Emergent Tectonic Control on Deep Critical Mineral Systems: A Fractal- Statistical Paradigm

Emergent Tectonic Control on Deep Critical Mineral Systems: A Fractal- Statistical Paradigm | 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 Emergent Tectonic Control on Deep Critical Mineral Systems: A Fractal- Statistical Paradigm Jianan Zhao, Yingru Pei, Chonghao Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8881137/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Structural fault frameworks strictly constrain hydrothermal uranium metallogenic systems, making the precise characterization of structural ore-controlling mechanisms decisive for the exploration of deep concealed mineral resources. However, conventional assessment methodologies typically remain confined to qualitative or semi-quantitative analyses of two-dimensional surface traces, failing to quantify deep three-dimensional fault architectural attributes effectively. Furthermore, processes involving multi-source information fusion frequently suffer from biases inherent in subjective weighting schemes. To surmount these limitations, this research establishes a novel quantitative evaluation framework that integrates three-dimensional fault geometric characteristics with multivariate statistical analysis. Using the typical granite-hosted uranium field in the southern Zhuguang Mountain region of Northern Guangdong, South China, as a case study, the investigation initially employs the theoretical fault-displacement-length fractal scaling law to quantitatively invert fault penetration depths, thereby extending structural elements from planar representations into the volumetric domain. Subsequently, the study selects estimated fault depth, fault linear density, fault intersection kernel density, and Euclidean distances to faults and intersections as critical spatial parameters. Principal Component Analysis deciphers the intrinsic correlation structures among these multidimensional variables to objectively determine factor weights, facilitating the construction of a comprehensive Tectonic Control Index model. Results demonstrate that favorable metallogenic zones, delineated using a statistical threshold method based on the index's typical distribution characteristics, accurately capture the spatial distribution patterns of known deposits. The core innovation lies in establishing a new paradigm for the quantitative characterization of structural controls that fuses fractal three-dimensional depth estimation with data-driven objective weighting, significantly enhancing predictive capabilities for spatially locating deep, concealed mineralization networks. These findings provide a scientifically robust, data-driven solution for the deep, synergistic exploration of concealed deposits within complex geological settings. Structural mineralized control fractal depth estimation Principal Component Analysis Tectonic Control Index quantitative metallogenic potential assessment Granite-hosted uranium deposit. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Highlights 1. A fractal-statistical framework reconstructs the 3D tectonic architecture for deep uranium targeting. 2. The tectonic control index reveals an emergent Gaussian distribution of crustal permeability. 3. The model yields an AUC of 0.81, capturing 75% of known deposits within 30% of the study area. 4. Structural self-organization drives high focusing efficiency in mineralization systems. 5. The research method offers a geologically constrained, mathematically robust tool for concealed hydrothermal deposits. 1. Introduction Amid the accelerating macroeconomic transition of the global energy architecture toward low-carbon paradigms, uranium serves as the material foundation of the nuclear energy industry, and the capacity to secure this strategic resource directly affects achieving carbon-neutrality objectives and sustaining global energy security. Driven by the substantial expansion of installed nuclear power capacity in emerging economies, demand for uranium resources has shifted from traditional shallow, easily accessible deposits to deep, concealed reserves. Consensus within the international exploration community indicates that, following prolonged periods of high-intensity extraction, outcrop-style uranium deposits are severely depleted; consequently, future resource potential resides primarily in the deep crust or beneath thick overburden sequences. Particularly in typical granite-hosted metallogenic provinces such as the Zhuguang Mountain complex, mineralization is governed by intricate deep geodynamic processes, rendering the occurrence of ore bodies extremely subtle. Nevertheless, contemporary exploration practices reveal a significant paradox: superficial geological observations capture only the two-dimensional manifestations of the metallogenic system, failing to characterize its spatiotemporal evolution. Such cognitive limitations severely constrain the efficient assessment of concealed deposits, necessitating the urgent establishment of a novel quantitative prediction theory capable of penetrating shallow cover to elucidate deep metallogenic mechanisms (Chi et al. 2020 ; Chen et al. 2022b ; Jin et al. 2022 ; Li et al. 2022a ; Li et al. 2022b ; Song et al. 2022 ; Zhang et al. 2022b ; Liu et al. 2023a ; Wang et al. 2023c ; Yan et al. 2023 ; Zhang et al. 2023 ; Zhao and Liu 2024 ; Guan et al. 2025 ; Guo et al. 2025 ; Liu et al. 2025a ; Quiroga-Barriga et al. 2025 ; Yang et al. 2025a ; Zhang et al. 2025d ; Zhao and Liu 2025 ; Lai et al. 2026 ; Ruan et al. 2026 ). The essence of hydrothermal uranium metallogenesis lies in crustal fluid migration and focusing, a process fundamentally controlled by deep, cryptic fluid-conduit systems. Although surface-visible fault traces furnish geometric constraints on the structural framework, the paramount control on metallogenic fluid flux resides in the three-dimensional connectivity of fracture networks and their deep permeability architecture. Investigations in the Zhuguang Mountain region demonstrate that polyphase tectonic reactivation from the Indosinian to Yanshanian episodes induced differential lithospheric fracturing, generating three-dimensional structural damage zones that channel fluid upwelling and discharge. Reconstructing the deep permeability architecture from limited two-dimensional surface traces requires incorporating physical scaling laws and fractal geometry. Quantitative characterization of displacement-length relationships and fractal dimensions enables reconstruction of vertical fault penetration depths and spatial connectivity. This kinematic advancement over purely geometric description reveals that concealed metallogenic systems commonly exhibit statistical self-organization, with mineralization centers preferentially concentrating within discrete structural intensity thresholds, thereby providing a robust physics-based foundation for blind ore prediction (Aubert et al. 2022 ; Chen et al. 2022a ; Kim et al. 2022 ; Poh et al. 2022 ; Zhang et al. 2022a ; Bonnetti et al. 2023 ; Halldórsdóttir et al. 2023 ; Luo et al. 2023 ; Shi et al. 2023 ; Xue et al. 2023 ; Yu et al. 2023 ; Chang et al. 2024 ; Liang et al. 2024 ; Liu et al. 2024 ; Zhang et al. 2024 ; Yang et al. 2025b ; Zhang et al. 2025a ). Although structural ore-control prediction has emerged as a pivotal tool for delineating exploration targets, conventional methodologies remain hampered by linear superposition assumptions and subjective empirical biases. Routine buffer analysis and index-overlay models often neglect nonlinear interactions and multicollinearity among geological variables and lack statistically rigorous criteria for anomaly recognition. Consequently, predictions suffer from pervasive background noise and fail to pinpoint deep targets with precision. The prevailing scientific bottleneck thus centers on constructing an objective, nonlinear, and statistically grounded quantitative evaluation paradigm (Chen et al. 2022b ; Wang et al. 2022b ; Chen et al. 2023 ; Zhang et al. 2023 ; Bark and Butcher 2025 ; Liu et al. 2025a ; Wu et al. 2025 ; Lai et al. 2026 ; Ruan et al. 2026 ). To address this challenge, this study develops a data-driven, integrated framework: principal component analysis (PCA) reduces dimensionality across multiple structural parameters—including kernel density, line density, and Euclidean distance—to extract the first principal component of regional structural intensity, serving as the tectonic ore-control index (TCI). Anomalies are subsequently delineated objectively through the mean–standard deviation method, leveraging the inherent Gaussian distribution of TCI values. Application in southern Zhuguang Mountain unequivocally demonstrates the superiority of this approach, with the prediction-area (P-A) plot yielding an area under the receiver operating characteristic curve (AUC) of 0.81. This result confirms that the model effectively captures spatial associations of concealed deposits, achieving a transformative shift from qualitative geological interpretation to rigorous quantitative statistical prediction. 2. Geological Setting The study area occupies the critical junction between the interior of the Cathaysia Block and the Nanling Metallogenic Belt, representing one of South China's most representative granite-hosted uranium provinces (Fig. 1 ). Its geological evolution transcends simple stratigraphic superposition; instead, it manifests as spatiotemporal coupling between deep-seated magmatic-thermal events and inherited structural frameworks, with polyphase tectonic reactivation constituting the defining hallmark. The Zhuguang Mountain pluton comprises a gigantic composite batholith formed through multistage Indosinian to Yanshanian magma emplacement, serving not only as a fertile uranium source but also as ideal brittle host rocks and thermal drivers for hydrothermal metallogenic systems. This exceptional mineralization potential stems from the region's protracted position at the dynamic transition between the Tethyan and paleo-Pacific tectonic domains—a unique tectonic setting that subjected pre-existing fault systems to repeated mechanical inversion and structural reconfiguration throughout geological history (Tian et al. 2023 ; Hu et al. 2024 ; Li et al. 2024 ; Zhao and Liu 2024 ; Bu et al. 2025 ; Liu et al. 2025b ; Zhao and Liu 2025 ). Regional tectonic regime evolution profoundly governs stress-field reconfiguration trajectories (Fig. 2 ). Since the Mesozoic, variations in the subduction angle and velocity of the paleo-Pacific plate beneath Eurasia have driven South China through a dramatic shift from Indosinian compressional orogeny to Yanshanian lithospheric extension and thinning. This extensional regime triggered asthenospheric upwelling and marked elevation of crustal heat flow, thereby fueling widespread Yanshanian magmatism and deep fluid circulation. Microstructural evidence, including S-C fabrics and dynamic quartz recrystallization preserved within the Nanxiong fault zone, documents an early history of high-temperature sinistral ductile shearing; contemporaneous late Triassic (ca. 230 − 210 Ma) felsic dykes signal the onset of transition from ductile to brittle-ductile deformation (Fig. 3 ). Such progressive mechanical evolution sustained the long-term activity of fault zones as persistent crustal weakness zones, thereby establishing the prerequisite structural template for subsequent migration and focusing of metallogenic fluids (Wang et al. 2022a ; Yan et al. 2022 ; Yang et al. 2022 ; Zhu et al. 2022 ; Wang et al. 2023b ; Xu et al. 2023a ; Yao et al. 2023 ; Zhao et al. 2023 ; Cheng et al. 2024 ; Ke et al. 2024 ; Zhao and Liu 2024 ; Li et al. 2025 ; Tan et al. 2025 ; Zhao and Liu 2025 ). The principal metallogenic episode (primarily Early Cretaceous, ca. 125 − 105 Ma) exerted direct control over the ore-conducting efficiency of fluid conduit systems through tectonic reactivation. During this interval, intense intraplate extensional dynamics reorganized the regional stress field, triggering pronounced transtensional reactivation of NE-trending basement faults while imparting extensional normal-fault character to SN-oriented structures. This differential reactivation generated high-permeability dilational jogs and extensive damage zones at fault intersections, thereby establishing three-dimensional fluid networks that linked deep uranium sources to shallow unloading domains. Contemporaneous mafic dyke emplacement further corroborates the exchange of heat from the deep mantle into the metallogenic system (Zhang et al. 2018 ; Zhang et al. 2020a ; Wang et al. 2022b ; Gong et al. 2023 ; Wang et al. 2023a ; Aboayanah et al. 2024 ; Jin et al. 2024 ; Pichavant et al. 2024 ; Wang et al. 2024 ; Yin et al. 2024 ; Zhao and Liu 2024 ; Bu et al. 2025 ; Zhao and Liu 2025 ). Consequently, uranium mineralization in southern Zhuguang Mountain fundamentally arises from structurally induced heterogeneous fluid flow and physicochemical trapping, wherein dilatational opening of faults under specific stress regimes and concomitant surges in fluid flux constitute the critical geological constraints for pinpointing the spatial distribution of concealed deposits (Fig. 4 ). 3. Methodology To address the challenges of nonlinearity and uncertainty in predicting deep, concealed metallogenic systems, this study establishes a quantitative evaluation framework that integrates geometry, kinematics, and statistics. Transcending traditional empirical qualitative descriptions, the methodology adopts a composite framework integrating physical scaling laws, information-theoretic dimensionality reduction, and stochastic statistical processes. It aims to invert deep-crustal architecture from surface two-dimensional observations and to identify the statistical fingerprints of metallogenic anomalies objectively. 3.1. Quantification of crustal architecture: deep inversion via displacement-length scaling laws The vertical extension capacity of crustal tectonic networks is a critical physical parameter for assessing ore-conducting efficiency; however, remote sensing interpretation of the surface retrieves only two-dimensional geometric traces of faults. To surmount this limitation and invert the three-dimensional spatial attributes of fracture systems, the displacement-length ( D - L ) fractal scaling law is introduced as the theoretical basis for deep architecture reconstruction. Modern rock mechanics and fault growth theory indicate that fracture system development is not a random process but a physical one adhering to self-organized criticality growth laws. Although classical linear elastic fracture mechanics (LEFM) typically predicts a power-law relationship between fault displacement/depth and length, vertical penetration of fault growth within granite batholiths, constrained by crustal rheological stratification, often exhibits specific scale effects (Cowie and Scholz 1992 ; Cowie 1998 ; Cowie and Shipton 1998 ; Cooper et al. 2003 ; Schultz et al. 2006 ; Bergen and Shaw 2010 ; Nicol et al. 2017 ; Kolyukhin et al. 2018 ; Lathrop et al. 2022 ; Xu et al. 2023b ). Drawing upon datasets comprising measured lengths ( L ) of known faults and penetration depths ( D ) revealed by boreholes and geophysical exploration in the Zhuguang Mountain area, a semi-logarithmic scaling model tailored to the regional structural rheological characteristics was established: D = 2.5×lg( L ) + 4.0 (R 2 = 0.85). This parameterized equation not only shows high statistical significance but also captures the self-similarity and energy-dissipation mechanisms that characterize the evolution from micro-fractures to macro-faults in the region. The model reveals that for every order-of-magnitude increase in fault length, vertical conduction capacity increases logarithmically rather than linearly, a phenomenon likely attributable to physical constraints imposed on downward fault propagation by the brittle-ductile transition zone. By employing this scaling law, calibrated using physical principles and empirical data, surface two-dimensional linear elements are transformed into structural-intensity proxies with vertical dimensionality. It facilitates the construction of a quasi-three-dimensional solid model that reflects the deep crustal permeability architecture, thereby providing a robust physical basis for identifying "penetrative conduits" that link deep uranium sources with shallow traps. 3.2. Signal extraction and dimensionality reduction: modeling tectonic intensity via PCA Crustal architecture controls metallogenic systems by coupling multidimensional spatial variables, including line density reflecting fluid permeability, intersection kernel density indicating structural complexity, and Euclidean distance representing transport proximity. Nevertheless, multi-source spatial data frequently contain substantial explanatory redundancy and random noise. This study employs PCA as the core algorithm, predicated on the scientific rationale of mapping correlated structural factors onto an orthogonal spatial basis via linear transformation, thereby "extracting the signal from noise." Within this framework, the first principal component (PC1) transcends simple mathematical synthesis to represent the dominant mode of regional tectonic intensity, the primary geological driver governing hydrothermal fluid accumulation. Analysis of the eigenvector loading structure facilitates objective weighting of kernel density characterizing fluid focusing centers, line density characterizing fluid migration pathways, and distance factors characterizing fluid influence zones, while effectively eliminating the subjective uncertainty inherent in manual expert scoring. This unsupervised dimensionality reduction approach eliminates human bias inherent to traditional weighting methods, ensuring the objectivity and mathematical rigor of the evaluation model in characterizing the spatial heterogeneity of the crustal permeability field (Huang et al. 2020 ; Jansson et al. 2022 ; Liu et al. 2022 ; Li and Qin 2024 ; Sun et al. 2024 ; Zuo et al. 2024 ; Rahman Ulfa et al. 2025 ; Yang et al. 2025c ). 3.3. Construction of tectonic ore-control index (TCI): quantitative characterization of crustal permeability field Following the physical quantification and dimensionality reduction of multidimensional structural parameters, this study constructs the TCI to transform discrete structural geometric information into a continuous quantitative representation of the crustal permeability field. Rather than relying on simple empirical superposition, TCI construction employs data-driven modeling based on PCA-derived PC1 scores. To capture multi-scale structural ore-controlling characteristics within the Zhuguang Mountain region, the model integrates three critical spatial variables: kernel density with a search radius of 2000 m, which reflects the spatial clustering effect of structural intersections; line density with a search radius of 5000 m, which characterizes the intensity of regional fracture network development; and Euclidean distance with a maximum threshold of 10,000 m, which delineates the potential range of fluid migration. These spatial parameters are rasterized and resampled via Geographic Information Systems (GIS) to construct a unified spatial data cube. Based on the eigenvector matrix extracted via PCA, PC1 serves as the statistical variable explaining the dominant contribution to regional structural variance, with its loading coefficients objectively determining weight allocation. Specifically, TCI is mathematically expressed as TCI = α × KD + β × LD + γ × ED, where α , β , and γ correspond to the feature loadings of kernel density, line density, and Euclidean distance on PC1, respectively. This linear combination not only eliminates multicollinearity but also profoundly aligns with the source-transport-trap dynamics of hydrothermal metallogenic systems. Positive contributions from line and kernel densities reflect the control of high-permeability conduits and fluid-focusing centers, whereas the negative constraint imposed by Euclidean distance embodies the spatial law in which mineralization probability decays with increasing distance from faults. To eliminate dimensional discrepancies and enhance spatial comparability, the Min-Max Normalization algorithm maps the raw calculated TCI values to the dimensionless interval [0, 1], thereby generating the final continuous probability field. The physical significance of TCI lies in its role as a comprehensive geological proxy; it not only quantifies the connectivity of fracture networks and the extent of deep damage zones but also reveals the spatiotemporal modulation of crustal fluid flux and uranium precipitation by Indosinian to Yanshanian tectonic reactivation. High TCI values correspond to structural singularities characterized by high stress concentration, intense fracturing, and maximal fluid flux, whereas low TCI values correspond to relatively stable tectonic blocks. This quantitative framework transcends traditional qualitative descriptions and supports the development of predictive models grounded in physical laws and stochastic processes. Its application in analogous hydrothermal systems has significantly enhanced the precision and efficiency of concealed deposit exploration, providing a reproducible scientific paradigm for the sustainable assessment of deep resources (Mao et al. 2020 ; Chen et al. 2021 ; Chen et al. 2025 ; Lou and Liu 2025 ; Zhang et al. 2025b ). 3.4. Statistical Anomaly Detection: Outlier Identification Based on Stochastic Processes The identification of metallogenic prospect areas fundamentally entails detecting "anomalous outliers" within the geological fluid flux field. Grounded in spatial stochastic process theory, the generated TCI spatial field exhibits significant Gaussian behavior. This statistical order reveals the tectonic self-organization logic inherent within the metallogenic system. Within the present framework, the delineation of mineralization potential relies not on artificially imposed absolute thresholds but on scientific classification based on the statistical dispersion characteristics of a normal distribution. Adopting µ + 2 σ (mean plus two standard deviations) as the critical criterion for defining extremely high-potential zones statistically signifies the identification of "statistical anomalies"—regions constituting a minimal proportion of the spatial field yet possessing decisive significance for mineralization. This evaluation paradigm, based on outlier detection via stochastic processes, precisely pinpoints singularity spaces characterized by surges in tectonic intensity. Validation using Receiver Operating Characteristic (ROC) and P-A curves yields an AUC of 0.81, demonstrating a high degree of coupling between these statistical anomaly zones and the spatial distribution of known deposits, thereby vigorously confirming the efficiency and reliability of data-driven statistical thresholds in revealing concealed mineralization traps (Hong 2009 ; Yousef et al. 2009 ; Shatnawi 2017 ; Zhang et al. 2020b ; Numminen et al. 2023 ; Ibrar et al. 2024 ; Zhou et al. 2025 ). 4. Results 4.1. Spatial heterogeneity of crustal structural architecture Quantitative parameterization of the remote-sensing interpreted fracture network reveals significant spatial heterogeneity in the crustal structural architecture of southern Zhuguang Mountain. The distribution map of fracture cutting depths, inverted using fractal scaling laws (Fig. 5 a), shows that the NE-trending major faults, such as the Nanxiong Fault, exhibit the most significant vertical extension capacity; their theoretical penetration extends to the deep crust, making them regional conduits for fluid ascent. In contrast, the secondary fracture network displays shallower penetration depths, primarily functioning to regulate and distribute fluids. This framework receives further reinforcement from structural spatial density patterns. The kernel density map (Fig. 5 b) identifies multiple high-intensity structural intersection centers; these "hotspots" are distributed primarily in a beaded pattern along major fault zones, indicating critical nodes of local stress concentration and fluid focusing. Concurrently, the line density map (Fig. 5 c) clearly delineates a reticulate skeleton formed by the interlacing of NE- and SN-trending faults, where high-value zones not only cover the main fault belts but also extend laterally to form broad damage zones. The Euclidean distance field (Fig. 5 d) geometrically quantifies the decay gradient of fault influence, with low-value regions (proximal to faults) constituting advantageous spaces for metallogenic fluid migration. The heterogeneous distribution of these fundamental spatial parameters provides multidimensional physical constraints for the subsequent construction of the comprehensive ore-control model. 4.2. Emergent statistical properties and the "mineralization fingerprint" Global statistical analysis of the constructed TCI field reveals that regional tectonic intensity obeys the ubiquitous self-organized criticality prevalent in natural systems. The frequency histogram of TCI values (Fig. 6 a) exhibits a pronounced unimodal pattern, with substantial conformity to a Gaussian distribution and slight positive skewness toward higher values. The statistical mean ( µ ≈ 0.34) coincides closely with the histogram peak, defining the steady-state background tectonic field, whereas the pronounced long-tail structure on the right flank (TCI > 0.61, corresponding to the µ + 2 σ interval) captures the statistical outliers (Table 1 ). This emergent statistical behavior implies that mineralization, as a low-probability geological event, preferentially localizes within structural singularities that deviate markedly from the background and occupy the extreme tail of the Gaussian distribution—regions of exceptionally concentrated stress and fluid flux. PCA further dissects the intrinsic driving mechanism of this system, extracting a distinctive "structural fingerprint" for uranium mineralization. The loading structure of PC1 (Fig. 6 b) demonstrates that line density exerts overwhelming positive control (0.872), far surpassing kernel density (0.327), while Euclidean distance imposes a negative constraint (− 0.364) (Table 2 ). This mathematical relationship carries profound dynamic implications: in the Zhuguang Mountain granite-hosted uranium system, neither the mere presence of faults nor localized point-like intersections constitutes the primary ore-controlling factor; instead, fracture network connectivity and developmental intensity emerge as the decisive regulators of crustal permeability flux. This line-density-dominated regime underscores that fluids preferentially migrate and focus along highly interconnected structural corridors over long distances. Table 1 Statistical classification of metallogenic potential and geological implications based on TCI thresholds Threshold Range TCI Value Metallogenic Potential Classification Geological Interpretation > µ + 2 σ > 0.61 Class I: Extremely High-Potential Zone Structural core / main conduit: Characterized by intense fluid enrichment and severe fracturing. µ + σ ~ µ + 2 σ 0.48–0.61 Class II: High-to-Moderate Potential Zone Structural subsidiary zone: Hosts fluid migration networks and developed secondary faults. µ ~ µ + σ 0.34–0.48 Class III: Low-Potential/Background Zone Weak deformation zone: Exhibits minor structural influence and low mineralization probability. < µ < 0.34 Class IV: Non-Prospective Zone Stable block: Characterized by an absence of significant tectonic activity; effectively impermeable to fluid ingress. Table 2 Eigenvectors and eigenvalues of the principal component analysis. Variables PC1 PC2 PC3 Kernel density 0.327 0.348 -0.878 Line density 0.872 0.246 0.423 Euclidean distance -0.364 0.904 0.223 Eigenvalue 0.0159 0.0036 0.0022 Variance contribution (%) 73.41 16.62 9.97 Cumulative variance (%) 73.41 90.03 100.00 4.3 Spatial Targeting and Deep Structural Coupling The metallogenic prediction map delineated using the statistical anomaly threshold ( µ + 2 σ ) (Fig. 6 ) demonstrates striking spatial coupling between high-potential zones and the deep-seated major fault framework. Extremely high-potential zones do not distribute randomly; instead, they form distinct linear and knot-like patterns along the NE-trending Nanxiong Fault belt and its intersections with the SN-trending Niulan Fault belt. These high-TCI anomaly zones precisely delineate the surface projections of deep high-permeability damage zones, exhibiting remarkable coincidence with known typical uranium deposits such as Baishun and Renhua. Overlay analysis and ROC validation further quantify the model's predictive power. Although Class I targets occupy only approximately 5% of the total study area, they capture the vast majority of known ore occurrences. The P-A curve yields an AUC of 0.81, confirming an exceptionally high signal-to-noise ratio. This spatial precision unequivocally demonstrates that the TCI model not only identifies surficial mineralization outcrops but, more critically, illuminates the deep structural roots governing the emplacement of concealed orebodies. High-TCI domains represent vertical plumbing systems that sustained maximum fluid flux during tectonic reactivation episodes, efficiently linking deep uranium source regions to shallow physicochemical traps and enabling trans-crustal spatiotemporal coupling and focused precipitation of ore-forming components. 5. Discussion 5.1 From Geometry to Hydrodynamics: Physical Mechanisms of Permeability Regulation in High-Damage Zones The spatially heterogeneous distribution of the TCI represents more than a mere mathematical projection of surface fault geometry; it fundamentally constitutes the surficial physical manifestation of deep-crustal hydrodynamic processes. Geological observations and numerical simulations consistently demonstrate that fault zones do not exist as singular geometric segments but rather as complex three-dimensional entities comprising a fault core flanked by damage zones characterized by intense fracture development. Rheologically, high-TCI anomaly regions—particularly Class I targets exceeding the µ + 2 σ threshold—correspond to high-permeability windows within the crust. Integrated with fracture-cutting-depth data inverted using fractal scaling laws, these domains represent more than mere two-dimensional structural intersections; they function as fractal conduits that penetrate the brittle-ductile transition zone. Under the intense Yanshanian extensional dynamics governing the Zhuguang Mountain region, these deep-seated fault systems underwent transtensional reactivation, inducing dilatancy within internal fracture networks and generating pronounced zones of low fluid potential. In accordance with fault-valve theory, this tectonic activation mechanism propels the rapid upwelling of deep, uranium-rich hydrothermal fluids along the vertical channels delineated by high TCI values. The dominant line-density characteristic of the TCI model further elucidates that fluid migration operates primarily through highly connected, fracture-controlled, channelized flow rather than porous flow. Upon the ascent of these high-temperature, high-pressure fluids into shallow, high-TCI structural dilatancy zones, abrupt pressure drops trigger boiling and phase separation, resulting in drastic physicochemical fluctuations that destabilize and precipitate uranyl complexes. Consequently, TCI anomaly zones precisely delineate the "source-transport-trap" coupling interfaces where fluid flux and energy dissipation are most concentrated. It validates the physical trajectory governing the transformation of structural configuration into hydrodynamic efficiency, establishing that structural physical complexity directly dictates both the efficiency of metallogenic fluid migration and the localization of mineralization (Henley and Berger 2000 ; Liu et al. 2021 ; Lan et al. 2022 ; Poh et al. 2022 ; Sun et al. 2022 ; Liu et al. 2023b ; Petrov et al. 2023 ; Zhang et al. 2025c ). 5.2 Efficiency of the Mineral System: Statistical Convergence and Spatial Singularity Analysis of the P-A curve provides a profound elucidation of the exceptional focusing efficiency inherent to the uranium metallogenic system in southern Zhuguang Mountain. Statistical validation shows that the TCI model achieves an AUC of 0.81, far surpassing the random-prediction baseline of 0.5. More critically, the steep rise of the curve within the low-area-percentage interval indicates that high-TCI zones, comprising only 30% of the total study area, capture approximately 75% of known deposits (Fig. 7 ). This statistical signature carries significant metallogenic implications: it attests that ore-bearing fluids did not undergo extensive lateral dispersion within the crust during migration but were instead confined by the structural framework, thereby focusing within a select few high-permeability structural cores. This phenomenon, in which "small volumes control large reserves," reflects the highly self-organized nature and nonlinear threshold characteristics of the metallogenic system. Only when TCI exceeds a specific critical value, statistically defined as µ + 2 σ , does rock permeability undergo an exponential surge, thereby creating effective fluid traps. Such spatial singularity aligns with self-organized criticality theory, suggesting that the evolution of metallogenic systems tends to constrain dispersed ore-forming elements forcefully onto structural nodes characterized by specific energy gradients. In exploration practice, this implies that targeting strategies can shift from broad-spectrum reconnaissance to "precision-guided" deep drilling focused on this critical 30% core area. This remarkably high capture efficiency not only validates the predictive robustness of the TCI model but also substantially reduces the trial-and-error costs and investment risks associated with exploring deep blind deposits, underscoring the significant economic value of quantitative prediction models. 5.3 Comparability and Generalizability: Shifting from Empirical Overlay to Statistical-Physical Paradigms Compared with conventional structural ore-control prediction approaches, the integrated "fractal-PCA-statistical" framework developed here exhibits marked methodological superiority. Traditional buffer analysis or simplistic Boolean overlay methods typically rely on linear assumptions, struggle to accommodate complex nonlinear interactions among structural variables, and use subjective, expert-derived weighting, resulting in predictions that lack comparability across regions. In stark contrast, the present study leverages PCA to objectively extract intrinsic modes of tectonic intensity, eliminating human bias and informational redundancy while establishing a unified statistical criterion for anomaly recognition grounded in Gaussian distribution theory. Crucially, this framework demonstrates broad geological generalizability. Its core logic—deep architecture inversion via fractal geometry, dominant mode extraction through multivariate statistics, and anomaly detection via stochastic processes—extends far beyond granite-hosted uranium systems and applies equally to other structurally controlled hydrothermal deposits, including orogenic gold and porphyry copper systems. Wherever mineralization is governed by fluid migration and focusing within crustal fracture networks, this quantitative paradigm can be readily transferred to diverse tectonic settings and commodity types by targeted adjustments to structural parameters and scaling relationships. Consequently, it delivers a replicable, standardized scientific toolkit for deep exploration of critical metals worldwide, marking a decisive paradigm shift from subjective empiricism to rigorously data-driven statistical-physical prediction. 6. Conclusion This study constructs and validates an integrated quantitative evaluation framework that seamlessly couples fractal geometry, multidimensional spatial analysis, and unsupervised statistical learning to tackle the inherent nonlinearity and geological uncertainty in predicting deep concealed metallogenic systems. By incorporating displacement-length scaling laws, PCA-based dimensionality reduction, and stochastic-process-driven anomaly detection, the approach successfully inverts two-dimensional surface structural geometry into three-dimensional crustal permeability architecture, with robust performance demonstrated in the granite-hosted uranium province of Zhuguang Mountain. The principal conclusions are as follows: (1) The study proposes and validates a TCI evaluation model that rigorously integrates geophysical constraints with data-driven inference. Through PCA dimensionality reduction of kernel density, line density, and spatial proximity metrics, the model objectively extracts the dominant mode of regional tectonic intensity. Eigenvector analysis reveals that fracture network connectivity—reflected by a line-density loading of 0.87—rather than isolated fault scale, constitutes the primary control on crustal permeability heterogeneity. This finding marks a paradigm shift from qualitative structural description to quantitative physical representation, providing a high-resolution digital proxy for deciphering source-transport-trap dynamics of hydrothermal fluids under polyphase tectonic reactivation. (2) Statistical analysis uncovers pronounced self-organized criticality in regional structural evolution and mineralization response. The near-Gaussian distribution of TCI values illuminates nonlinear emergent behavior within the metallogenic system. An anomaly delineation scheme based on the Gaussian-derived threshold ( µ + 2 σ ) not only successfully delineates deep high-permeability damage zones in the Zhuguang Mountain region but also achieves an AUC of 0.81 and remarkable focusing efficiency, whereby the top 30% of prospective area captures 75% of known deposits. These results confirm that uranium mineralization fundamentally manifests as a spatially singular response triggered when tectonic intensity exceeds a critical threshold, exhibiting strong statistical convergence and predictability. (3) The methodological framework exhibits broad applicability and profound scientific value in predicting concealed deposits within complex structural domains. Unlike traditional approaches hampered by subjective expert weighting and surface observational limitations, the fractal-statistical paradigm extrapolates deep architecture via self-similar scaling laws with exceptional robustness, eliminating empirical bias. Transcending regional geological specificities, the model applies not only to granite-hosted uranium systems but also extends to structurally controlled hydrothermal deposits worldwide, including orogenic gold and porphyry copper systems. In summary, this study delivers a geologically constrained, mathematically robust quantitative prediction toolkit that significantly advances mineral exploration from empirical intuition to physics-informed statistical prediction, thereby elevating the scientific standard for the sustainable assessment of globally critical metal resources. Abbreviations Principal component analysis PCA Tectonic ore-control index TCI Prediction-area P-A Area Under the Receiver Operating Characteristic Curve AUC Linear elastic fracture mechanics LEFM First principal component PC1 Geographic Information Systems GIS Receiver Operating Characteristic ROC 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. Funding the Development Research Center of the China Geological Survey, Geological Survey Project numbers 121201004000150017-65, 121201004000160901-77, 121201004000172201-61, DD20190159-10; Guangdong Provincial Geological Joint Fund, General Project number 601145539054. Author Contribution Jianan Zhao: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing-original draft, Writing-review & editing. Yingru Pei: Investigation, Methodology, Software, Supervision, Validation, Visualization, Writing-review & editing. Chonghao Liu: Methodology, Software, Validation, Writing-review & editing. Acknowledgement This work was supported by the Development Research Center of the China Geological Survey [grant numbers 121201004000150017-65, 121201004000160901-77, 121201004000172201-61, DD20190159-10] and the Guangdong Provincial Geological Joint Fund (General Project) [grant number 601145539054]. Data Availability All data presented in this article are publicly available as open-access resources. The supplementary materials also include tables of key calculation processes. 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Earth Sci Inf 18:182. 10.1007/s12145-024-01678-9 Zhu X, Wang L, Zhou X (2022) Structural features of the Jiangshao Fault Zone inferred from aeromagnetic data for South China and the East China Sea. Tectonophysics 826:229252. https://doi.org/10.1016/j.tecto.2022.229252 Zuo R, Cheng Q, Xu Y, Yang F, Xiong Y, Wang Z, Kreuzer OP (2024) Explainable artificial intelligence models for mineral prospectivity mapping. Sci China Earth Sci 67:2864–2875. 10.1007/s11430-024-1309-9 Additional Declarations No competing interests reported. Supplementary Files Supplementarymaterials.xlsx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 11 May, 2026 Reviewers agreed at journal 11 May, 2026 Reviewers agreed at journal 10 May, 2026 Reviewers agreed at journal 10 May, 2026 Reviewers agreed at journal 10 May, 2026 Reviews received at journal 27 Feb, 2026 Reviewers agreed at journal 21 Feb, 2026 Reviewers agreed at journal 21 Feb, 2026 Reviewers invited by journal 19 Feb, 2026 Editor assigned by journal 19 Feb, 2026 Submission checks completed at journal 16 Feb, 2026 First submitted to journal 14 Feb, 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. 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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-8881137","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":595211663,"identity":"a182dde9-fdfc-4fd6-b46d-3b55403dbaf0","order_by":0,"name":"Jianan Zhao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYDACCRA2ALEYGx98qLDh4edvIFoLc7PhjDNpMpIzDhChBQLY26R52w7bGDQk4NchP7v54QOLArs8/tmNbZIz287zGDAcYPzwMQe3FsY5x4wNJAySiyXuHGy2+HDuNo85cwOz5MxtuLUwSySYSUgYMCc23EhsvDmj7DaPZcMBNmZePFrYJNK/AbXUJ86/kdggzcN2jsfgQAJ+LTwSOSBbDiduuJHYJM3TdoCwFgmJnGKgX44nbryRCArkZB7JGQeb8fpFfkb6xscSf6oT591IfwiMSjt7fv7mgx8+4tECCQJUPmMDfvUgJR8IKhkFo2AUjIIRDQBeXFS9aKj4/AAAAABJRU5ErkJggg==","orcid":"","institution":"Guangdong Provincial Institute of Mineral Resources Exploration, Guangdong Provincial Institute of Nuclear Geological Exploration, Guangdong Geological Bureau","correspondingAuthor":true,"prefix":"","firstName":"Jianan","middleName":"","lastName":"Zhao","suffix":""},{"id":595211664,"identity":"8bf8e620-e8d8-4dd5-a5a6-085f40a16b10","order_by":1,"name":"Yingru Pei","email":"","orcid":"","institution":"Institute of Geomechanics, Chinese Academy of Geological Sciences","correspondingAuthor":false,"prefix":"","firstName":"Yingru","middleName":"","lastName":"Pei","suffix":""},{"id":595211665,"identity":"4a7ce151-72db-4dfc-b973-c61205d9e050","order_by":2,"name":"Chonghao Liu","email":"","orcid":"","institution":"Chinese Academy of Geological Sciences","correspondingAuthor":false,"prefix":"","firstName":"Chonghao","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2026-02-14 15:38:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8881137/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8881137/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103397920,"identity":"d8e6fde5-c321-4a0e-9e03-503b9f1b5f52","added_by":"auto","created_at":"2026-02-25 08:58:18","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":232639,"visible":true,"origin":"","legend":"\u003cp\u003eTectonic map of the Zhuguang Mountain region in northern Guangdong Province, South China, illustrating major faults, fold axes, and known granite-hosted uranium deposits within the Nanling Orogenic Belt and adjacent structural domains.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/f0f10d135db2b829d34556c0.jpeg"},{"id":103397945,"identity":"735cb273-8c0a-497d-8a71-a551d4ab7c65","added_by":"auto","created_at":"2026-02-25 08:58:29","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":196416,"visible":true,"origin":"","legend":"\u003cp\u003eFracture distribution map of the study area in the southern Zhuguang Mountain uranium exploration district, illustrating hierarchical fractures (primary to fourth-order) overlaid on satellite imagery, with an inset rose diagram depicting predominant fracture orientations.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/663673b076d087631bb59c23.jpeg"},{"id":103397866,"identity":"0853b7a3-ad4d-4ed2-926b-83a99bb52eb6","added_by":"auto","created_at":"2026-02-25 08:58:00","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":219474,"visible":true,"origin":"","legend":"\u003cp\u003eGeochronological study and distribution of granitic masses in the southern Zhuguang Mountain region of northern Guangdong.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/f04cca6d3819198b7ffccf9e.jpeg"},{"id":103397905,"identity":"be9f4475-e266-40ea-9c3c-64c26d41b35c","added_by":"auto","created_at":"2026-02-25 08:58:12","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":272364,"visible":true,"origin":"","legend":"\u003cp\u003eHierarchical classification of fault intersection points (a) and horizontal influence zones of faults (b) in the study area (horizontal influence ranges, empirically defined based on regional geological background, are as follows: 1500 m for primary faults, 800 m for secondary faults, 300 m for tertiary faults, 100 m for quaternary faults, and 2000 m for fault intersection points; vertical influence ranges differ accordingly).\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/61c8761938954c07dda696fe.jpeg"},{"id":103397871,"identity":"7f54a698-f9da-441b-8cbc-901c83c921ba","added_by":"auto","created_at":"2026-02-25 08:58:04","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":154328,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distribution of quantified structural parameters in the southern Zhuguang Mountain. (a) Estimated fault cutting depth derived from the fractal D-L scaling law, highlighting the deep-seated nature of NE-trending faults. (b) Kernel density map showing clusters of structural intersections. (c) Line density map reflecting the intensity of the fracture network. (d) Euclidean distance map illustrating the proximity to fault traces.\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/449f7802743ceec9a0f5b0da.jpeg"},{"id":103397868,"identity":"298b34f4-75d3-4914-b698-8b3c29f39eba","added_by":"auto","created_at":"2026-02-25 08:58:00","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":113957,"visible":true,"origin":"","legend":"\u003cp\u003eStatistical properties and spatial distribution of the Tectonic Control Index (TCI). (a) Frequency distribution histogram of TCI values fitted with a Gaussian curve. (b) Spatial map of TCI anomaly zones overlaid with known uranium deposits, illustrating gradient-based prospectivity levels.\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/93c011964a75a43971a799ea.jpeg"},{"id":103397867,"identity":"6c2123e9-0c12-4493-ae42-d12e8f90e539","added_by":"auto","created_at":"2026-02-25 08:58:00","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":77388,"visible":true,"origin":"","legend":"\u003cp\u003ePrediction-area (P-A) plot evaluating the focusing efficiency of the Tectonic Ore-Controlling Index (TCI) model in the southern Zhuguang Mountain uranium district, showing that high-prospectivity zones comprising 30% of the total area capture 75% of known deposits (AUC = 0.81).\u003c/p\u003e","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/e2ca7a27e89a83810f0d8fad.jpeg"},{"id":103398151,"identity":"18e88b20-1c67-4df0-b774-547c6910a9fd","added_by":"auto","created_at":"2026-02-25 08:58:58","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2336187,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/dd8126df-b130-4b92-babf-26ce9f382360.pdf"},{"id":103397982,"identity":"61d9d8ef-4433-4258-832e-e727bf1ae7dc","added_by":"auto","created_at":"2026-02-25 08:58:34","extension":"xlsx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":17634,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterials.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8881137/v1/d3810642caee718d8480bcbd.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Emergent Tectonic Control on Deep Critical Mineral Systems: A Fractal- Statistical Paradigm","fulltext":[{"header":"Highlights","content":"\u003cp\u003e1. A fractal-statistical framework reconstructs the 3D tectonic architecture for deep uranium targeting.\u003c/p\u003e\u003cp\u003e2. The tectonic control index reveals an emergent Gaussian distribution of crustal permeability.\u003c/p\u003e\u003cp\u003e3. The model yields an AUC of 0.81, capturing 75% of known deposits within 30% of the study area.\u003c/p\u003e\u003cp\u003e4. Structural self-organization drives high focusing efficiency in mineralization systems.\u003c/p\u003e\u003cp\u003e5. The research method offers a geologically constrained, mathematically robust tool for concealed hydrothermal deposits.\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eAmid the accelerating macroeconomic transition of the global energy architecture toward low-carbon paradigms, uranium serves as the material foundation of the nuclear energy industry, and the capacity to secure this strategic resource directly affects achieving carbon-neutrality objectives and sustaining global energy security. Driven by the substantial expansion of installed nuclear power capacity in emerging economies, demand for uranium resources has shifted from traditional shallow, easily accessible deposits to deep, concealed reserves. Consensus within the international exploration community indicates that, following prolonged periods of high-intensity extraction, outcrop-style uranium deposits are severely depleted; consequently, future resource potential resides primarily in the deep crust or beneath thick overburden sequences. Particularly in typical granite-hosted metallogenic provinces such as the Zhuguang Mountain complex, mineralization is governed by intricate deep geodynamic processes, rendering the occurrence of ore bodies extremely subtle. Nevertheless, contemporary exploration practices reveal a significant paradox: superficial geological observations capture only the two-dimensional manifestations of the metallogenic system, failing to characterize its spatiotemporal evolution. Such cognitive limitations severely constrain the efficient assessment of concealed deposits, necessitating the urgent establishment of a novel quantitative prediction theory capable of penetrating shallow cover to elucidate deep metallogenic mechanisms (Chi et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e; Jin et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2022a\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e; Song et al. \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2023c\u003c/span\u003e; Yan et al. \u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Guan et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Guo et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2025a\u003c/span\u003e; Quiroga-Barriga et al. \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Yang et al. \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2025a\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR98\" class=\"CitationRef\"\u003e2025d\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Lai et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2026\u003c/span\u003e; Ruan et al. \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2026\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe essence of hydrothermal uranium metallogenesis lies in crustal fluid migration and focusing, a process fundamentally controlled by deep, cryptic fluid-conduit systems. Although surface-visible fault traces furnish geometric constraints on the structural framework, the paramount control on metallogenic fluid flux resides in the three-dimensional connectivity of fracture networks and their deep permeability architecture. Investigations in the Zhuguang Mountain region demonstrate that polyphase tectonic reactivation from the Indosinian to Yanshanian episodes induced differential lithospheric fracturing, generating three-dimensional structural damage zones that channel fluid upwelling and discharge. Reconstructing the deep permeability architecture from limited two-dimensional surface traces requires incorporating physical scaling laws and fractal geometry. Quantitative characterization of displacement-length relationships and fractal dimensions enables reconstruction of vertical fault penetration depths and spatial connectivity. This kinematic advancement over purely geometric description reveals that concealed metallogenic systems commonly exhibit statistical self-organization, with mineralization centers preferentially concentrating within discrete structural intensity thresholds, thereby providing a robust physics-based foundation for blind ore prediction (Aubert et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022a\u003c/span\u003e; Kim et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Poh et al. \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e2022a\u003c/span\u003e; Bonnetti et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Halld\u0026oacute;rsd\u0026oacute;ttir et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Luo et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Shi et al. \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Xue et al. \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Yu et al. \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Chang et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Liang et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Yang et al. \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2025b\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e2025a\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAlthough structural ore-control prediction has emerged as a pivotal tool for delineating exploration targets, conventional methodologies remain hampered by linear superposition assumptions and subjective empirical biases. Routine buffer analysis and index-overlay models often neglect nonlinear interactions and multicollinearity among geological variables and lack statistically rigorous criteria for anomaly recognition. Consequently, predictions suffer from pervasive background noise and fail to pinpoint deep targets with precision. The prevailing scientific bottleneck thus centers on constructing an objective, nonlinear, and statistically grounded quantitative evaluation paradigm (Chen et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Bark and Butcher \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2025a\u003c/span\u003e; Wu et al. \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Lai et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2026\u003c/span\u003e; Ruan et al. \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2026\u003c/span\u003e). To address this challenge, this study develops a data-driven, integrated framework: principal component analysis (PCA) reduces dimensionality across multiple structural parameters\u0026mdash;including kernel density, line density, and Euclidean distance\u0026mdash;to extract the first principal component of regional structural intensity, serving as the tectonic ore-control index (TCI). Anomalies are subsequently delineated objectively through the mean\u0026ndash;standard deviation method, leveraging the inherent Gaussian distribution of TCI values. Application in southern Zhuguang Mountain unequivocally demonstrates the superiority of this approach, with the prediction-area (P-A) plot yielding an area under the receiver operating characteristic curve (AUC) of 0.81. This result confirms that the model effectively captures spatial associations of concealed deposits, achieving a transformative shift from qualitative geological interpretation to rigorous quantitative statistical prediction.\u003c/p\u003e"},{"header":"2. Geological Setting","content":"\u003cp\u003eThe study area occupies the critical junction between the interior of the Cathaysia Block and the Nanling Metallogenic Belt, representing one of South China's most representative granite-hosted uranium provinces (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Its geological evolution transcends simple stratigraphic superposition; instead, it manifests as spatiotemporal coupling between deep-seated magmatic-thermal events and inherited structural frameworks, with polyphase tectonic reactivation constituting the defining hallmark. The Zhuguang Mountain pluton comprises a gigantic composite batholith formed through multistage Indosinian to Yanshanian magma emplacement, serving not only as a fertile uranium source but also as ideal brittle host rocks and thermal drivers for hydrothermal metallogenic systems. This exceptional mineralization potential stems from the region's protracted position at the dynamic transition between the Tethyan and paleo-Pacific tectonic domains\u0026mdash;a unique tectonic setting that subjected pre-existing fault systems to repeated mechanical inversion and structural reconfiguration throughout geological history (Tian et al. \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Hu et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Bu et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2025b\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRegional tectonic regime evolution profoundly governs stress-field reconfiguration trajectories (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Since the Mesozoic, variations in the subduction angle and velocity of the paleo-Pacific plate beneath Eurasia have driven South China through a dramatic shift from Indosinian compressional orogeny to Yanshanian lithospheric extension and thinning. This extensional regime triggered asthenospheric upwelling and marked elevation of crustal heat flow, thereby fueling widespread Yanshanian magmatism and deep fluid circulation. Microstructural evidence, including S-C fabrics and dynamic quartz recrystallization preserved within the Nanxiong fault zone, documents an early history of high-temperature sinistral ductile shearing; contemporaneous late Triassic (ca. 230\u0026thinsp;\u0026minus;\u0026thinsp;210 Ma) felsic dykes signal the onset of transition from ductile to brittle-ductile deformation (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Such progressive mechanical evolution sustained the long-term activity of fault zones as persistent crustal weakness zones, thereby establishing the prerequisite structural template for subsequent migration and focusing of metallogenic fluids (Wang et al. \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2022a\u003c/span\u003e; Yan et al. \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yang et al. \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhu et al. \u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2023b\u003c/span\u003e; Xu et al. \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e; Yao et al. \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhao et al. \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Cheng et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Ke et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Tan et al. \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe principal metallogenic episode (primarily Early Cretaceous, ca. 125\u0026thinsp;\u0026minus;\u0026thinsp;105 Ma) exerted direct control over the ore-conducting efficiency of fluid conduit systems through tectonic reactivation. During this interval, intense intraplate extensional dynamics reorganized the regional stress field, triggering pronounced transtensional reactivation of NE-trending basement faults while imparting extensional normal-fault character to SN-oriented structures. This differential reactivation generated high-permeability dilational jogs and extensive damage zones at fault intersections, thereby establishing three-dimensional fluid networks that linked deep uranium sources to shallow unloading domains. Contemporaneous mafic dyke emplacement further corroborates the exchange of heat from the deep mantle into the metallogenic system (Zhang et al. \u003cspan citationid=\"CR92\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e; Gong et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e; Aboayanah et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Jin et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Pichavant et al. \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Yin et al. \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Bu et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Zhao and Liu \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Consequently, uranium mineralization in southern Zhuguang Mountain fundamentally arises from structurally induced heterogeneous fluid flow and physicochemical trapping, wherein dilatational opening of faults under specific stress regimes and concomitant surges in fluid flux constitute the critical geological constraints for pinpointing the spatial distribution of concealed deposits (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eTo address the challenges of nonlinearity and uncertainty in predicting deep, concealed metallogenic systems, this study establishes a quantitative evaluation framework that integrates geometry, kinematics, and statistics. Transcending traditional empirical qualitative descriptions, the methodology adopts a composite framework integrating physical scaling laws, information-theoretic dimensionality reduction, and stochastic statistical processes. It aims to invert deep-crustal architecture from surface two-dimensional observations and to identify the statistical fingerprints of metallogenic anomalies objectively.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Quantification of crustal architecture: deep inversion via displacement-length scaling laws\u003c/h2\u003e \u003cp\u003eThe vertical extension capacity of crustal tectonic networks is a critical physical parameter for assessing ore-conducting efficiency; however, remote sensing interpretation of the surface retrieves only two-dimensional geometric traces of faults. To surmount this limitation and invert the three-dimensional spatial attributes of fracture systems, the displacement-length (\u003cem\u003eD\u003c/em\u003e-\u003cem\u003eL\u003c/em\u003e) fractal scaling law is introduced as the theoretical basis for deep architecture reconstruction. Modern rock mechanics and fault growth theory indicate that fracture system development is not a random process but a physical one adhering to self-organized criticality growth laws. Although classical linear elastic fracture mechanics (LEFM) typically predicts a power-law relationship between fault displacement/depth and length, vertical penetration of fault growth within granite batholiths, constrained by crustal rheological stratification, often exhibits specific scale effects (Cowie and Scholz \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1992\u003c/span\u003e; Cowie \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Cowie and Shipton \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Cooper et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Schultz et al. \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Bergen and Shaw \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Nicol et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Kolyukhin et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Lathrop et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Xu et al. \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023b\u003c/span\u003e). Drawing upon datasets comprising measured lengths (\u003cem\u003eL\u003c/em\u003e) of known faults and penetration depths (\u003cem\u003eD\u003c/em\u003e) revealed by boreholes and geophysical exploration in the Zhuguang Mountain area, a semi-logarithmic scaling model tailored to the regional structural rheological characteristics was established: \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.5\u0026times;lg(\u003cem\u003eL\u003c/em\u003e)\u0026thinsp;+\u0026thinsp;4.0 (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.85). This parameterized equation not only shows high statistical significance but also captures the self-similarity and energy-dissipation mechanisms that characterize the evolution from micro-fractures to macro-faults in the region. The model reveals that for every order-of-magnitude increase in fault length, vertical conduction capacity increases logarithmically rather than linearly, a phenomenon likely attributable to physical constraints imposed on downward fault propagation by the brittle-ductile transition zone. By employing this scaling law, calibrated using physical principles and empirical data, surface two-dimensional linear elements are transformed into structural-intensity proxies with vertical dimensionality. It facilitates the construction of a quasi-three-dimensional solid model that reflects the deep crustal permeability architecture, thereby providing a robust physical basis for identifying \"penetrative conduits\" that link deep uranium sources with shallow traps.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Signal extraction and dimensionality reduction: modeling tectonic intensity via PCA\u003c/h2\u003e \u003cp\u003eCrustal architecture controls metallogenic systems by coupling multidimensional spatial variables, including line density reflecting fluid permeability, intersection kernel density indicating structural complexity, and Euclidean distance representing transport proximity. Nevertheless, multi-source spatial data frequently contain substantial explanatory redundancy and random noise. This study employs PCA as the core algorithm, predicated on the scientific rationale of mapping correlated structural factors onto an orthogonal spatial basis via linear transformation, thereby \"extracting the signal from noise.\" Within this framework, the first principal component (PC1) transcends simple mathematical synthesis to represent the dominant mode of regional tectonic intensity, the primary geological driver governing hydrothermal fluid accumulation. Analysis of the eigenvector loading structure facilitates objective weighting of kernel density characterizing fluid focusing centers, line density characterizing fluid migration pathways, and distance factors characterizing fluid influence zones, while effectively eliminating the subjective uncertainty inherent in manual expert scoring. This unsupervised dimensionality reduction approach eliminates human bias inherent to traditional weighting methods, ensuring the objectivity and mathematical rigor of the evaluation model in characterizing the spatial heterogeneity of the crustal permeability field (Huang et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Jansson et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li and Qin \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Sun et al. \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zuo et al. \u003cspan citationid=\"CR105\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Rahman Ulfa et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Yang et al. \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e2025c\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Construction of tectonic ore-control index (TCI): quantitative characterization of crustal permeability field\u003c/h2\u003e \u003cp\u003eFollowing the physical quantification and dimensionality reduction of multidimensional structural parameters, this study constructs the TCI to transform discrete structural geometric information into a continuous quantitative representation of the crustal permeability field. Rather than relying on simple empirical superposition, TCI construction employs data-driven modeling based on PCA-derived PC1 scores. To capture multi-scale structural ore-controlling characteristics within the Zhuguang Mountain region, the model integrates three critical spatial variables: kernel density with a search radius of 2000 m, which reflects the spatial clustering effect of structural intersections; line density with a search radius of 5000 m, which characterizes the intensity of regional fracture network development; and Euclidean distance with a maximum threshold of 10,000 m, which delineates the potential range of fluid migration. These spatial parameters are rasterized and resampled via Geographic Information Systems (GIS) to construct a unified spatial data cube. Based on the eigenvector matrix extracted via PCA, PC1 serves as the statistical variable explaining the dominant contribution to regional structural variance, with its loading coefficients objectively determining weight allocation. Specifically, TCI is mathematically expressed as TCI\u0026thinsp;=\u0026thinsp;\u003cem\u003eα\u003c/em\u003e\u0026thinsp;\u0026times;\u0026thinsp;KD\u0026thinsp;+\u0026thinsp;\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;\u0026times;\u0026thinsp;LD\u0026thinsp;+\u0026thinsp;γ\u0026thinsp;\u0026times;\u0026thinsp;ED, where \u003cem\u003eα\u003c/em\u003e, \u003cem\u003eβ\u003c/em\u003e, and \u003cem\u003eγ\u003c/em\u003e correspond to the feature loadings of kernel density, line density, and Euclidean distance on PC1, respectively. This linear combination not only eliminates multicollinearity but also profoundly aligns with the source-transport-trap dynamics of hydrothermal metallogenic systems. Positive contributions from line and kernel densities reflect the control of high-permeability conduits and fluid-focusing centers, whereas the negative constraint imposed by Euclidean distance embodies the spatial law in which mineralization probability decays with increasing distance from faults. To eliminate dimensional discrepancies and enhance spatial comparability, the Min-Max Normalization algorithm maps the raw calculated TCI values to the dimensionless interval [0, 1], thereby generating the final continuous probability field. The physical significance of TCI lies in its role as a comprehensive geological proxy; it not only quantifies the connectivity of fracture networks and the extent of deep damage zones but also reveals the spatiotemporal modulation of crustal fluid flux and uranium precipitation by Indosinian to Yanshanian tectonic reactivation. High TCI values correspond to structural singularities characterized by high stress concentration, intense fracturing, and maximal fluid flux, whereas low TCI values correspond to relatively stable tectonic blocks. This quantitative framework transcends traditional qualitative descriptions and supports the development of predictive models grounded in physical laws and stochastic processes. Its application in analogous hydrothermal systems has significantly enhanced the precision and efficiency of concealed deposit exploration, providing a reproducible scientific paradigm for the sustainable assessment of deep resources (Mao et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Lou and Liu \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e2025b\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Statistical Anomaly Detection: Outlier Identification Based on Stochastic Processes\u003c/h2\u003e \u003cp\u003eThe identification of metallogenic prospect areas fundamentally entails detecting \"anomalous outliers\" within the geological fluid flux field. Grounded in spatial stochastic process theory, the generated TCI spatial field exhibits significant Gaussian behavior. This statistical order reveals the tectonic self-organization logic inherent within the metallogenic system. Within the present framework, the delineation of mineralization potential relies not on artificially imposed absolute thresholds but on scientific classification based on the statistical dispersion characteristics of a normal distribution. Adopting \u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e (mean plus two standard deviations) as the critical criterion for defining extremely high-potential zones statistically signifies the identification of \"statistical anomalies\"\u0026mdash;regions constituting a minimal proportion of the spatial field yet possessing decisive significance for mineralization. This evaluation paradigm, based on outlier detection via stochastic processes, precisely pinpoints singularity spaces characterized by surges in tectonic intensity. Validation using Receiver Operating Characteristic (ROC) and P-A curves yields an AUC of 0.81, demonstrating a high degree of coupling between these statistical anomaly zones and the spatial distribution of known deposits, thereby vigorously confirming the efficiency and reliability of data-driven statistical thresholds in revealing concealed mineralization traps (Hong \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Yousef et al. \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Shatnawi \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020b\u003c/span\u003e; Numminen et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Ibrar et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhou et al. \u003cspan citationid=\"CR103\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Spatial heterogeneity of crustal structural architecture\u003c/h2\u003e \u003cp\u003eQuantitative parameterization of the remote-sensing interpreted fracture network reveals significant spatial heterogeneity in the crustal structural architecture of southern Zhuguang Mountain. The distribution map of fracture cutting depths, inverted using fractal scaling laws (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea), shows that the NE-trending major faults, such as the Nanxiong Fault, exhibit the most significant vertical extension capacity; their theoretical penetration extends to the deep crust, making them regional conduits for fluid ascent. In contrast, the secondary fracture network displays shallower penetration depths, primarily functioning to regulate and distribute fluids. This framework receives further reinforcement from structural spatial density patterns. The kernel density map (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb) identifies multiple high-intensity structural intersection centers; these \"hotspots\" are distributed primarily in a beaded pattern along major fault zones, indicating critical nodes of local stress concentration and fluid focusing. Concurrently, the line density map (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec) clearly delineates a reticulate skeleton formed by the interlacing of NE- and SN-trending faults, where high-value zones not only cover the main fault belts but also extend laterally to form broad damage zones. The Euclidean distance field (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed) geometrically quantifies the decay gradient of fault influence, with low-value regions (proximal to faults) constituting advantageous spaces for metallogenic fluid migration. The heterogeneous distribution of these fundamental spatial parameters provides multidimensional physical constraints for the subsequent construction of the comprehensive ore-control model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Emergent statistical properties and the \"mineralization fingerprint\"\u003c/h2\u003e \u003cp\u003eGlobal statistical analysis of the constructed TCI field reveals that regional tectonic intensity obeys the ubiquitous self-organized criticality prevalent in natural systems. The frequency histogram of TCI values (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea) exhibits a pronounced unimodal pattern, with substantial conformity to a Gaussian distribution and slight positive skewness toward higher values. The statistical mean (\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;0.34) coincides closely with the histogram peak, defining the steady-state background tectonic field, whereas the pronounced long-tail structure on the right flank (TCI\u0026thinsp;\u0026gt;\u0026thinsp;0.61, corresponding to the \u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e interval) captures the statistical outliers (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This emergent statistical behavior implies that mineralization, as a low-probability geological event, preferentially localizes within structural singularities that deviate markedly from the background and occupy the extreme tail of the Gaussian distribution\u0026mdash;regions of exceptionally concentrated stress and fluid flux. PCA further dissects the intrinsic driving mechanism of this system, extracting a distinctive \"structural fingerprint\" for uranium mineralization. The loading structure of PC1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb) demonstrates that line density exerts overwhelming positive control (0.872), far surpassing kernel density (0.327), while Euclidean distance imposes a negative constraint (\u0026minus;\u0026thinsp;0.364) (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This mathematical relationship carries profound dynamic implications: in the Zhuguang Mountain granite-hosted uranium system, neither the mere presence of faults nor localized point-like intersections constitutes the primary ore-controlling factor; instead, fracture network connectivity and developmental intensity emerge as the decisive regulators of crustal permeability flux. This line-density-dominated regime underscores that fluids preferentially migrate and focus along highly interconnected structural corridors over long distances.\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\u003eStatistical classification of metallogenic potential and geological implications based on TCI thresholds\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" 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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThreshold Range\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTCI Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMetallogenic Potential Classification\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeological Interpretation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026gt; \u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026gt;\u0026thinsp;0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eClass I: Extremely High-Potential Zone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStructural core / main conduit: Characterized by intense fluid enrichment and severe fracturing.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eσ\u003c/em\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.48\u0026ndash;0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eClass II: High-to-Moderate Potential Zone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStructural subsidiary zone: Hosts fluid migration networks and developed secondary faults.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eσ\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.34\u0026ndash;0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eClass III: Low-Potential/Background Zone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWeak deformation zone: Exhibits minor structural influence and low mineralization probability.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026lt; \u003cem\u003e\u0026micro;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eClass IV: Non-Prospective Zone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStable block: Characterized by an absence of significant tectonic activity; effectively impermeable to fluid ingress.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\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\u003eEigenvectors and eigenvalues of the principal component analysis.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePC3\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKernel density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.327\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.878\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLine density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.423\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEuclidean distance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.904\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEigenvalue\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0022\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariance contribution (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e73.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCumulative variance (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e73.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e90.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Spatial Targeting and Deep Structural Coupling\u003c/h2\u003e \u003cp\u003eThe metallogenic prediction map delineated using the statistical anomaly threshold (\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) demonstrates striking spatial coupling between high-potential zones and the deep-seated major fault framework. Extremely high-potential zones do not distribute randomly; instead, they form distinct linear and knot-like patterns along the NE-trending Nanxiong Fault belt and its intersections with the SN-trending Niulan Fault belt. These high-TCI anomaly zones precisely delineate the surface projections of deep high-permeability damage zones, exhibiting remarkable coincidence with known typical uranium deposits such as Baishun and Renhua. Overlay analysis and ROC validation further quantify the model's predictive power. Although Class I targets occupy only approximately 5% of the total study area, they capture the vast majority of known ore occurrences. The P-A curve yields an AUC of 0.81, confirming an exceptionally high signal-to-noise ratio. This spatial precision unequivocally demonstrates that the TCI model not only identifies surficial mineralization outcrops but, more critically, illuminates the deep structural roots governing the emplacement of concealed orebodies. High-TCI domains represent vertical plumbing systems that sustained maximum fluid flux during tectonic reactivation episodes, efficiently linking deep uranium source regions to shallow physicochemical traps and enabling trans-crustal spatiotemporal coupling and focused precipitation of ore-forming components.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Discussion","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e5.1 From Geometry to Hydrodynamics: Physical Mechanisms of Permeability Regulation in High-Damage Zones\u003c/h2\u003e \u003cp\u003eThe spatially heterogeneous distribution of the TCI represents more than a mere mathematical projection of surface fault geometry; it fundamentally constitutes the surficial physical manifestation of deep-crustal hydrodynamic processes. Geological observations and numerical simulations consistently demonstrate that fault zones do not exist as singular geometric segments but rather as complex three-dimensional entities comprising a fault core flanked by damage zones characterized by intense fracture development. Rheologically, high-TCI anomaly regions\u0026mdash;particularly Class I targets exceeding the \u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e threshold\u0026mdash;correspond to high-permeability windows within the crust. Integrated with fracture-cutting-depth data inverted using fractal scaling laws, these domains represent more than mere two-dimensional structural intersections; they function as fractal conduits that penetrate the brittle-ductile transition zone. Under the intense Yanshanian extensional dynamics governing the Zhuguang Mountain region, these deep-seated fault systems underwent transtensional reactivation, inducing dilatancy within internal fracture networks and generating pronounced zones of low fluid potential. In accordance with fault-valve theory, this tectonic activation mechanism propels the rapid upwelling of deep, uranium-rich hydrothermal fluids along the vertical channels delineated by high TCI values. The dominant line-density characteristic of the TCI model further elucidates that fluid migration operates primarily through highly connected, fracture-controlled, channelized flow rather than porous flow. Upon the ascent of these high-temperature, high-pressure fluids into shallow, high-TCI structural dilatancy zones, abrupt pressure drops trigger boiling and phase separation, resulting in drastic physicochemical fluctuations that destabilize and precipitate uranyl complexes. Consequently, TCI anomaly zones precisely delineate the \"source-transport-trap\" coupling interfaces where fluid flux and energy dissipation are most concentrated. It validates the physical trajectory governing the transformation of structural configuration into hydrodynamic efficiency, establishing that structural physical complexity directly dictates both the efficiency of metallogenic fluid migration and the localization of mineralization (Henley and Berger \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Lan et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Poh et al. \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Sun et al. \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Liu et al. \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2023b\u003c/span\u003e; Petrov et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2025c\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Efficiency of the Mineral System: Statistical Convergence and Spatial Singularity\u003c/h2\u003e \u003cp\u003eAnalysis of the P-A curve provides a profound elucidation of the exceptional focusing efficiency inherent to the uranium metallogenic system in southern Zhuguang Mountain. Statistical validation shows that the TCI model achieves an AUC of 0.81, far surpassing the random-prediction baseline of 0.5. More critically, the steep rise of the curve within the low-area-percentage interval indicates that high-TCI zones, comprising only 30% of the total study area, capture approximately 75% of known deposits (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). This statistical signature carries significant metallogenic implications: it attests that ore-bearing fluids did not undergo extensive lateral dispersion within the crust during migration but were instead confined by the structural framework, thereby focusing within a select few high-permeability structural cores. This phenomenon, in which \"small volumes control large reserves,\" reflects the highly self-organized nature and nonlinear threshold characteristics of the metallogenic system. Only when TCI exceeds a specific critical value, statistically defined as \u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e, does rock permeability undergo an exponential surge, thereby creating effective fluid traps. Such spatial singularity aligns with self-organized criticality theory, suggesting that the evolution of metallogenic systems tends to constrain dispersed ore-forming elements forcefully onto structural nodes characterized by specific energy gradients. In exploration practice, this implies that targeting strategies can shift from broad-spectrum reconnaissance to \"precision-guided\" deep drilling focused on this critical 30% core area. This remarkably high capture efficiency not only validates the predictive robustness of the TCI model but also substantially reduces the trial-and-error costs and investment risks associated with exploring deep blind deposits, underscoring the significant economic value of quantitative prediction models.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Comparability and Generalizability: Shifting from Empirical Overlay to Statistical-Physical Paradigms\u003c/h2\u003e \u003cp\u003eCompared with conventional structural ore-control prediction approaches, the integrated \"fractal-PCA-statistical\" framework developed here exhibits marked methodological superiority. Traditional buffer analysis or simplistic Boolean overlay methods typically rely on linear assumptions, struggle to accommodate complex nonlinear interactions among structural variables, and use subjective, expert-derived weighting, resulting in predictions that lack comparability across regions. In stark contrast, the present study leverages PCA to objectively extract intrinsic modes of tectonic intensity, eliminating human bias and informational redundancy while establishing a unified statistical criterion for anomaly recognition grounded in Gaussian distribution theory. Crucially, this framework demonstrates broad geological generalizability. Its core logic\u0026mdash;deep architecture inversion via fractal geometry, dominant mode extraction through multivariate statistics, and anomaly detection via stochastic processes\u0026mdash;extends far beyond granite-hosted uranium systems and applies equally to other structurally controlled hydrothermal deposits, including orogenic gold and porphyry copper systems. Wherever mineralization is governed by fluid migration and focusing within crustal fracture networks, this quantitative paradigm can be readily transferred to diverse tectonic settings and commodity types by targeted adjustments to structural parameters and scaling relationships. Consequently, it delivers a replicable, standardized scientific toolkit for deep exploration of critical metals worldwide, marking a decisive paradigm shift from subjective empiricism to rigorously data-driven statistical-physical prediction.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis study constructs and validates an integrated quantitative evaluation framework that seamlessly couples fractal geometry, multidimensional spatial analysis, and unsupervised statistical learning to tackle the inherent nonlinearity and geological uncertainty in predicting deep concealed metallogenic systems. By incorporating displacement-length scaling laws, PCA-based dimensionality reduction, and stochastic-process-driven anomaly detection, the approach successfully inverts two-dimensional surface structural geometry into three-dimensional crustal permeability architecture, with robust performance demonstrated in the granite-hosted uranium province of Zhuguang Mountain. The principal conclusions are as follows:\u003c/p\u003e \u003cp\u003e(1) The study proposes and validates a TCI evaluation model that rigorously integrates geophysical constraints with data-driven inference. Through PCA dimensionality reduction of kernel density, line density, and spatial proximity metrics, the model objectively extracts the dominant mode of regional tectonic intensity. Eigenvector analysis reveals that fracture network connectivity\u0026mdash;reflected by a line-density loading of 0.87\u0026mdash;rather than isolated fault scale, constitutes the primary control on crustal permeability heterogeneity. This finding marks a paradigm shift from qualitative structural description to quantitative physical representation, providing a high-resolution digital proxy for deciphering source-transport-trap dynamics of hydrothermal fluids under polyphase tectonic reactivation.\u003c/p\u003e \u003cp\u003e(2) Statistical analysis uncovers pronounced self-organized criticality in regional structural evolution and mineralization response. The near-Gaussian distribution of TCI values illuminates nonlinear emergent behavior within the metallogenic system. An anomaly delineation scheme based on the Gaussian-derived threshold (\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;2\u003cem\u003eσ\u003c/em\u003e) not only successfully delineates deep high-permeability damage zones in the Zhuguang Mountain region but also achieves an AUC of 0.81 and remarkable focusing efficiency, whereby the top 30% of prospective area captures 75% of known deposits. These results confirm that uranium mineralization fundamentally manifests as a spatially singular response triggered when tectonic intensity exceeds a critical threshold, exhibiting strong statistical convergence and predictability.\u003c/p\u003e \u003cp\u003e(3) The methodological framework exhibits broad applicability and profound scientific value in predicting concealed deposits within complex structural domains. Unlike traditional approaches hampered by subjective expert weighting and surface observational limitations, the fractal-statistical paradigm extrapolates deep architecture via self-similar scaling laws with exceptional robustness, eliminating empirical bias. Transcending regional geological specificities, the model applies not only to granite-hosted uranium systems but also extends to structurally controlled hydrothermal deposits worldwide, including orogenic gold and porphyry copper systems. In summary, this study delivers a geologically constrained, mathematically robust quantitative prediction toolkit that significantly advances mineral exploration from empirical intuition to physics-informed statistical prediction, thereby elevating the scientific standard for the sustainable assessment of globally critical metal resources.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003ePrincipal component analysis \u0026nbsp;PCA\u003c/p\u003e\n\u003cp\u003eTectonic ore-control index \u0026nbsp;TCI\u003c/p\u003e\n\u003cp\u003ePrediction-area \u0026nbsp;P-A\u003c/p\u003e\n\u003cp\u003eArea Under the Receiver Operating Characteristic Curve \u0026nbsp;AUC\u003c/p\u003e\n\u003cp\u003eLinear elastic fracture mechanics \u0026nbsp;LEFM\u003c/p\u003e\n\u003cp\u003eFirst principal component \u0026nbsp;PC1\u003c/p\u003e\n\u003cp\u003eGeographic Information Systems \u0026nbsp;GIS\u003c/p\u003e\n\u003cp\u003eReceiver Operating Characteristic \u0026nbsp;ROC\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of competing interest\u003c/h2\u003e \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 \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003ethe Development Research Center of the China Geological Survey, Geological Survey Project numbers 121201004000150017-65, 121201004000160901-77, 121201004000172201-61, DD20190159-10; Guangdong Provincial Geological Joint Fund, General Project number 601145539054.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJianan Zhao: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing-original draft, Writing-review \u0026amp; editing. Yingru Pei: Investigation, Methodology, Software, Supervision, Validation, Visualization, Writing-review \u0026amp; editing. Chonghao Liu: Methodology, Software, Validation, Writing-review \u0026amp; editing.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis work was supported by the Development Research Center of the China Geological Survey [grant numbers 121201004000150017-65, 121201004000160901-77, 121201004000172201-61, DD20190159-10] and the Guangdong Provincial Geological Joint Fund (General Project) [grant number 601145539054].\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data presented in this article are publicly available as open-access resources. The supplementary materials also include tables of key calculation processes.\u0026nbsp;For further inquiries, researchers interested in the content may contact the corresponding author directly via email.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAboayanah KR, Abdelaziz A, Haile BF, Zhao Q, Grasselli G (2024) Evaluation of Damage Stress Thresholds and Mechanical Properties of Granite: New Insights from Digital Image Correlation and GB-FDEM. Rock Mech Rock Eng 57:4679\u0026ndash;4706. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s00603-024-03789-7\u003c/span\u003e\u003cspan address=\"10.1007/s00603-024-03789-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAubert I, Lamarche J, Richard P, Leonide P (2022) Imbricated structure and hydraulic path induced by strike slip reactivation of a normal fault. 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Sci China Earth Sci 67:2864\u0026ndash;2875. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s11430-024-1309-9\u003c/span\u003e\u003cspan address=\"10.1007/s11430-024-1309-9\" 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":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"earth-science-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"esin","sideBox":"Learn more about [Earth Science Informatics](http://link.springer.com/journal/12145)","snPcode":"12145","submissionUrl":"https://submission.nature.com/new-submission/12145/3","title":"Earth Science Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Structural mineralized control, fractal depth estimation, Principal Component Analysis, Tectonic Control Index, quantitative metallogenic potential assessment, Granite-hosted uranium deposit.","lastPublishedDoi":"10.21203/rs.3.rs-8881137/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8881137/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStructural fault frameworks strictly constrain hydrothermal uranium metallogenic systems, making the precise characterization of structural ore-controlling mechanisms decisive for the exploration of deep concealed mineral resources. However, conventional assessment methodologies typically remain confined to qualitative or semi-quantitative analyses of two-dimensional surface traces, failing to quantify deep three-dimensional fault architectural attributes effectively. Furthermore, processes involving multi-source information fusion frequently suffer from biases inherent in subjective weighting schemes. To surmount these limitations, this research establishes a novel quantitative evaluation framework that integrates three-dimensional fault geometric characteristics with multivariate statistical analysis. Using the typical granite-hosted uranium field in the southern Zhuguang Mountain region of Northern Guangdong, South China, as a case study, the investigation initially employs the theoretical fault-displacement-length fractal scaling law to quantitatively invert fault penetration depths, thereby extending structural elements from planar representations into the volumetric domain. Subsequently, the study selects estimated fault depth, fault linear density, fault intersection kernel density, and Euclidean distances to faults and intersections as critical spatial parameters. Principal Component Analysis deciphers the intrinsic correlation structures among these multidimensional variables to objectively determine factor weights, facilitating the construction of a comprehensive Tectonic Control Index model. Results demonstrate that favorable metallogenic zones, delineated using a statistical threshold method based on the index's typical distribution characteristics, accurately capture the spatial distribution patterns of known deposits. The core innovation lies in establishing a new paradigm for the quantitative characterization of structural controls that fuses fractal three-dimensional depth estimation with data-driven objective weighting, significantly enhancing predictive capabilities for spatially locating deep, concealed mineralization networks. These findings provide a scientifically robust, data-driven solution for the deep, synergistic exploration of concealed deposits within complex geological settings.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"Emergent Tectonic Control on Deep Critical Mineral Systems: A Fractal- Statistical Paradigm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-25 08:55:30","doi":"10.21203/rs.3.rs-8881137/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"333590312829828861071189698675625826700","date":"2026-05-12T00:12:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"72983647341609495248779729588666904575","date":"2026-05-11T06:39:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"320478999162138230998471211012529276791","date":"2026-05-11T01:00:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"139706117953880526654603959707883235999","date":"2026-05-10T14:26:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"290459409934970601679333202267622657843","date":"2026-05-10T05:49:46+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-27T19:32:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"136962213445750146122238799243469237772","date":"2026-02-21T14:36:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"88132547305311133266733737932121680635","date":"2026-02-21T09:26:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-19T13:24:45+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-19T13:22:34+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-16T23:49:23+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth Science Informatics","date":"2026-02-14T15:35:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"earth-science-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"esin","sideBox":"Learn more about [Earth Science Informatics](http://link.springer.com/journal/12145)","snPcode":"12145","submissionUrl":"https://submission.nature.com/new-submission/12145/3","title":"Earth Science Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"9c565001-c0dc-4ff1-8b69-488219d7a6df","owner":[],"postedDate":"February 25th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"333590312829828861071189698675625826700","date":"2026-05-12T00:12:36+00:00","index":75,"fulltext":""},{"type":"reviewerAgreed","content":"72983647341609495248779729588666904575","date":"2026-05-11T06:39:22+00:00","index":74,"fulltext":""},{"type":"reviewerAgreed","content":"320478999162138230998471211012529276791","date":"2026-05-11T01:00:52+00:00","index":72,"fulltext":""},{"type":"reviewerAgreed","content":"139706117953880526654603959707883235999","date":"2026-05-10T14:26:58+00:00","index":71,"fulltext":""},{"type":"reviewerAgreed","content":"290459409934970601679333202267622657843","date":"2026-05-10T05:49:46+00:00","index":70,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-02-25T08:55:30+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-25 08:55:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8881137","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8881137","identity":"rs-8881137","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}