward Feature Selection\u0026thinsp;+\u0026thinsp;Spatial CV\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePredictor autocorrelation leading to overfitting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSequential variable addition evaluated via spatial cross-validation folds\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHigh (iterative)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTemporal variables can be evaluated separately\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003eCAST\u003c/em\u003e package; Python: custom pipelines\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePrevents selection of spatially autocorrelated but non-predictive features; up to 47% performance difference vs non-spatial\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMeyer et al. (\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2019\u003c/span\u003e); Schratz et al. (\u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpatial Fair Train-Test Split\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNon-representative training/test partitions due to spatial clustering\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSemi-variogram range determines buffer; modified rejection sampling for balanced splits\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eModerate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot explicitly temporal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR/Python: custom; conceptual framework transferable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMore representative validation sets for clustered sampling designs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSalazar et al. (\u003cspan citationid=\"CR92\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpatial Bagging\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpatial autocorrelation inflating effective sample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBootstrap with effective sample size adjustment based on spatial autocorrelation range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLow-Moderate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCan incorporate temporal structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: custom; integrates with existing bagging frameworks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eComparable accuracy to full samples using significantly fewer observations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eOzbayrak et al. (2024)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eStandard k-fold CV\u003c/b\u003e (baseline)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRandom partitioning ignoring spatial structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLow\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAll ML frameworks (sklearn, caret, mlr3, tidymodels)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eOverestimates performance by up to 47% when spatial autocorrelation present; appropriate only as non-spatial benchmark\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSchratz et al. (\u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cem\u003eComputational cost is relative to standard k-fold CV. All spatial methods add overhead but prevent optimistic bias. The 47% performance difference (\u003c/em\u003eSchratz et al., \u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) \u003cem\u003ewas observed for spatial prediction of disease in forests, demonstrating that the bias from ignoring spatial autocorrelation can be substantial. Implementation packages listed are as of 2025.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5 Uncertainty Quantification in Spatial Prediction","content":"\u003cp\u003eSpatial predictive modelling has traditionally focused on point predictions, yet these inherently contain uncertainty requiring quantification (Bauer, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1958\u003c/span\u003e). Probability distributions offer richer information content than point predictions alone, enabling better-informed decision-making under uncertainty. The theoretical foundation of predictive uncertainty combines Bayesian statistics, decision theory, and machine learning approaches (Tyralis and Papacharalampous, \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Understanding uncertainty is crucial in geophysical applications where decisions carry significant risks. In domains such as mineral exploration, reservoir management, groundwater protection, natural hazard mitigation, and carbon storage, geophysical predictions directly influence investments, safety, and environmental outcomes. These predictions are inherently uncertain due to limited data coverage, indirect measurements, and complex subsurface processes.\u003c/p\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Taxonomy of Spatial Uncertainty\u003c/h2\u003e \u003cp\u003eSpatial uncertainty manifests primarily through aleatory and epistemic uncertainty, each representing distinct aspects of predictive modelling challenges (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e; Monarch, \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Hullermeier and Waegeman, 2021). Aleatory uncertainty represents inherent variability in natural phenomena, encompassing both homoscedastic uncertainty with constant prediction residual variation and heteroscedastic uncertainty with spatially varying noise patterns. This statistical uncertainty persists even with perfect modelling and represents a fundamental precision limit that cannot be reduced through additional sampling. In geophysical contexts, aleatory uncertainty includes natural variability in seismic ground motion at a given site, intrinsic geological heterogeneity at scales below measurement resolution, and stochastic variation in groundwater recharge processes.\u003c/p\u003e \u003cp\u003eEpistemic uncertainty stems from incomplete knowledge, manifesting through measurement errors, missing data, and model parameter uncertainty (Hullermeier and Waegeman, 2021). Unlike aleatory uncertainty, epistemic uncertainty can be reduced through additional data collection or improved model structures. In geophysics, this includes uncertainty from limited drill-hole coverage in mineral deposits, sparse seismic station networks in regions of interest, and simplified representations of complex hydrogeological boundary conditions. The distinction is practically important: areas with high epistemic uncertainty are candidates for additional data collection, while areas dominated by aleatory uncertainty require probabilistic treatment regardless of sampling density (Gal and Ghahramani, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Kendall and Gal, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Methods for Aleatory Uncertainty Estimation\u003c/h2\u003e \u003cp\u003eQuantile regression (QR) algorithms have emerged as powerful tools for approximating predictive probability distributions to address aleatory uncertainty. Originally introduced by Koenker and Bassett (1978), QR models the inherent randomness by estimating different conditional quantiles of the response variable. For each quantile, a linear relationship between observed and predicted values is assumed, with parameters determined by minimising a piecewise linear loss function that asymmetrically penalises over- and under-prediction (Kasraei et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Quantile regression forests (QRF), introduced by Meinshausen (\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), extend random forests for uncertainty quantification and have been widely applied in spatial prediction (Papacharalampous et al., \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). While QR effectively characterises aleatory uncertainty, it does not explicitly address epistemic uncertainty; comprehensive uncertainty quantification requires combining QR with approaches that represent model-form and parameter uncertainty.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Methods for Epistemic Uncertainty Estimation\u003c/h2\u003e \u003cp\u003eSpatial bootstrapping provides a powerful framework for estimating epistemic uncertainty by generating multiple realisations of the spatial data structure. Unlike traditional bootstrapping, spatial bootstrap methods preserve spatial autocorrelation during resampling, maintaining the integrity of spatial relationships (Brenning, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Spatial block bootstrap methods are particularly effective at quantifying epistemic uncertainties in regions with sparse observations (Russ and Brenning, 2010). For spatial machine learning, ensemble-based approaches have gained prominence: Meyer et al. (\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) showed that spatial random effects models can effectively separate aleatory variability from epistemic uncertainty, while Hengl et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) demonstrated that machine learning methods with spatial components can characterise epistemic uncertainty through uncertainty maps revealing areas of deficient model knowledge.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Integrated Uncertainty Quantification Frameworks\u003c/h2\u003e \u003cp\u003eSeveral frameworks address both aleatory and epistemic uncertainty simultaneously, as comprehensively compared in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and conceptually presented as a framework in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (Butvinik \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Bayesian neural networks provide a principled approach by placing distributions over network weights, yielding predictions with uncertainty estimates that decompose into data noise (aleatory) and model uncertainty (epistemic) components (Kendall and Gal, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Monte Carlo (MC) Dropout offers a computationally cheaper approximation to full Bayesian inference by using dropout at test time to generate multiple stochastic forward passes, typically 50\u0026ndash;100 passes, producing mean predictions with variance estimates (Gal and Ghahramani, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The Uncertainty Estimation based on Local Errors and Clustering (UNEEC) method considers multiple uncertainty sources through residual analysis, clustering residuals spatially to capture location-varying uncertainty patterns (Rahmati et al., \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eKriging variance, derived directly from the variogram model and data configuration, provides inherent spatial uncertainty estimates at no additional computational cost beyond the prediction itself, though it assumes Gaussian distributions. Implementation is widely available through established packages including \u0026lsquo;gstat\u0026rsquo; and \u0026lsquo;geoR\u0026rsquo; in R, and \u0026lsquo;pykrige\u0026rsquo; and \u0026lsquo;GSTools\u0026rsquo; in Python (Goovaerts, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Fouedjio and Klump, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Geostatistical conditional simulation extends this by generating multiple equiprobable realisations that reproduce both the data values and the spatial variability structure, providing full uncertainty envelopes essential for mineral resource evaluation and three-dimensional geological domain boundary assessment, though it requires 50\u0026ndash;100 or more realisations for reliable uncertainty characterisation (Fouedjio et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Fouedjio and Talebi, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eConformal prediction has emerged as a promising distribution-free approach that provides guaranteed marginal coverage prediction intervals, requiring only a post-hoc calibration step on held-out data. Recent extensions address exchangeability violations inherent in spatial data, though geophysical applications remain limited to date and represent an active research frontier (Tyralis and Papacharalampous, \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Ensemble variance decomposition offers another practical pathway by decomposing total prediction variance into model disagreement (epistemic) and within-model noise (aleatory) components, building on established ensemble methods such as random forests and gradient boosting (Hengl et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Meyer et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Our systematic analysis found that fewer than 15% of the 122 reviewed studies explicitly decompose prediction uncertainty into aleatory and epistemic sources, highlighting a significant gap between conceptual recognition and operational implementation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of Uncertainty Quantification Methods for Spatial Prediction\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUQ Method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUncertainty Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSpatial Awareness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOutput Form\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eComp. Cost\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSoftware / Implementation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDemonstrated Geophysical Application\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKey Reference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eQuantile Regression (QR)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAleatory\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIndirect: via spatial covariates in feature set\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eConditional quantiles (e.g. Q10, Q50, Q90); prediction intervals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLow: single model per quantile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003equantreg\u003c/em\u003e; Python: \u003cem\u003estatsmodels\u003c/em\u003e, \u003cem\u003esklearn\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDigital soil mapping; uncertainty in soil property prediction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKoenker \u0026amp; Bassett (1978); Kasraei et al. (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eQuantile Regression Forest (QRF)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAleatory (heteroscedastic)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIndirect: captures spatial variation through features; can include coordinates\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFull conditional distribution approximation; any quantile extractable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModerate: retains all tree predictions rather than just means\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003equantregForest\u003c/em\u003e; Python: \u003cem\u003esklearn-quantile\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePrecipitation uncertainty; environmental monitoring\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMeinshausen (\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2006\u003c/span\u003e); Papacharalampous et al. (\u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpatial Block Bootstrap\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEpistemic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDirect: preserves spatial autocorrelation by resampling spatial blocks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eConfidence intervals for model parameters and predictions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModerate: requires multiple model fits on resampled blocks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003esperrorest\u003c/em\u003e; custom blocking by variogram range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRemote sensing accuracy assessment; precision agriculture\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eBrenning (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e); Russ \u0026amp; Brenning (2010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBayesian Neural Networks (BNN)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth (decomposable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eArchitecture-dependent; spatial layers can be incorporated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePosterior predictive distribution; decomposable into aleatoric\u0026thinsp;+\u0026thinsp;epistemic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh: MCMC or variational inference over weight distributions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePython: \u003cem\u003eTensorFlow Probability\u003c/em\u003e, \u003cem\u003ePyro\u003c/em\u003e, \u003cem\u003eBayesFlow\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSubsurface property prediction; CO2 leakage detection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKendall \u0026amp; Gal (\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2017\u003c/span\u003e); He et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMC Dropout\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEpistemic (approximate Bayesian)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eArchitecture-dependent; approximates BNN via dropout at test time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMean prediction\u0026thinsp;+\u0026thinsp;variance from multiple stochastic forward passes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModerate: N forward passes (typically 50\u0026ndash;100)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAny framework with dropout: \u003cem\u003ePyTorch\u003c/em\u003e, \u003cem\u003eTensorFlow\u003c/em\u003e, \u003cem\u003eKeras\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDeep learning for Earth system science applications\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eGal \u0026amp; Ghahramani (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2016\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eUNEEC\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLocal: clusters residuals spatially to capture location-varying uncertainty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePrediction intervals based on local error distribution\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModerate: requires clustering\u0026thinsp;+\u0026thinsp;residual analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCustom implementation (R/Python)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGroundwater nitrate pollution modelling\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRahmati et al. (\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eKriging Variance\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth (under Gaussian assumption)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInherent: directly derived from variogram model and data configuration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKriging variance (conditional variance); conditional simulation envelopes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLow-Moderate: computed alongside predictions at no extra model cost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003egstat\u003c/em\u003e, \u003cem\u003egeoR\u003c/em\u003e; Python: \u003cem\u003epykrige\u003c/em\u003e, \u003cem\u003eGSTools\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMineral resource estimation; grade control; soil mapping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eGoovaerts (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1997\u003c/span\u003e); Fouedjio \u0026amp; Klump (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eConformal Prediction\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth (distribution-free)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWith spatial calibration: recent extensions address exchangeability violations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGuaranteed coverage prediction intervals (marginal coverage)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLow: post-hoc calibration step on held-out data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003econformalInference\u003c/em\u003e; Python: \u003cem\u003eMAPIE\u003c/em\u003e, \u003cem\u003econformal-prediction\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEmerging in spatial contexts; limited geophysical applications to date\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eTyralis \u0026amp; Papacharalampous (\u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGeostatistical Conditional Simulation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFull spatial model: reproduces spatial variability and honours conditioning data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMultiple equiprobable realisations; full uncertainty envelope\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh: multiple realisations required (typically 50\u0026ndash;200+); variogram fitting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR: \u003cem\u003egstat\u003c/em\u003e; Python: \u003cem\u003eGSTools\u003c/em\u003e; GSLIB; SGeMS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMineral resource classification; 3D geological domain boundaries; reservoir modelling\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eFouedjio et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Fouedjio \u0026amp; Talebi (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eEnsemble Variance Decomposition\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth (decomposable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCan incorporate spatial effects via spatially structured base learners\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDecomposition of total variance into model disagreement (epistemic) and within-model noise (aleatory)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModerate-High: requires training multiple diverse models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCustom; builds on \u003cem\u003eranger\u003c/em\u003e, \u003cem\u003exgboost\u003c/em\u003e, etc.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEnvironmental prediction; digital soil mapping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eHengl et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e); Meyer et al. (\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cem\u003eUncertainty Type: Aleatory\u0026thinsp;=\u0026thinsp;irreducible data noise; Epistemic\u0026thinsp;=\u0026thinsp;reducible model/knowledge uncertainty; Both =\u0026thinsp;method captures or decomposes both sources. Computational cost is relative to a single point-prediction model. Software listings are non-exhaustive and current as of 2025. Conformal prediction for spatial data remains an active research frontier with limited geophysical validation to date.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e5.5 Uncertainty-Aware Feature Selection\u003c/h2\u003e \u003cp\u003eUncertainty fundamentally shapes feature selection in spatial ML applications. Aleatory uncertainty can mask true feature importance, particularly in heteroscedastic spatial datasets where noise varies geographically. Epistemic uncertainty affects how consistently features are selected across model specifications (Fouedjio et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Probabilistic feature selection methods incorporating uncertainty quantification offer more stable variable rankings, improved generalisability, and transparent reliability assessments (Kalousis et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Gheyas and Smith, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). In spatial contexts, autocorrelation structures can artificially inflate feature significance if uncertainty is ignored (Darst et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Uncertainty-aware feature selection has proven critical in applications from environmental modelling to remote sensing classification, where neglecting uncertainty leads to overconfident predictions and potentially misleading spatial patterns (Degenhardt et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Calle and Urrea, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Krawczyk, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"6 Applications in Geophysical Sciences","content":"\u003cp\u003eThis section synthesises how the SML frameworks, uncertainty quantification methods, and validation approaches reviewed in Sections \u0026lt;link rid=\"Sec1\u003cspan refid=\"Sec21\" class=\"InternalRef\"\u003e5\u003c/span\u003e\"\u0026gt;4\u0026lt;/link\u0026gt; and \u003cspan refid=\"Sec21\" class=\"InternalRef\"\u003e5\u003c/span\u003e are deployed across major geophysical application domains. Rather than merely cataloguing applications, we identify which methodological combinations have proven most effective, where transferable patterns emerge, and where domain-specific solutions remain necessary.\u003c/p\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e6.1 Seismic Hazard Assessment and Ground Motion Prediction\u003c/h2\u003e \u003cp\u003eML has transformed seismological applications across the full processing chain, from event detection to ground motion prediction (Kubo et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Ground motion prediction equations (GMPEs), traditionally constructed through regression of past records, are increasingly augmented or replaced by ML approaches that capture nonlinear site-path-source interactions. Neural networks, random forests, and gradient boosting models have been applied to predict ground motion intensities, often outperforming empirical equations for specific regional datasets (Anjom et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Spatial autocorrelation in seismic hazard maps presents validation challenges: standard cross-validation overestimates predictive performance because nearby stations experience correlated ground motions, making spatially blocked validation essential.\u003c/p\u003e \u003cp\u003eUncertainty quantification in seismic hazard assessment requires separating site-specific aleatory variability (inherent randomness in ground motion at a given site) from epistemic uncertainty arising from limited ground motion recordings. Physics-informed approaches that embed seismological constraints, such as attenuation relationships and site amplification models, into neural network architectures have shown promise in maintaining physical consistency while capturing complex nonlinear patterns (Reichstein et al., \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Future directions include developing spatially varying residual models that account for regional differences in ground motion variability and integrating real-time seismic monitoring data with ML-based rapid hazard assessment systems.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e6.2 Natural Resource Evaluation and Geological Modelling\u003c/h2\u003e \u003cp\u003eMineral exploration and resource modelling represent some of the most mature applications of spatial machine learning in the geosciences. Geostatistical clustering for ore body domaining, incorporating spatial dependency metrics, has improved domain delineation accuracy (Fouedjio et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The integration of geostatistical conditional simulation with supervised learning enables effective utilisation of both labelled and unlabelled spatial data in geological classification (Fouedjio and Talebi, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Hybrid approaches combining CCSIM with CNNs address limitations in subsurface modelling by improving hard data reproduction and geological feature connectivity (Bai and Tahmasebi, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e). Stochastic modelling of mineral exploration targets using spatial random forests provides both prediction and associated uncertainty crucial for exploration decision-making (Talebi et al., \u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, \u003cspan citationid=\"CR98\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eUncertainty quantification is particularly critical in mineral resource classification, where the distinction between Measured, Indicated, and Inferred resource categories directly depends on prediction confidence. Geostatistical implicit modelling frameworks provide uncertainty quantification of three-dimensional geological domain boundaries essential for resource reporting (Fouedjio et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The locally varying geostatistical machine learning approach addresses spatial non-stationarity in geological domains through local regression functions and conditional simulation (Fouedjio and Arya, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Spatial random forests that incorporate local spatial-spectral information demonstrate superior performance for geological mapping compared to conventional random forests (Talebi et al., \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec30\" class=\"Section2\"\u003e \u003ch2\u003e6.3 Hydrogeological Forecasting\u003c/h2\u003e \u003cp\u003eHydrogeological applications of spatial machine learning have expanded rapidly, driven by the need for reliable groundwater level prediction and quality assessment. Graph-based deep learning frameworks model complex spatial dependencies between monitoring wells by characterising multiple relationship types, including physical proximity, hydrological connectivity, and environmental similarity (Wu et al., \u003cspan citationid=\"CR110\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Physics-based, conceptual, and machine learning models are increasingly compared through Bayesian Model Averaging, which provides multi-model uncertainty estimates that account for structural model uncertainty (Wohling et al., \u003cspan citationid=\"CR107\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Deep learning has been incorporated into hydrogeological modelling for time series analysis, spatial data analysis, and inverse modelling, with LSTM networks showing much promise for temporal prediction (Dai et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eUncertainty quantification in hydrogeological prediction faces unique challenges. Groundwater systems are characterised by high spatial heterogeneity, limited observability, and incomplete information regarding aquifer properties (Kunz et al., 2024). The sparse and irregular distribution of monitoring wells means that epistemic uncertainty dominates in many regions, making uncertainty maps particularly valuable for guiding additional data collection. Physics-informed constraints, particularly water balance equations and Darcy's law, provide opportunities for hybrid models that respect hydraulic principles while learning complex nonlinear patterns from data (Sun, \u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003e6.4 Environmental and Geochemical Monitoring\u003c/h2\u003e \u003cp\u003eEnvironmental monitoring applications benefit from the full suite of spatial ML methods. Digital soil mapping combines machine learning with geostatistical approaches for soil property prediction with uncertainty estimation (Kasraei et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Wadoux et al., \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Hengl et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Air quality prediction using Kriging-Land-use Regression with machine learning has significantly improved pollutant concentration predictions (Hsu et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Geochemical anomaly detection for mineral exploration uses spatial random forests and spatial-spectral clustering to identify geologically meaningful patterns (Talebi et al., \u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Multi-resolution remote sensing data integration through deep learning architectures enables monitoring across varying spatial and temporal scales (Chen et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ghamisi et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e6.5 Cross-Domain Synthesis\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCross-Domain Application Synthesis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApplication Domain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMost Effective ML Framework(s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePreferred UQ Approach\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eValidation Strategy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDominant Challenge\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMaturity Level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKey References\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSeismic Hazard Assessment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeural networks (MLP, CNN) for GMPEs; gradient boosting (XGBoost) for intensity; RNN/LSTM for waveform forecasting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBetween-event / within-event residual decomposition; Bayesian site effect models; physics-guided NN uncertainty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSpatial block CV by region/cluster; temporal holdout for earthquake sequences; leave-one-station-out\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaintaining physical consistency (attenuation, site effects); real-time processing demands; sparse data in low-seismicity regions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHigh for GMPE; Emerging for real-time prediction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKubo et al. (\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); Anjom et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); Reichstein et al. (\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMineral Resource Evaluation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid geostat-ML (kriging\u0026thinsp;+\u0026thinsp;RF, SL); spatial random forests; geostat. semi-supervised learning; locally varying geostat-ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGeostatistical conditional simulation (grade uncertainty); QRF for continuous variables; geostat. implicit modelling for domain boundaries\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSpatial CV with domain-aware folds; leave-domain-out; conditioning to hard data validation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3D spatial heterogeneity; preferential sampling bias; support-change (core-to-block); geological domain definition\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHigh: most mature geophysical application of hybrid geostat-ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFouedjio et al. (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2017\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Fouedjio \u0026amp; Talebi (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Talebi et al. (\u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Bai \u0026amp; Tahmasebi (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHydrogeological Forecasting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGraph neural networks (TGCN); LSTM/N-HiTS for temporal; Bayesian model averaging of physics-based\u0026thinsp;+\u0026thinsp;ML models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBayesian model averaging (multi-model UQ); quantile prediction from graph networks; conformal intervals for GWL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTemporal CV with spatial holdout; rolling-window validation; split-sample temporal test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSparse and irregular monitoring networks; temporal non-stationarity; subsurface heterogeneity poorly constrained; static feature uncertainty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eModerate: growing rapidly; benchmark datasets lacking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWu et al. (\u003cspan citationid=\"CR110\" class=\"CitationRef\"\u003e2025\u003c/span\u003e); Kunz et al. (2024); Dai et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e); Wohling et al. (\u003cspan citationid=\"CR107\" class=\"CitationRef\"\u003e2025\u003c/span\u003e); Sun (\u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnvironmental Monitoring (soil, air, water)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKriging-ML hybrids (regression kriging\u0026thinsp;+\u0026thinsp;RF/XGBoost); ensemble RF with spatial features; EDM framework\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eQR and QRF for continuous variables; spatial bootstrap for accuracy assessment; UNEEC for local error estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIBCV for distribution shift; spatial bagging with effective sample size; forward feature selection\u0026thinsp;+\u0026thinsp;spatial CV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMulti-resolution data fusion (MAUP); measurement support differences; spatial-temporal misalignment of data sources\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHigh for soil mapping; Moderate for air quality; Emerging for integrated environmental systems\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKasraei et al. (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); Hsu et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e); Hengl et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e); Wadoux et al. (\u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2019\u003c/span\u003e); Behrens et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubsurface Characterisation (3D geological)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCNN\u0026thinsp;+\u0026thinsp;MPS (CCSIM, RCNN); deep generative models (VAE, GAN); physics-guided ML for seismic inversion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFull geostatistical simulation (multiple realisations); BNN for inversion uncertainty; ensemble disagreement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eConditioning to hard data (well control); blind-well validation; comparison with physics-based forward models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTraining data scarcity; 3D computational cost; non-unique inversion solutions; geological realism enforcement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEmerging: rapid progress but limited operational deployment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBai \u0026amp; Tahmasebi (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003eb\u003c/span\u003e); Avalos \u0026amp; Ortiz (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e); Xu et al. (2025); Fouedjio et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cem\u003eMaturity levels reflect the authors' assessment based on the volume and quality of published studies, availability of benchmark datasets, and degree of operational deployment. High\u0026thinsp;=\u0026thinsp;well-established with operational use; Moderate\u0026thinsp;=\u0026thinsp;active research with growing applications; Emerging\u0026thinsp;=\u0026thinsp;promising early results with limited deployment. GMPE\u0026thinsp;=\u0026thinsp;Ground Motion Prediction Equation; GWL\u0026thinsp;=\u0026thinsp;Groundwater Level.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eSeveral patterns emerge across domains, as synthesised in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e with maturity assessments. First, hybrid geostatistical-ML approaches consistently outperform pure ML methods when spatial autocorrelation is strong, which is the norm in geophysical applications. Mineral exploration and environmental monitoring represent the most mature application domains, with well-established operational workflows, while subsurface characterisation and hydrogeological forecasting are developing rapidly but lack the standardised benchmark datasets needed for systematic method comparison.\u003c/p\u003e \u003cp\u003eSecond, uncertainty quantification remains underdeveloped relative to point prediction: most studies focus on predictive accuracy metrics rather than calibration of uncertainty estimates. Our systematic analysis found that fewer than 15% of the 122 reviewed studies explicitly decompose prediction uncertainty into aleatory and epistemic sources, despite the practical importance of this distinction for guiding data collection decisions. Third, validation methodologies lag behind modelling advances, with many studies still relying on random cross-validation despite documented biases of up to 47% from spatial autocorrelation (Schratz et al., \u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Fourth, physics-informed constraints are most advanced in hydrogeology and seismology, where governing equations (Darcy's law, wave equations) are well established, but remain largely unexplored in geological mapping and environmental monitoring. Fifth, software implementations are unevenly distributed across methods: spatial validation packages such as CAST, sperrorest, and mlr3spatiotempcv have matured in R, while Python implementations remain more fragmented, particularly for integrated spatial UQ workflows. These findings collectively inform the structured research roadmap presented in Section \u003cspan refid=\"Sec38\" class=\"InternalRef\"\u003e7.5\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"7 Research Frontiers and Actionable Directions","content":"\u003cp\u003eThe field of spatial machine learning and uncertainty quantification stands at a crucial juncture where traditional geostatistical approaches converge with modern machine learning capabilities. The cross-domain synthesis in Section \u003cspan refid=\"Sec27\" class=\"InternalRef\"\u003e6\u003c/span\u003e reveals persistent gaps alongside emerging opportunities. This section identifies specific research frontiers and provides a structured roadmap with concrete methodological directions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec34\" class=\"Section2\"\u003e \u003ch2\u003e7.1 Physics-Informed Spatial Machine Learning\u003c/h2\u003e \u003cp\u003eThe fusion of physics-informed constraints with machine learning architectures represents a critical frontier. Current approaches, while promising, often struggle to maintain physical consistency while leveraging data-driven insights. In hydrology, Daw et al. (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) pioneered physics-guided neural networks enforcing mass conservation in lake temperature modelling. Beucler et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) developed parameterisations preserving energy conservation while accelerating climate simulations. Willard et al. (\u003cspan citationid=\"CR106\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) showed how physics-constrained deep learning improves satellite imagery retrieval by incorporating radiative transfer principles. Sun (\u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) integrated physical flow equations with neural networks for hydraulic modelling. Specific research needs include developing physics-constrained loss functions for geophysical inversions, creating benchmark datasets pairing simulations with observations, and establishing evaluation protocols for physical consistency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec35\" class=\"Section2\"\u003e \u003ch2\u003e7.2 Multi-Scale Uncertainty Quantification\u003c/h2\u003e \u003cp\u003eCurrent approaches often assume spatial stationarity or simplified dependency structures, limiting applicability in complex geophysical scenarios (Wang et al., \u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Key research directions include methods for propagating uncertainty across spatial scales in hierarchical geological models, adaptive uncertainty estimation frameworks that adjust to local data density, and real-time uncertainty updating for monitoring systems. In climate impact assessments, Zscheischler et al. (\u003cspan citationid=\"CR119\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) showed that compound extreme events require sophisticated spatial uncertainty models capturing complex dependencies. For precision agriculture, Wadoux et al. (\u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) highlighted how spatially-aware uncertainty quantification improves resource allocation. For landslide susceptibility, Lombardo et al. (2018) illustrated the value of multi-scale uncertainty models.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec36\" class=\"Section2\"\u003e \u003ch2\u003e7.3 Interpretable Spatial Intelligence\u003c/h2\u003e \u003cp\u003eWhile explainable AI has advanced in general machine learning, spatial contexts present unique challenges due to complex dependencies and multi-scale interactions (Liu, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xing and Sieber, \u003cspan citationid=\"CR111\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Future research needs specialised interpretation methods accounting for spatial autocorrelation, scale dependencies, and temporal dynamics. The challenge is maintaining prediction accuracy while enhancing model transparency, particularly where decisions carry significant consequences (Fouedjio and Arya, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Specific needs include spatially aware SHAP variants that account for spatial autocorrelation in feature importance, methods to verify that local explanations are spatially consistent, and frameworks linking interpretability to physical plausibility.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec37\" class=\"Section2\"\u003e \u003ch2\u003e7.4 Scalable Spatial Computing\u003c/h2\u003e \u003cp\u003eScaling spatial ML to handle increasingly large datasets remains significant. Specific needs include GPU-optimised spatial algorithms for three-dimensional geophysical data, streaming spatial ML for real-time sensor network processing, federated learning approaches for distributed geophysical monitoring where data cannot be centralised, and efficient data structures for spatial information that maintain query performance at scale. Maxwell et al. (\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) demonstrated optimised architectures for large-scale land cover classification. Boeing (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) highlighted that scalable algorithms are essential for city-scale sensor networks. Camps-Valls et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) showed that computationally efficient emulators can accelerate climate projections while preserving spatial patterns.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec38\" class=\"Section2\"\u003e \u003ch2\u003e7.5 Research Roadmap\u003c/h2\u003e \u003cp\u003eBased on the systematic analysis conducted throughout this review, we propose a structured research roadmap (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) that identifies nine specific gaps across five research frontiers, each with proposed methodological approaches, target geophysical applications, expected impacts, timelines, and enabling factors. This roadmap is intended to provide actionable guidance for the research community rather than general aspirational statements. Each gap is grounded in evidence identified through our systematic review: for instance, the finding that fewer than 15% of reviewed studies operationalise the aleatory-epistemic decomposition directly motivates the near-term priority of developing spatially explicit uncertainty decomposition maps.\u003c/p\u003e \u003cp\u003eSeveral enabling factors underpin these priorities. Near-term goals (1\u0026ndash;3 years) are those where methodological foundations already exist and primarily require integration and validation: existing SHAP/LIME frameworks can be extended with spatial blocking, and established R packages such as CAST and \u0026lsquo;sperrorest\u0026rsquo; provide infrastructure for unified spatial-temporal validation. Critically, the community benchmark datasets modelled on successful precedents like CAMELS in surface hydrology (which provides standardised, spatially aligned static features supporting large-scale model comparison) could be hosted on existing geophysical data repositories such as GDR and PANGAEA. Medium-term goals (3\u0026ndash;5 years) require new theoretical development, particularly hierarchical Bayesian inference for multi-scale uncertainty propagation and GPU-native spatial kernels building on libraries such as GPyTorch and KeOps. The single long-term goal, federated learning for distributed geophysical monitoring, depends on institutional changes beyond individual research groups, including inter-agency data sharing agreements and privacy frameworks. The advancement of all these priorities requires interdisciplinary collaboration between statisticians, computer scientists, and domain experts from earth sciences.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStructured Research Roadmap for Spatial Machine Learning in Geophysics\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResearch Frontier\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpecific Gap Identified (with evidence)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eProposed Methodological Approach\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePrimary Target Application\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eExpected Impact\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTimeline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEnabling Factors / Dependencies\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhysics-Informed ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo unified framework for embedding geophysical conservation laws (mass, energy, momentum) into spatial ML loss functions. Current physics-informed NNs (Daw et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Beucler et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) address individual constraints but lack generalisable spatial formulation.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDifferentiable physics layers with spatial attention mechanisms; conservation-law penalty terms in spatially structured loss functions; physics-constrained normalising flows for geological simulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSeismic hazard (attenuation models); groundwater flow (Darcy's law); reservoir simulation (material balance)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePhysically consistent predictions that extrapolate reliably beyond training domain; reduced epistemic uncertainty from physics constraints\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNear-term (1\u0026ndash;3\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRequires collaboration between ML researchers and domain physicists; existing JAX/PyTorch differentiable physics libraries provide foundation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhysics-Informed ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLack of community benchmark datasets pairing physics-based simulations with spatially distributed field observations. Current studies use proprietary or site-specific datasets preventing reproducible comparison.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCommunity-driven open benchmark datasets with: (a) known physical constraints, (b) realistic spatial heterogeneity, (c) multiple fidelity levels (simulation\u0026thinsp;+\u0026thinsp;field data), (d) defined evaluation protocols\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCross-domain validation and method comparison\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReproducible comparison of spatial ML methods; accelerated method development; reduced duplication of effort\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNear-term (1\u0026ndash;3\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eInstitutional support for data sharing; existing models from CAMELS (hydrology) provide templates; geophysical data repositories (GDR, PANGAEA) can host\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMulti-Scale UQ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUncertainty propagation across spatial scales is rarely addressed. Most UQ methods operate at a single scale; hierarchical geological models require uncertainty characterisation from core-scale to deposit-scale.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHierarchical Bayesian frameworks with scale-dependent priors; nested variogram models with scale-specific nugget estimation; multi-resolution conditional simulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMineral resource classification (core to block to panel); regional groundwater modelling (well to aquifer)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReliable uncertainty estimates at decision-relevant scales; appropriate resource classification confidence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMedium-term (3\u0026ndash;5\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRequires multi-scale datasets (rare); computational advances in hierarchical Bayesian inference; change-of-support theory from geostatistics\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMulti-Scale UQ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAleatory-epistemic decomposition is conceptually recognised (Hullermeier \u0026amp; Waegeman, 2021) but rarely operationalised in spatial prediction. Fewer than 15% of reviewed studies explicitly separate these sources.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSpatially explicit decomposition maps: ensemble variance (epistemic) vs. within-model noise (aleatory); adaptive sampling designs guided by epistemic uncertainty maps\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAll geophysical domains; particularly valuable for exploration targeting and monitoring network design\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTargeted data collection in high-epistemic regions; quantified irreducible uncertainty for risk assessment; optimal sensor/well placement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNear-term (1\u0026ndash;3\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEnsemble methods already available; requires validation against ground truth; connects to optimal experimental design theory\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterpretable ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSHAP and LIME do not account for spatial autocorrelation, leading to inflated importance of spatially correlated but non-causal features. No spatial XAI methods currently exist.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSpatially weighted permutation importance; conditional SHAP with spatial blocking; spatial partial dependence profiles that account for neighbourhood effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEnvironmental monitoring (identifying pollution drivers); geological mapping (understanding lithological controls)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTrustworthy feature importance in spatial contexts; spatially consistent explanations that domain experts can validate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNear-term (1\u0026ndash;3\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eExtensions of existing SHAP/LIME frameworks; spatial blocking infrastructure from validation literature; R/Python packages can be extended\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterpretable ML\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo framework links ML model interpretation to physical plausibility. A model can achieve high accuracy with physically implausible feature relationships.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePhysics-consistency scoring: evaluate whether learned feature-response relationships align with known physical mechanisms; constrained SHAP with physical monotonicity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeological modelling (e.g., grade-depth relationships); hydrogeology (recharge-level relationships)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModels that are both accurate and physically defensible; increased stakeholder trust in ML predictions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMedium-term (3\u0026ndash;5\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eRequires domain knowledge formalisation; connects to physics-informed ML frontier; interdisciplinary collaboration essential\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValidation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStandard CV overestimates performance by up to 47% (Schratz et al., \u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) yet remains the default in many studies. No unified framework handles spatial\u0026thinsp;+\u0026thinsp;temporal\u0026thinsp;+\u0026thinsp;scale dependencies simultaneously.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnified spatiotemporal CV framework with automatic blocking based on empirical variogram/correlogram analysis; integrated treatment of spatial, temporal, and cross-scale dependencies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAll spatial prediction tasks; mandatory for any operational deployment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRealistic performance assessment; prevention of optimistic bias in reported accuracy; reproducible model evaluation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNear-term (1\u0026ndash;3\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBuilding on existing \u003cem\u003eCAST\u003c/em\u003e, \u003cem\u003esperrorest\u003c/em\u003e, \u003cem\u003emlr3spatiotempcv\u003c/em\u003e packages; automatic variogram estimation for blocking; needs consensus guidelines from the community\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScalability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3D spatial ML is limited by memory and computation: geostatistical simulation for a 10M-cell geological model requires days on conventional hardware.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGPU-native spatial kernels using CUDA/ROCm; sparse approximations for large covariance matrices; streaming algorithms for incremental learning; model distillation for deployment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3D subsurface characterisation; real-time seismic monitoring; large-scale environmental mapping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFeasibility of spatial ML at operational scales; real-time uncertainty estimation for monitoring systems\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMedium-term (3\u0026ndash;5\u0026nbsp;year)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGPU hardware advances; sparse GP approximations (inducing points); existing work on scalable GPs (GPyTorch, KeOps) provides foundation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScalability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFederated learning is unexplored for distributed geophysical monitoring networks where raw data cannot be centralised due to privacy, sovereignty, or bandwidth constraints.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePrivacy-preserving spatial federated learning: local model training at each monitoring site with aggregation of spatial parameters; federated variogram estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMulti-site mining operations; international groundwater monitoring; multi-agency environmental networks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eML deployment across organisational boundaries; leveraging distributed data without centralisation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLong-term (5\u0026thinsp;+\u0026thinsp;yr)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFederated learning frameworks maturing (Flower, PySyft); geophysical challenge is preserving spatial structure across federated nodes; requires inter-institutional agreements\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cem\u003eTimelines are indicative and assume active research effort. Near-term priorities are those where methodological foundations exist and primarily require integration and validation. Medium-term priorities require new theoretical development. Long-term priorities depend on infrastructure and institutional changes beyond individual research groups. The 15% figure for aleatory-epistemic decomposition is based on the authors' systematic coding of the 122 included studies.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"8 Conclusions","content":"\u003cp\u003eThis review has provided a systematic, PRISMA-guided assessment of predictive SML in the big data era, with a specific focus on geophysical applications. Through the analysis of 122 studies, we have critically examined the evolution from traditional geostatistical approaches to advanced hybrid methodologies that address the unique challenges of spatial data, including spatial autocorrelation, non-stationarity, scale dependency, and three-dimensional heterogeneity. The conceptual decision pathway framework introduced in this work provides a structured approach for practitioners to navigate from data characterisation through methodology selection, uncertainty quantification, and validation to geophysical application.\u003c/p\u003e \u003cp\u003eOur cross-domain synthesis across seismology, mineral exploration, hydrogeology, and environmental monitoring reveals both transferable patterns and domain-specific requirements. Hybrid geostatistical-ML frameworks consistently outperform pure ML approaches when spatial autocorrelation is strong, yet uncertainty quantification remains underdeveloped relative to point prediction accuracy. The six synthesis tables presented throughout this review provide quantitative comparisons that enable direct method selection based on specific application requirements, spatial assumptions, and computational constraints.\u003c/p\u003e \u003cp\u003eThe structured research roadmap identifies concrete near-term priorities including spatially aware interpretability methods, operationalised aleatory-epistemic decomposition, and unified spatial-temporal validation frameworks, alongside medium-term goals such as hierarchical multi-scale uncertainty propagation and GPU-native spatial computing. The advancement of these priorities requires the interdisciplinary collaboration between spatial statisticians, machine learning researchers, and geoscience domain experts that this review aims to foster. By bridging the gap between methodological innovation and geophysical application, SML can fulfil its potential to provide meaningful insights and reliable predictions for critical decisions in resource management, hazard assessment, and environmental stewardship.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDeclaration of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo new data was generated for this work. The PRISMA screening records and data extraction tables are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eE Afrifa-Yamoah \u0026ndash; conceptualization, methodology, investigation, resources, visualization, supervision and wrote the original draft; YK Awuah-Mensah, BW Nuakoh \u0026amp; WH Tan \u0026ndash; performed literature search, visualization, and resources; F Fouedjio \u0026amp; E Arya \u0026ndash; \u0026nbsp; conceptualization, methodology, supervision, and provided critical review and edit. All authors reviewed and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAdeniyi OD, Brenning A, Bernini A, Brenna S, Maerker M (2023) Digital Mapping of Soil Properties Using Ensemble Machine Learning Approaches in an Agricultural Lowland Area of Lombardy, Italy. 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Nat Clim Change 8:469\u0026ndash;477. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41558-018-0156-3\u003c/span\u003e\u003cspan address=\"10.1038/s41558-018-0156-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":false,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"acta-geophysica","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"agph","sideBox":"Learn more about [Acta Geophysica](http://link.springer.com/journal/11600)","snPcode":"11600","submissionUrl":"https://www.editorialmanager.com/agph/default2.aspx","title":"Acta Geophysica","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"uncertainty quantification, geostatistics-ML integration, spatial validation, feature engineering, probabilistic prediction","lastPublishedDoi":"10.21203/rs.3.rs-9340991/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9340991/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePredictive spatial machine learning has become essential across the geosciences, yet three critical challenges remain insufficiently addressed: the integration of spatial structure into machine learning architectures, the rigorous quantification of prediction uncertainty, and the validation of models under spatial autocorrelation. This systematic review reveals that hybrid geostatistical-ML frameworks consistently outperform pure machine learning methods when spatial autocorrelation is strong with reported accuracy gains of 10\u0026ndash;40% across seismic hazard assessment, mineral resource estimation, hydrogeological forecasting, and environmental monitoring. However, the review identifies a fundamental disconnect between methodological capability and practice: fewer than 15% of studies explicitly decompose prediction uncertainty into its aleatory (irreducible) and epistemic (reducible) components, despite the practical importance of this distinction for guiding data collection and risk assessment. Validation practices lag further behind, with standard cross-validation overestimating model performance by up to 47% when spatial autocorrelation is ignored, yet spatially aware alternatives such as Importance-Weighted Buffered Cross-Validation and spatial block bootstrap remain underutilised. Physics-informed spatial constraints show promise in hydrogeology and seismology, where governing equations provide natural regularisation, but lack unified frameworks transferable across geophysical domains. A conceptual decision pathway framework linking data characterisation, methodology selection, uncertainty quantification, and validation is proposed to guide practitioners through these interdependent choices. The review identifies specific research frontiers with actionable directions, including the operationalisation of aleatory-epistemic uncertainty decomposition for targeted spatial sampling design, the development of spatially aware interpretability methods that account for autocorrelation in feature importance, and community benchmark datasets modelled on existing hydrological standards to enable reproducible cross-method comparison in the geosciences.\u003c/p\u003e","manuscriptTitle":"Predictive Spatial Machine Learning in the Era of Big Data: A Critical Analysis of Methods, Technical Advances, and Research Frontiers for Geophysical Applications","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-18 05:49:14","doi":"10.21203/rs.3.rs-9340991/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-05-08T05:19:42+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-07T21:48:27+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Acta Geophysica","date":"2026-04-30T07:16:02+00:00","index":"","fulltext":""},{"type":"submitted","content":"Acta Geophysica","date":"2026-04-21T10:07:09+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-17T12:38:51+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"acta-geophysica","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"agph","sideBox":"Learn more about [Acta Geophysica](http://link.springer.com/journal/11600)","snPcode":"11600","submissionUrl":"https://www.editorialmanager.com/agph/default2.aspx","title":"Acta Geophysica","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d5a2565c-be23-49a4-8d79-7712c8cd6e9e","owner":[],"postedDate":"May 18th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"","date":"2026-05-08T05:19:42+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-07T21:48:27+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T05:49:15+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-18 05:49:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9340991","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9340991","identity":"rs-9340991","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}