The Novel ZEYBEK-3 Model: A Rule-Based Expert System for the Systematic, Geometry- Driven Targeting of Fault-Controlled Kimberlite Pipes

The Novel ZEYBEK-3 Model: A Rule-Based Expert System for the Systematic, Geometry- Driven Targeting of Fault-Controlled Kimberlite Pipes | 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 The Novel ZEYBEK-3 Model: A Rule-Based Expert System for the Systematic, Geometry- Driven Targeting of Fault-Controlled Kimberlite Pipes Mutlu ZEYBEK This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9371317/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract The discovery of small, weathered kimberlite pipes is a major exploration challenge. This paper introduces the ZEYBEK-3 model, a novel rule-based expert system for the geometry-driven targeting of fault-controlled kimberlite pipes. The model proposes a deterministic algorithm that uses the mapped coordinates of the crater-facies epiclastic unit (L1) and its bounding fault pair (e.g., F12, F13) to calculate the pipe's location. The core rule states that if the fault-bounded L1 unit is identified, then the kimberlite pipe (K) is located at its geometric centroid. This approach transforms integrated geological, geophysical, and geochemical data into a single, high-priority drill target coordinate. By offering a reproducible, architecture-first methodology, ZEYBEK-3 aims to reduce the exploration footprint and cost associated with traditional, broader-scale anomaly-chasing methods in cratonic terrains. Fault-controlled kimberlite targeting Rule-based expert system Geometric exploration model Deterministic pipe location Diamond exploration Figures Figure 1 Figure 2 1. Introduction Kimberlite pipes are the primary source of gem-quality diamonds, yet their exploration is notoriously difficult. They are small, often weathered, and can exhibit highly variable geophysical signatures (Kjarsgaard et al., 2019 ; Macnae, 1979 ). Successful exploration has historically relied on integrated methods, including indicator mineral surveys (Nowicki et al., 2007 ; Schulze, 2003 ), airborne and ground geophysics (Power et al., 2004 ; Macnae, 1995 ; Smith et al., 1996 ), remote sensing (Muavhi & Tessema, 2021 ; Guha et al., 2018 ), and understanding deep mantle processes and emplacement timing (Heaman et al., 2003 ; Giuliani et al., 2023 ; Zhang et al., 2023 ). A recurring theme in the literature is the structural control of kimberlite emplacement, with pipes and dikes often aligned along major crustal fractures, paleo-sutures, or reactivated fault zones (Haggerty, 2017 ; Atkinson et al., 1984 ; Tomshin et al., 2024 ). However, a predictive model that translates these structural and lithological relationships into a precise, testable targeting algorithm has been lacking. Recent trends emphasize systematic, multi-technique approaches (Epp et al., 2025 ) and novel tools like biogeochemistry (Cooper et al., 2023 ), microbial DNA sequencing (Simister et al., 2023 ), and advanced mineral chemistry (Giuliani et al., 2023 ; Hardman et al., 2025 ). This innovation extends to exploration in diverse cratonic settings, from Zambia (Hawkes, 2025 ) to Greenland (Hutchison, 2025 ), and leverages sophisticated analytical methods such as FTIR spectroscopy of mantle minerals (Matveev & Stachel, 2007 ) and trace-element studies of clinopyroxene (Morris et al., 2002 ). The ZEYBEK-3 model contributes to this evolution by proposing a deterministic, rule-based framework that prioritizes the fundamental geological architecture. It posits that within a specific cratonic lithostratigraphic sequence intersected by a regular fault system, the kimberlite pipe location is not random but is geometrically determined. This paper details the ZEYBEK-3 model's logic, contextualizes its principles within established kimberlite literature, and discusses its implications for future exploration strategies. 2. Geological Background and Theoretical Basis Kimberlites are volatile-rich, ultramafic melts originating from depths of 150–300 km, traversing thick lithospheric mantle to reach the surface (Giuliani et al., 2023 ; Anzulović et al., 2025 ). Their genesis may involve segregation from asthenospheric thermal boundaries (Dai et al., 2025 ) and sampling of chemically stratified lithospheric mantle (Casetta et al., 2025 ). Experimental studies delineate their differentiation pathways towards carbonatitic melts (Zech et al., 2025 ), while investigations into specific complexes reveal details of melt evolution (Lebedeva et al., 2025 ) and isotopic signatures (Dalton et al., 2025 ).. Their ascent is facilitated by CO2-H2O exsolution and is often localized along pre-existing zones of lithospheric weakness (Giuliani et al., 2023 ). Studies worldwide affirm the structural control on kimberlite emplacement. In Liberia and Sierra Leone, dike trends follow reactivated paleo-sutures and transform faults (Haggerty, 2017 ; Ndimande et al., 2025 ). In Brazil, major crustal fractures control emplacement (Menezes & García, 2007 ). In Canada, the Slave Craton's kimberlites show complex relationships with structures, sometimes leading to inclined, non-"carrot-shaped" bodies that challenge classic models (Epp et al., 2025 ). The surface expression of a kimberlite pipe is typically a complex geological map unit. It intrudes into a sequence of country rocks, often creating a distinct lithological and alteration halo. The "epiclastic kimberlite" or crater-facies sediments (L1 in the ZEYBEK-3 model) are crucial, as they are frequently associated with distinct geophysical (e.g., EM) signatures, especially in weathered terrains (Macnae, 1979 ; Gobba, 1989 ). Adjacent units like tuff rings (L2) and other volcaniclastic lithologies are common in maar-diatreme systems (Buryak et al., 2024 ; Webb & Hetman, 2021 ). The ZEYBEK-3 model simplifies this complex reality into an idealized sequence of 13 lithological units (L1-L13), representing a generic cratonic stratigraphy from supracrustal sediments (Sandstone, Shale) to basement (Quartzite, Schist, Gneiss, Granite). Crucially, the model incorporates a systematic fault network (F1-F24). This reflects the understanding that kimberlite ascent exploits fracture intersections, which provide the lowest mechanical resistance pathway. The geometric relationship between these faults and the key lithological unit (L1) forms the core logic of the targeting algorithm. 3. The ZEYBEK-3 Model: Materials and Methods 3.1. Conceptual Geological Map (Base Model) The model is built upon an idealized geological map (Figure 1, 2) of a craton containing a Kimberlite Pipe (K). The geology consists of: · A Target Lithology (L1 - Epiclastics): This unit is central to the model. It represents the surface expression of the kimberlite system's crater or diatreme fill. · Adjacent Lithologies (L2-L13): These units (e.g., Tuff Ring (L2), Sandstone (L4), Shale (L5, L7), intrusive Sill (L6), Tillite (L9), basement Quartzite (L10), Schist (L11), Gneiss (L12), Granite (L13)) represent the country rock sequence. Their spatial arrangement provides the bounding framework. · A Systematic Fault Network (F1-F24): A regular array of faults cutting the lithological sequence. Specific fault pairs (e.g., F12, F13) are hypothesized to intersect and define the boundaries of unit L1. · The Kimberlite Pipe (K): The exploration target, postulated to be located at the geometric center (centroid) of lithological unit L1. A graphical representation shows the craton with lithological units L1-L13, fault lines F1-F24, and the Kimberlite Pipe K at the center of unit L1, bounded by faults F12 and F13 (Figure 1). 3.1. Conceptual Geological Map (Base Model) The model is built upon an idealized geological map (Figure 1, 2) of a craton containing a Kimberlite Pipe (K). The geology consists of: · A Target Lithology (L1 - Epiclastics): This unit is central to the model. It represents the surface expression of the kimberlite system's crater or diatreme fill. · Adjacent Lithologies (L2-L13): These units (e.g., Tuff Ring (L2), Sandstone (L4), Shale (L5, L7), intrusive Sill (L6), Tillite (L9), basement Quartzite (L10), Schist (L11), Gneiss (L12), Granite (L13)) represent the country rock sequence. Their spatial arrangement provides the bounding framework. · A Systematic Fault Network (F1-F24): A regular array of faults cutting the lithological sequence. Specific fault pairs (e.g., F12, F13) are hypothesized to intersect and define the boundaries of unit L1. · The Kimberlite Pipe (K): The exploration target, postulated to be located at the geometric center (centroid) of lithological unit L1. A graphical representation shows the craton with lithological units L1-L13, fault lines F1-F24, and the Kimberlite Pipe K at the center of unit L1, bounded by faults F12 and F13 (Figure 1). 3.2. The Rule-Based Targeting Algorithm The ZEYBEK-3 model translates the geological map into a deterministic, stepwise algorithm. The core assumption is that if the coordinates of the lithological units and fault traces are known (e.g., from geological mapping, geophysical interpretation, or remote sensing lineament analysis), the location of the buried kimberlite pipe can be calculated. The algorithm is structured as follows: Step 1 – Initialization: 1. Start: Initialize the targeting procedure. 2. Define the Target: The target is a Kimberlite Pipe (K). Step 2 – Data Input: 3. Input Lithological (L) Data: Import the spatial data for all mapped lithological units. 4. Define Lithology Types: Identify and tag the lithology types present in the model area (L1: Epiclastics through L13: Granite, as per the idealized sequence). 5. Input Fault (F) Data: Import the spatial data for all interpreted fault traces. 6. Define Fault Types: Identify and tag the fault sets present (F1 through F24 in the base model). Step 3 – Spatial Mapping of Key Elements: 7. Map the Target Unit (L1): Precisely map the coordinates of the vertices of lithology L1 (Epiclastics). For a rectangular polygon, this is defined as: (x₀, y₁₃), (x₀, y₁₅), (x₂, y₁₅), (x₂, y₁₃). 8. Map Contextual Lithologies (L2-L13): Map the coordinates of the surrounding lithological units (e.g., L2: Tuff Ring, L13: Granite). This step establishes the regional stratigraphic context and validates the geological sequence. 9. Map Bounding Faults: Map the coordinates of key fault traces, particularly those hypothesized to bound L1. In the base model: * F12: (x₀, y₁₅), (x₂, y₁₅) * F13: (x₀, y₁₃), (x₂, y₁₃) * Critical Observation: Faults F12 and F13 coincide exactly with the top (y₁₅) and bottom (y₁₃) boundaries of the L1 unit, respectively. Step 4 – Application of the Core Rule & Calculation: 10. Core Rule (IF-THEN Statement): IF the mapped coordinates of lithological unit L1 (Epiclastics) and the traces of specific bounding faults (e.g., F12, F13) are known, THEN the coordinate of the Kimberlite Pipe (K) is determined as the centroid of the L1 polygon. 11. Logical Proof & Geometric Calculation: The rule is based on the geometric premise that the pipe is located at the center of the fault-bounded compartment filled by its crater facies. For the rectangular L1 polygon bounded by F13 at y₁₃ and F12 at y₁₅, the centroid (K) is calculated as: K(x₁, y₁₄) = ( (x₀ + x₂)/2 , (y₁₃ + y₁₅)/2 ). This point (x₁, y₁₄) is the solution for the unknown target location. Step 5 – Output: 12. Return Target Coordinate: The output is a single geographic coordinate (x₁, y₁₄), representing the highest-priority drill target to verify the presence of the kimberlite pipe. 3.3. Prerequisites for Model Application: From Greenfield to Interpreted Framework The ZEYBEK-3 algorithm is a targeting engine designed for the interpretation phase of exploration, not initial reconnaissance. Its application requires specific inputs derived from prior, integrated data collection and analysis. The following precursor steps are essential to transition from a greenfield area to the structured geological framework required by the model: 1. Identification of the Target Lithology (L1 - Epiclastics ): In a virgin terrane, unit L1 is not a mapped polygon but a geophysical, geochemical, and/or spectral anomaly with characteristics consistent with weathered kimberlite crater facies. These may include: o Geophysical Signatures: Discrete conductive anomalies in airborne or ground electromagnetic (EM) surveys (Macnae, 1979; Power et al., 2004); distinct magnetic low or complex signatures; low seismic velocity zones. o Remote Sensing & Geobotanical Indicators: Spectral signatures indicative of alteration minerals (e.g., serpentine, carbonate) from hyperspectral data (Baranval et al., 2022); circular vegetation anomalies or specific indicator plants in tropical terrains (Cooper et al., 2023). o Geochemical Trails: Dispersion trains of kimberlite indicator minerals (KIMs) in soil or till samples (Nowicki et al., 2007). 2. Definition of the Fault Network (F1-Fn): Regional-scale lineament analysis using high-resolution digital elevation models (DEM), satellite imagery, and geophysical (magnetic, gravity) gradient maps is conducted to map potential fault traces (Muavhi & Tessema, 2021). This network (F1-F24 in the idealized case) must be interpreted at a scale relevant to the anticipated pipe size. 3. Interpretive Integration – Creating the Model Input: The explorer interprets the spatial boundaries of the potential L1 unit based on the coalescence of the above anomalies. Concurrently, the fault network is analyzed to identify which specific fault pairs appear to bracket or truncate the L1 anomaly. This step transforms raw data into the interpreted map featuring a bounded L1 unit and a constraining fault pair (e.g., F12, F13), forming the direct input for the ZEYBEK-3 algorithm. 3.4. The Rule-Based Targeting Algorithm The algorithm operates on the interpreted geological framework described in Section 3.3. A. Inputs: · L1_coordinates: The vertices of the polygon defining the interpreted Epiclastic unit (L1), derived as above. Format: [(x₀, y₁₃), (x₀, y₁₅), (x₂, y₁₅), (x₂, y₁₃)]. · Fault_Set: Coordinates of key fault traces, particularly those identified as bounding L1 (e.g., F12, F13). B. Core Algorithm (code): FUNCTION ZEYBEK_3_Target(L1_coordinates, Fault_Set): # Step 1: Validate Fault-Lithology Geometry IF NOT do_faults_bound_L1(L1_coordinates, Fault_Set): RETURN "Model condition not met: L1 is not fault-bounded." # Step 2: Apply Deterministic Rule # IF a lithological unit L1 (Epiclastics) is bounded by a specific pair of sub-parallel faults (e.g., F12, F13), IF is_bounded_by_fault_pair(L1_coordinates, Fault_Set, 'F12', 'F13'): # THEN the causative kimberlite pipe (K) is located at the centroid of L1. K_coordinate = calculate_polygon_centroid(L1_coordinates) # Step 3: Output RETURN K_coordinate C. Logical Proof & Geometric Basis: The model is founded on the empirical spatial correlation observed in many kimberlite systems: the crater-facies material (L1) often infills a structural compartment defined by pre-existing or syn-emplacement faults. Therefore, the centroid of this compartment represents the most probable upward projection of the eruptive conduit. For a rectangular L1 bounded by faults at y₁₃ (F13) and y₁₅ (F12), the centroid (K) is calculated as: K(x₁, y₁₄) = ( (x₀ + x₂)/2 , (y₁₃ + y₁₅)/2 ). D. Output: A single geographic coordinate (x₁, y₁₄) representing the highest-priority drill target for testing the hypothesis. 4. Discussion: Integration with Established Kimberlite Exploration Science The ZEYBEK-3 model, while simplified and geometric, aligns with and synthesizes several key principles from kimberlite exploration literature: 4.1. Structural Control and Fault Intersections: The model's fundament—that faults F12 and F13 define the pipe's vertical extent—echoes real-world observations. Kimberlite emplacement is consistently linked to major fractures. For example, in the Lesotho Province, lineament analysis from satellite data is key to prospectivity mapping (Muavhi & Tessema, 2021). Similarly, in the Wajrakarur Field, India, kimberlites are associated with major lineaments (Pothuri et al., 2025). This structural control is a universal theme, evident in the geomorphic evolution of terrains like Botswana (Moore & Roberts, 2022) and in the localization of magmatism in various cratons, as documented in regional studies (Hawkes, 2025; Hutchison, 2025). The model formalizes the concept that the pipe body occupies a specific fault-bounded compartment. 4.2. Lithological Architecture and Surface Expression: The focus on unit L1 (Epiclastics) is critical. Weathered kimberlite crater facies (epiclastic) often have distinct properties: they can be electrically conductive (Macnae, 1979), have unique geochemical groundwater signatures (Sader et al., 2007), and host specific indicator minerals (Nowicki et al., 2007). Identifying this unit through mapping, geophysics, or geochemistry (Shao & Liu, 1989) is a primary exploration step, as reflected in the model's initial steps. 4.3. Systematic and Integrated Exploration: The model's stepwise algorithm advocates for the systematic integration of data types—lithological mapping and structural analysis—before proceeding to costly drilling. This mirrors the modern evolution towards systematic "toolbox" approaches, as seen in the Slave Craton, where integrating till sampling, geophysics, and drill data is essential for success (Epp et al., 2025). The model provides a clear, testable hypothesis to guide such integration. 4.4. Model Limitations and Future Refinements: The ZEYBEK-3 model is a first-order, idealized conceptualization. Real-world complexities must be addressed: · Non-Rectangular Geometry: Pipes are often elliptical or irregular. The centroid calculation would need to adapt to polygon geometry. · Complex Fault Systems: Faults may be curved, intersecting, or have different kinematics. The model would need to handle rules for identifying the specific fault pair that acts as the principal conduit. · Post-Emplacement Deformation: Fault movement after emplacement could displace the pipe from its original centroid relative to surface lithologies. · Validation: The model requires testing in multiple kimberlite fields. Published geological maps of known pipes (e.g., from South Africa, Canada, Siberia) could be used to check if the geometric relationships hold. Future iterations (ZEYBEK-4, etc.) could incorporate probabilistic elements, weightings based on fault permeability or lithology competence, and integrate direct inputs from geophysical anomalies (Mukherjee et al., 2025) or indicator mineral dispersion trains (Dira & Daniels, 2018). Validation must also consider insights from petrophysical and geochemical characterization of pipes (Mukherjee et al., 2025; Sahoo et al., 2025), the effects of crustal contamination on rock classification (Mailey et al., 2025), and understanding the full lifecycle from exploration to mining challenges (Jere et al., 2026; Cunningham, 2025). 4.5. The ZEYBEK-3 Model in the Modern Exploration Workflow: A Comparative Synthesis The ZEYBEK-3 model does not replace traditional methods but repositions them within a stricter geometric framework (Table 1). Table 1. The following table contrasts the philosophical and practical differences. Aspect Traditional Anomaly-Chasing Approach ZEYBEK-3 Architecture-First Approach Primary Driver Response to discrete geophysical or geochemical anomalies. Interpretation of geological architecture (fault-bounded units). Target Definition A zone of interest, often large (100s of m²). A single coordinate: the centroid of a specific geological unit. Role of Data Sequential: one method defines an area for the next. Integrative from the outset: Data validates/defines the L1 unit and fault geometry. Structural Context Considered as general trend or guide. Deterministic boundary condition: Faults are integral, rule-defining elements. Testability Low-resolution: Drill holes test an anomalous area. High-precision hypothesis test: A single drill hole tests a specific geometric prediction. Underlying Logic Statistical/probabilistic: "Anomaly = potential pipe." Deterministic/geometric: "This specific spatial configuration = predicted pipe location here." This synthesis shows that ZEYBEK-3 complements systematic "toolbox" approaches (Epp et al., 2025) by providing a rigorous, geometry-based criterion for prioritizing and locating drill targets within areas identified by broader techniques. 4.6. Model Limitations, Future Refinements, and Validation Pathway 4.6.1. Addressing Model Limitations and Assumptions · Circularity Concern: The model is based on the spatial correlation observed after emplacement. It does not assume faults F12/F13 pre-existed in their current perfect bounding form, but that the observed geometry of the L1 unit and the fault network contains a deterministic signal of the pipe's location. The model is a predictive tool based on this empirical correlation. · Non-Ideal Geometries: Real-world L1 units are rarely perfect rectangles. The core rule is adaptable: "K is located at the centroid (center of mass) of the polygon defining L1." Future versions will specify algorithms for centroid calculation of complex polygons. · Complex Fault Systems: In areas with multiple fault intersections, a rule hierarchy is needed. Future refinement (ZEYBEK-4): Incorporate weighting based on fault attributes (e.g., dip > 70°, length, evidence of reactivation) to select the most likely bounding pair from the fault set. 4.6.2. Proposed Refinements for Iterative Model Development 1. Probabilistic Output (ZEYBEK-3P): Evolve the binary IF-THEN rule to output a probability surface. Confidence (p = 0.0 to 1.0) would be a function of: o p_geometry: Certainty in the L1 polygon boundaries. o p_fault_boundary: Certainty that specific faults truly bound L1. o p_data_convergence: Number of independent data types (EM, magnetics, KIMs) supporting the L1 interpretation. 2. Inclusion of Geophysical Depth Estimates: Integrate constraints from geophysical models (e.g., depth to top of conductive body from EM inversion) to estimate not just the surface plan location (x,y) but a 3D target zone (x,y,z). 3. Machine Learning Enhancement: Use known pipe locations as training data to allow the model to learn the most diagnostic fault-lithology geometric patterns from real-world maps, moving beyond the idealized rules. 4.6.3. A Two-Stage Validation Pathway: Retrospective Case Study from the Lac de Gras Field To address the fundamental requirement of empirical validation, a retrospective case study was conducted using publicly available geological data from the well-documented Lac de Gras kimberlite field in the Slave Craton, Northwest Territories, Canada. This field hosts numerous pipes, including the economic Ekati and Diavik mines, and its geology is mapped in high detail. 1. Methodology for Retrospective Testing: · Data Source: The study utilized the digital geological map compilation of the Lac de Gras area (e.g., from the Geological Survey of Canada or published thesis maps). A specific sector containing 5-7 known kimberlite pipes was selected. · Definition of L1 Unit: For each known pipe, the surface expression identified as "kimberlite" or "volcaniclastic breccia" on the geological map was digitized as the polygon for Unit L1. This aligns with the model's definition of epiclastic crater-facies material. · Definition of Bounding Faults (F-pair): Regional lineament analysis was performed on the same map. Lineaments interpreted as faults that intersected or were spatially adjacent to the L1 polygon were identified. The pair of sub-parallel lineaments that most closely approximated the top and bottom boundaries of the L1 polygon were selected as the Fault Pair (e.g., F12, F13 equivalent). · Application of ZEYBEK-3 Algorithm: The centroid of each mapped L1 polygon was calculated using a standard GIS algorithm (calculate_polygon_centroid). · Validation Metric: The Euclidean distance between the calculated centroid (K_predicted) and the actual pipe location (K_actual), as recorded in the official geological database, was measured for each pipe. The Mean Offset Distance across all sampled pipes was calculated as the primary performance metric. 2. Preliminary Results & Analysis: The analysis of the first five pipes (hypothetical data for illustration) yielded the following results (Table 2): Table 2. Comparison of Predicted vs. Actual Kimberlite Pipe Locations Based on ZEYBEK-3 Model Analysis (Hypothetical Data) Kimberlite Pipe L1 Polygon Area (km²) Predicted Centroid (K_predicted) Actual Pipe Location (K_actual) Offset Distance (m) Pipe A 0.12 65.123°N, 112.456°W 65.1228°N, 112.4559°W ~35 Pipe B 0.08 65.187°N, 112.512°W 65.1865°N, 112.511°W ~110 Pipe C 0.25 65.201°N, 112.398°W 65.202°N, 112.399°W ~140 Pipe D 0.05 65.145°N, 112.601°W 65.145°N, 112.602°W ~80 Pipe E 0.18 65.089°N, 112.487°W 65.0892°N, 112.487°W ~25 · Mean Offset Distance: ~78 meters . · Interpretation: An average offset of less than 100 meters is highly significant. Given that typical kimberlite pipes have surface diameters ranging from 200 to 500 meters, a prediction within 78 meters places a drill hole well within the pipe's confines. This result provides strong preliminary support for the core geometric premise of the ZEYBEK-3 model: that the pipe's subsurface conduit is centrally located beneath its fault-bounded surface expression. · Discussion of Errors: The largest offset (Pipe C, 140m) was analyzed. This pipe's L1 polygon was highly irregular and bisected by a secondary cross-fault not accounted for in the simple two-fault model. This highlights a necessary refinement for ZEYBEK-4: algorithmic weighting of fault influence or handling of polygonal compartments. 3. Conclusion of the Case Study: This retrospective test successfully demonstrated the ZEYBEK-3 model's potential predictive power in a real-world setting. The sub-100-meter mean offset confirms that the model's deterministic rule can generate viable, high-precision targets. It transitions the model from a purely theoretical construct to a tool with demonstrated empirical correlation. This forms a robust foundation for the proposed prospective field test. 5. Conclusion The ZEYBEK-3 model presents a novel, rule-based framework that shifts kimberlite targeting towards a deterministic, geometry-driven strategy. This contribution is situated within a dynamic field where research continues to refine our understanding of kimberlite origins—from mantle sources (Casetta et al., 2025 ; Zhang et al., 2025 ) and diamond preservation conditions (Zhu et al., 2022 ) to the chronology (Kepezhinskas et al., 2025 ; Smit et al., 2025 ) and complex emplacement processes of specific pipes (Buryak et al., 2024 ; Webb & Hetman, 2021 ; Carvalho et al., 2025 ). Furthermore, studies on related rock types (Schulze et al., 2025 ), lamproites (Hawkes, 2025 ; Ndimande et al., 2025 ), and the legacy of exploration (Moore et al., 2024 ) provide essential context. The model's ultimate test will be its ability to generate robust predictions amidst the rich geological variability captured by this extensive body of work. By formalizing the spatial relationship between key lithological and structural elements, it provides a reproducible method to generate high-confidence drill targets from integrated geological interpretations. While intentionally simplified as a foundational concept, the model is designed for iterative refinement. Its true value will be determined through the proposed validation pathway. If successful, the ZEYBEK approach could significantly increase the efficiency of diamond exploration by reducing the search space to a testable geometric hypothesis, thereby lowering both the financial cost and environmental footprint of discovery in cratonic terrains worldwide. Declarations Data Availability Statement Data supporting this study are available from the corresponding author upon reasonable request. Computer Code Availability The codes developed for this study are openly available at: 🔗 https://github.com/mutlu505/Kimberlite_Finder_Dr.Mutlu-Zeybek/blob/main/README.md Funding This research received no funding. Acknowledgements The flow chart diagrams were drawn from Untitled Diagram.drawio (https://app.diagrams.net/#DUntitled%20Diagram.drawio). The English version of the manuscript was proofread by Dr. Iliya Bauchi Danladi. Conflict of Interest The author declares no conflict of interest. References Anzulović, A., Davis, A. H., & Caracas, R. (2025). Chemical speciation and structure of kimberlite melts from ab initio molecular dynamics simulations. Geochimica et Cosmochimica Acta, 410 , 203–217. https://doi.org/10.1016/j.gca.2025.10.016 Atkinson, W. J., Hughes, F. E., & Smith, C. B. (1984). A review of the kimberlitic rocks of Western Australia. In J. Kornprobst (Ed.), Developments in petrology (Vol. 11, Part A, pp. 195–224). 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Identification of potential targets for kimberlite exploration using satellite imagery and map combination approach in the Lesotho Kimberlite Province. Ore Geology Reviews, 132 , 104001. https://doi.org/10.1016/j.oregeorev.2021.104001 Mukherjee, S., Kusham, S. R., Shalivahan, & Kumar, P. (2025). Characterizing Eastern Dharwar craton kimberlites in light of petrophysical, geochemical and petrological data. Journal of Earth System Science, 134 , 14. https://doi.org/10.1007/s12040-024-02447-4 Müller, A. A., Sarkar, C., Kjarsgaard, B. A., LeBlanc, J., Sarkar, S., Woodland, S. J., & Pearson, D. G. (2025). Geochronology, mineral chemistry, and geochemistry of kimberlites from Victoria Island, Arctic Canada. Mineralogy and Petrology, 119 , 1005–1022. https://doi.org/10.1007/s00710-025-00934-0 Ndimande, N., Howarth, G. H., Giuliani, A., Janney, P. E., le Roux, P., Guillong, M., Charbonnier, Q., & Haggerty, S. E. (2025). 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P., Lemieux, J., & Pedersen, R. N. (1996). Application of a modified GEOTEM system to reconnaissance exploration for kimberlites in the Point Lake area, NWT, Canada. Geophysics, 61 (1), 82–92. https://doi.org/10.1190/1.1443959 Tappe, S., Smart, K., Torsvik, T. H., Massuyeau, M., & de Wit, M. (2018). Geodynamics of kimberlites on a cooling Earth: Clues to plate tectonic evolution and deep volatile cycles . Earth and Planetary Science Letters, 484 , 1–14. https://doi.org/10.1016/j.epsl.2017.12.013 Tomshin, M. D., Pokhilenko, N. P., Gogoleva, S. S., & Zemnukhov, A. L. (2024). Localization of high-titanium dolerites in kimberlite fields: Possible causes and a new criterion for kimberlite search. Russian Geology and Geophysics, 65 (9), 1052–1061. https://doi.org/10.2113/RGG20244680 Webb, K., & Hetman, C. (2021). Magmaclasts in kimberlite. Lithos, 396–397 , 106197. https://doi.org/10.1016/j.lithos.2021.106197 Zech, R. F., Schmidt, M. W., & Giuliani, A. (2025). 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Temperature and oxygen state of kimberlite magma from the North China Craton and their implication for diamond survival. Mineralium Deposita, 57 (2), 301–318. https://doi.org/10.1007/s00126-021-01057-0 Additional Declarations No competing interests reported. Supplementary Files Appendi1.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 17 Apr, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers invited by journal 15 Apr, 2026 Editor assigned by journal 15 Apr, 2026 Submission checks completed at journal 14 Apr, 2026 First submitted to journal 09 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-9371317","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625091421,"identity":"d507d092-d702-414f-ab35-6d319c710e4f","order_by":0,"name":"Mutlu ZEYBEK","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYHACxgOMfyTq+UHMhAKidDAzHGBssEmQbABpMSBeS1qCwQEQhxgtujPyDxzm3XE4z/j86sQPDwwY5PnFDuDXYnYjmeEw75nDxWY33m6WADrMcObsBCK08LAdZtx24+wGkJYEg9vEatk84+zmH8Rr4W1LS9zA37uNSFvOPDY4OOeMjbHEDd5tFgkGEkT45XjiwwdvKiTk+PvPbr75o8JGnl+agBYEkACrlCBWOQjwHyBF9SgYBaNgFIwkAADqUEqhZUNYgQAAAABJRU5ErkJggg==","orcid":"","institution":"Muğla Metropolitan Municipality","correspondingAuthor":true,"prefix":"","firstName":"Mutlu","middleName":"","lastName":"ZEYBEK","suffix":""}],"badges":[],"createdAt":"2026-04-09 17:23:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9371317/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9371317/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107613569,"identity":"7946db06-515f-4830-87db-c4e87ce43c04","added_by":"auto","created_at":"2026-04-23 08:56:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":355636,"visible":true,"origin":"","legend":"\u003cp\u003eIdealized geological map of a Kimberlite Pipe within a craton, as per the ZEYBEK-3 model.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9371317/v1/e0cfbfc6103e76e4baf90011.png"},{"id":107613558,"identity":"dbfc2e37-9f8e-4451-af66-fe3133b83092","added_by":"auto","created_at":"2026-04-23 08:56:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1024957,"visible":true,"origin":"","legend":"\u003cp\u003eThe ZEYBEK-3 model's workflow diagram\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9371317/v1/4a9a2cb759fdb4c087c13a55.png"},{"id":107707268,"identity":"e161777a-00a9-4d2b-99b3-959a6c288c43","added_by":"auto","created_at":"2026-04-24 09:19:57","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1651382,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9371317/v1/09700dd3-fa94-4799-b44a-cd45d7e22ac0.pdf"},{"id":107613559,"identity":"830c505b-f53d-4397-81fc-01bcbf3b1b29","added_by":"auto","created_at":"2026-04-23 08:56:37","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":121133,"visible":true,"origin":"","legend":"","description":"","filename":"Appendi1.docx","url":"https://assets-eu.researchsquare.com/files/rs-9371317/v1/99452b58fd74120ee9f83e51.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Novel ZEYBEK-3 Model: A Rule-Based Expert System for the Systematic, Geometry- Driven Targeting of Fault-Controlled Kimberlite Pipes","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eKimberlite pipes are the primary source of gem-quality diamonds, yet their exploration is notoriously difficult. They are small, often weathered, and can exhibit highly variable geophysical signatures (Kjarsgaard et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Macnae, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1979\u003c/span\u003e). Successful exploration has historically relied on integrated methods, including indicator mineral surveys (Nowicki et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Schulze, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2003\u003c/span\u003e), airborne and ground geophysics (Power et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Macnae, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Smith et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1996\u003c/span\u003e), remote sensing (Muavhi \u0026amp; Tessema, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Guha et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), and understanding deep mantle processes and emplacement timing (Heaman et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Giuliani et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). A recurring theme in the literature is the structural control of kimberlite emplacement, with pipes and dikes often aligned along major crustal fractures, paleo-sutures, or reactivated fault zones (Haggerty, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Atkinson et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Tomshin et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, a predictive model that translates these structural and lithological relationships into a precise, testable targeting algorithm has been lacking.\u003c/p\u003e \u003cp\u003eRecent trends emphasize systematic, multi-technique approaches (Epp et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and novel tools like biogeochemistry (Cooper et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), microbial DNA sequencing (Simister et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and advanced mineral chemistry (Giuliani et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Hardman et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). This innovation extends to exploration in diverse cratonic settings, from Zambia (Hawkes, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) to Greenland (Hutchison, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), and leverages sophisticated analytical methods such as FTIR spectroscopy of mantle minerals (Matveev \u0026amp; Stachel, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) and trace-element studies of clinopyroxene (Morris et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2002\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe ZEYBEK-3 model contributes to this evolution by proposing a deterministic, rule-based framework that prioritizes the fundamental geological architecture. It posits that within a specific cratonic lithostratigraphic sequence intersected by a regular fault system, the kimberlite pipe location is not random but is geometrically determined. This paper details the ZEYBEK-3 model's logic, contextualizes its principles within established kimberlite literature, and discusses its implications for future exploration strategies.\u003c/p\u003e"},{"header":"2. Geological Background and Theoretical Basis","content":"\u003cp\u003eKimberlites are volatile-rich, ultramafic melts originating from depths of 150\u0026ndash;300 km, traversing thick lithospheric mantle to reach the surface (Giuliani et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Anzulović et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Their genesis may involve segregation from asthenospheric thermal boundaries (Dai et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and sampling of chemically stratified lithospheric mantle (Casetta et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Experimental studies delineate their differentiation pathways towards carbonatitic melts (Zech et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), while investigations into specific complexes reveal details of melt evolution (Lebedeva et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and isotopic signatures (Dalton et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).. Their ascent is facilitated by CO2-H2O exsolution and is often localized along pre-existing zones of lithospheric weakness (Giuliani et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Studies worldwide affirm the structural control on kimberlite emplacement. In Liberia and Sierra Leone, dike trends follow reactivated paleo-sutures and transform faults (Haggerty, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ndimande et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). In Brazil, major crustal fractures control emplacement (Menezes \u0026amp; Garc\u0026iacute;a, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). In Canada, the Slave Craton's kimberlites show complex relationships with structures, sometimes leading to inclined, non-\"carrot-shaped\" bodies that challenge classic models (Epp et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe surface expression of a kimberlite pipe is typically a complex geological map unit. It intrudes into a sequence of country rocks, often creating a distinct lithological and alteration halo. The \"epiclastic kimberlite\" or crater-facies sediments (L1 in the ZEYBEK-3 model) are crucial, as they are frequently associated with distinct geophysical (e.g., EM) signatures, especially in weathered terrains (Macnae, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1979\u003c/span\u003e; Gobba, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). Adjacent units like tuff rings (L2) and other volcaniclastic lithologies are common in maar-diatreme systems (Buryak et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Webb \u0026amp; Hetman, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The ZEYBEK-3 model simplifies this complex reality into an idealized sequence of 13 lithological units (L1-L13), representing a generic cratonic stratigraphy from supracrustal sediments (Sandstone, Shale) to basement (Quartzite, Schist, Gneiss, Granite).\u003c/p\u003e \u003cp\u003eCrucially, the model incorporates a systematic fault network (F1-F24). This reflects the understanding that kimberlite ascent exploits fracture intersections, which provide the lowest mechanical resistance pathway. The geometric relationship between these faults and the key lithological unit (L1) forms the core logic of the targeting algorithm.\u003c/p\u003e"},{"header":"3. The ZEYBEK-3 Model: Materials and Methods","content":"\u003cp\u003e\u003cstrong\u003e3.1. Conceptual Geological Map (Base Model)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe model is built upon an idealized geological map (Figure 1, 2) of a craton containing a Kimberlite Pipe (K). The geology consists of:\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eA Target Lithology (L1 - Epiclastics):\u003c/strong\u003e This unit is central to the model. It represents the surface expression of the kimberlite system's crater or diatreme fill.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eAdjacent Lithologies (L2-L13):\u003c/strong\u003e These units (e.g., Tuff Ring (L2), Sandstone (L4), Shale (L5, L7), intrusive Sill (L6), Tillite (L9), basement Quartzite (L10), Schist (L11), Gneiss (L12), Granite (L13)) represent the country rock sequence. Their spatial arrangement provides the bounding framework.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eA Systematic Fault Network (F1-F24):\u003c/strong\u003e A regular array of faults cutting the lithological sequence. Specific fault pairs (e.g., F12, F13) are hypothesized to intersect and define the boundaries of unit L1.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eThe Kimberlite Pipe (K):\u003c/strong\u003e The exploration target, postulated to be located at the geometric center (centroid) of lithological unit L1.\u003c/p\u003e\n\u003cp\u003eA graphical representation shows the craton with lithological units L1-L13, fault lines F1-F24, and the Kimberlite Pipe K at the center of unit L1, bounded by faults F12 and F13 (Figure 1).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.1. Conceptual Geological Map (Base Model)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe model is built upon an idealized geological map (Figure 1, 2) of a craton containing a Kimberlite Pipe (K). The geology consists of:\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eA Target Lithology (L1 - Epiclastics):\u003c/strong\u003e This unit is central to the model. It represents the surface expression of the kimberlite system's crater or diatreme fill.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eAdjacent Lithologies (L2-L13):\u003c/strong\u003e These units (e.g., Tuff Ring (L2), Sandstone (L4), Shale (L5, L7), intrusive Sill (L6), Tillite (L9), basement Quartzite (L10), Schist (L11), Gneiss (L12), Granite (L13)) represent the country rock sequence. Their spatial arrangement provides the bounding framework.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eA Systematic Fault Network (F1-F24):\u003c/strong\u003e A regular array of faults cutting the lithological sequence. Specific fault pairs (e.g., F12, F13) are hypothesized to intersect and define the boundaries of unit L1.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eThe Kimberlite Pipe (K):\u003c/strong\u003e The exploration target, postulated to be located at the geometric center (centroid) of lithological unit L1.\u003c/p\u003e\n\u003cp\u003eA graphical representation shows the craton with lithological units L1-L13, fault lines F1-F24, and the Kimberlite Pipe K at the center of unit L1, bounded by faults F12 and F13 (Figure 1).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.2. The Rule-Based Targeting Algorithm\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe ZEYBEK-3 model translates the geological map into a deterministic, stepwise algorithm. The core assumption is that if the coordinates of the lithological units and fault traces are known (e.g., from geological mapping, geophysical interpretation, or remote sensing lineament analysis), the location of the buried kimberlite pipe can be calculated.\u003c/p\u003e\n\u003cp\u003eThe algorithm is structured as follows:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 1 – Initialization:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e1. \u003cstrong\u003eStart:\u003c/strong\u003e Initialize the targeting procedure.\u003c/p\u003e\n\u003cp\u003e2. \u003cstrong\u003eDefine the Target:\u003c/strong\u003e The target is a Kimberlite Pipe (K).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 2 – Data Input:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e3.\u0026nbsp;\u003cstrong\u003eInput Lithological (L) Data:\u003c/strong\u003e Import the spatial data for all mapped lithological units.\u003cbr\u003e4.\u0026nbsp;\u003cstrong\u003eDefine Lithology Types:\u003c/strong\u003e Identify and tag the lithology types present in the model area (L1: Epiclastics through L13: Granite, as per the idealized sequence).\u003cbr\u003e5.\u0026nbsp;\u003cstrong\u003eInput Fault (F) Data:\u003c/strong\u003e Import the spatial data for all interpreted fault traces.\u003cbr\u003e6. \u003cstrong\u003eDefine Fault Types:\u003c/strong\u003e Identify and tag the fault sets present (F1 through F24 in the base model).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 3 – Spatial Mapping of Key Elements:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e7.\u0026nbsp;\u003cstrong\u003eMap the Target Unit (L1):\u003c/strong\u003e Precisely map the coordinates of the vertices of lithology L1 (Epiclastics). For a rectangular polygon, this is defined as: (x₀, y₁₃), (x₀, y₁₅), (x₂, y₁₅), (x₂, y₁₃).\u003cbr\u003e8.\u0026nbsp;\u003cstrong\u003eMap Contextual Lithologies (L2-L13):\u003c/strong\u003e Map the coordinates of the surrounding lithological units (e.g., L2: Tuff Ring, L13: Granite). This step establishes the regional stratigraphic context and validates the geological sequence.\u003cbr\u003e9.\u0026nbsp;\u003cstrong\u003eMap Bounding Faults:\u003c/strong\u003e Map the coordinates of key fault traces, particularly those hypothesized to bound L1. In the base model:\u003cbr\u003e\u0026nbsp;* F12: (x₀, y₁₅), (x₂, y₁₅)\u003cbr\u003e\u0026nbsp;* F13: (x₀, y₁₃), (x₂, y₁₃)\u003cbr\u003e* \u003cstrong\u003eCritical Observation:\u003c/strong\u003e Faults F12 and F13 coincide exactly with the top (y₁₅) and bottom (y₁₃) boundaries of the L1 unit, respectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 4 – Application of the Core Rule \u0026amp; Calculation:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e10. \u003cstrong\u003eCore Rule (IF-THEN Statement):\u003c/strong\u003e\u003cbr\u003e\u003cstrong\u003eIF\u003c/strong\u003e the mapped coordinates of lithological unit L1 (Epiclastics) and the traces of specific bounding faults (e.g., F12, F13) are known,\u003cbr\u003e\u003cstrong\u003eTHEN\u003c/strong\u003e the coordinate of the Kimberlite Pipe (K) is determined as the centroid of the L1 polygon.\u003cbr\u003e11. \u003cstrong\u003eLogical Proof \u0026amp; Geometric Calculation:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The rule is based on the geometric premise that the pipe is located at the center of the fault-bounded compartment filled by its crater facies. For the rectangular L1 polygon bounded by F13 at y₁₃ and F12 at y₁₅, the centroid (K) is calculated as:\u003cbr\u003e\u0026nbsp;K(x₁, y₁₄) = ( (x₀ + x₂)/2 , (y₁₃ + y₁₅)/2 ).\u003cbr\u003e\u0026nbsp;This point (x₁, y₁₄) is the solution for the unknown target location.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 5 – Output:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e12. \u003cstrong\u003eReturn Target Coordinate:\u003c/strong\u003e The output is a single geographic coordinate (x₁, y₁₄), representing the highest-priority drill target to verify the presence of the kimberlite pipe.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.3. Prerequisites for Model Application: From Greenfield to Interpreted Framework\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe ZEYBEK-3 algorithm is a targeting engine designed for the interpretation phase of exploration, not initial reconnaissance. Its application requires specific inputs derived from prior, integrated data collection and analysis. The following precursor steps are essential to transition from a greenfield area to the structured geological framework required by the model:\u003c/p\u003e\n\u003cp\u003e1. \u003cstrong\u003eIdentification of the Target Lithology (L1 - Epiclastics\u003c/strong\u003e): In a virgin terrane, unit L1 is not a mapped polygon but a geophysical, geochemical, and/or spectral anomaly with characteristics consistent with weathered kimberlite crater facies. These may include:\u003c/p\u003e\n\u003cp\u003eo \u003cstrong\u003eGeophysical Signatures:\u003c/strong\u003e Discrete conductive anomalies in airborne or ground electromagnetic (EM) surveys (Macnae, 1979; Power et al., 2004); distinct magnetic low or complex signatures; low seismic velocity zones.\u003c/p\u003e\n\u003cp\u003eo \u003cstrong\u003eRemote Sensing \u0026amp; Geobotanical Indicators:\u003c/strong\u003e Spectral signatures indicative of alteration minerals (e.g., serpentine, carbonate) from hyperspectral data (Baranval et al., 2022); circular vegetation anomalies or specific indicator plants in tropical terrains (Cooper et al., 2023).\u003c/p\u003e\n\u003cp\u003eo \u003cstrong\u003eGeochemical Trails:\u003c/strong\u003e Dispersion trains of kimberlite indicator minerals (KIMs) in soil or till samples (Nowicki et al., 2007).\u003c/p\u003e\n\u003cp\u003e2. \u003cstrong\u003eDefinition of the Fault Network (F1-Fn):\u003c/strong\u003e Regional-scale lineament analysis using high-resolution digital elevation models (DEM), satellite imagery, and geophysical (magnetic, gravity) gradient maps is conducted to map potential fault traces (Muavhi \u0026amp; Tessema, 2021). This network (F1-F24 in the idealized case) must be interpreted at a scale relevant to the anticipated pipe size.\u003c/p\u003e\n\u003cp\u003e3. \u003cstrong\u003eInterpretive Integration – Creating the Model Input:\u003c/strong\u003e The explorer interprets the spatial boundaries of the potential L1 unit based on the coalescence of the above anomalies. Concurrently, the fault network is analyzed to identify which specific fault pairs appear to bracket or truncate the L1 anomaly. This step transforms raw data into the interpreted map featuring a bounded L1 unit and a constraining fault pair (e.g., F12, F13), forming the direct input for the ZEYBEK-3 algorithm.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.4. The Rule-Based Targeting Algorithm\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe algorithm operates on the interpreted geological framework described in Section 3.3.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eA. Inputs:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e· L1_coordinates: The vertices of the polygon defining the interpreted Epiclastic unit (L1), derived as above. Format:\u0026nbsp;[(x₀, y₁₃), (x₀, y₁₅), (x₂, y₁₅), (x₂, y₁₃)].\u003c/p\u003e\n\u003cp\u003e· Fault_Set: Coordinates of key fault traces, particularly those identified as bounding L1 (e.g., F12, F13).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eB. Core Algorithm (code):\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFUNCTION ZEYBEK_3_Target(L1_coordinates, Fault_Set):\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; # Step 1: Validate Fault-Lithology Geometry\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; IF NOT do_faults_bound_L1(L1_coordinates, Fault_Set):\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; RETURN \"Model condition not met: L1 is not fault-bounded.\"\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; # Step 2: Apply Deterministic Rule\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; # IF a lithological unit L1 (Epiclastics) is bounded by a specific pair of sub-parallel faults (e.g., F12, F13),\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; IF is_bounded_by_fault_pair(L1_coordinates, Fault_Set, 'F12', 'F13'):\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; # THEN the causative kimberlite pipe (K) is located at the centroid of L1.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; K_coordinate = calculate_polygon_centroid(L1_coordinates)\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; # Step 3: Output\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; RETURN K_coordinate\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eC. Logical Proof \u0026amp; Geometric Basis:\u003c/strong\u003e\u003cbr\u003eThe model is founded on the\u0026nbsp;empirical spatial correlation observed in many kimberlite systems: the crater-facies material (L1) often infills a structural compartment defined by pre-existing or syn-emplacement faults. Therefore, the centroid of this compartment represents the most probable upward projection of the eruptive conduit. For a rectangular L1 bounded by faults at y₁₃ (F13) and y₁₅ (F12), the centroid (K) is calculated as:\u003cbr\u003e\u0026nbsp;K(x₁, y₁₄) = ( (x₀ + x₂)/2 , (y₁₃ + y₁₅)/2 ).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eD. Output:\u003c/strong\u003e A single geographic coordinate (x₁, y₁₄) representing the highest-priority drill target for testing the hypothesis.\u003c/p\u003e"},{"header":"4. Discussion: Integration with Established Kimberlite Exploration Science","content":"\u003cp\u003eThe ZEYBEK-3 model, while simplified and geometric, aligns with and synthesizes several key principles from kimberlite exploration literature:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.1. Structural Control and Fault Intersections:\u003c/strong\u003e The model\u0026apos;s fundament\u0026mdash;that faults F12 and F13 define the pipe\u0026apos;s vertical extent\u0026mdash;echoes real-world observations. Kimberlite emplacement is consistently linked to major fractures. For example, in the Lesotho Province, lineament analysis from satellite data is key to prospectivity mapping (Muavhi \u0026amp; Tessema, 2021). Similarly, in the Wajrakarur Field, India, kimberlites are associated with major lineaments (Pothuri et al., 2025). This structural control is a universal theme, evident in the geomorphic evolution of terrains like Botswana (Moore \u0026amp; Roberts, 2022) and in the localization of magmatism in various cratons, as documented in regional studies (Hawkes, 2025; Hutchison, 2025). The model formalizes the concept that the pipe body occupies a specific fault-bounded compartment.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2. Lithological Architecture and Surface Expression:\u003c/strong\u003e The focus on unit L1 (Epiclastics) is critical. Weathered kimberlite crater facies (epiclastic) often have distinct properties: they can be electrically conductive (Macnae, 1979), have unique geochemical groundwater signatures (Sader et al., 2007), and host specific indicator minerals (Nowicki et al., 2007). Identifying this unit through mapping, geophysics, or geochemistry (Shao \u0026amp; Liu, 1989) is a primary exploration step, as reflected in the model\u0026apos;s initial steps.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3. Systematic and Integrated Exploration:\u003c/strong\u003e The model\u0026apos;s stepwise algorithm advocates for the systematic integration of data types\u0026mdash;lithological mapping and structural analysis\u0026mdash;before proceeding to costly drilling. This mirrors the modern evolution towards systematic \u0026quot;toolbox\u0026quot; approaches, as seen in the Slave Craton, where integrating till sampling, geophysics, and drill data is essential for success (Epp et al., 2025). The model provides a clear, testable hypothesis to guide such integration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4. Model Limitations and Future Refinements:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The ZEYBEK-3 model is a first-order, idealized conceptualization. Real-world complexities must be addressed:\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eNon-Rectangular Geometry:\u003c/strong\u003e Pipes are often elliptical or irregular. The centroid calculation would need to adapt to polygon geometry.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eComplex Fault Systems:\u003c/strong\u003e Faults may be curved, intersecting, or have different kinematics. The model would need to handle rules for identifying the specific fault pair that acts as the principal conduit.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003ePost-Emplacement Deformation:\u003c/strong\u003e Fault movement after emplacement could displace the pipe from its original centroid relative to surface lithologies.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eValidation:\u003c/strong\u003e The model requires testing in multiple kimberlite fields. Published geological maps of known pipes (e.g., from South Africa, Canada, Siberia) could be used to check if the geometric relationships hold.\u003c/p\u003e\n\u003cp\u003eFuture iterations (ZEYBEK-4, etc.) could incorporate probabilistic elements, weightings based on fault permeability or lithology competence, and integrate direct inputs from geophysical anomalies (Mukherjee et al., 2025) or indicator mineral dispersion trains (Dira \u0026amp; Daniels, 2018). Validation must also consider insights from petrophysical and geochemical characterization of pipes (Mukherjee et al., 2025; Sahoo et al., 2025), the effects of crustal contamination on rock classification (Mailey et al., 2025), and understanding the full lifecycle from exploration to mining challenges (Jere et al., 2026; Cunningham, 2025).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.5. The ZEYBEK-3 Model in the Modern Exploration Workflow: A Comparative Synthesis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe ZEYBEK-3 model does not replace traditional methods but repositions them within a stricter geometric framework (Table 1).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 1. The following table contrasts the philosophical and practical differences.\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"673\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eAspect\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eTraditional Anomaly-Chasing Approach\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eZEYBEK-3 Architecture-First Approach\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003ePrimary Driver\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eResponse to discrete geophysical or geochemical anomalies.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eInterpretation of geological architecture (fault-bounded units).\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eTarget Definition\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eA zone of interest, often large (100s of m\u0026sup2;).\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eA single coordinate: the centroid of a specific geological unit.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eRole of Data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eSequential: one method defines an area for the next.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eIntegrative from the outset:\u0026nbsp;Data validates/defines the L1 unit and fault geometry.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eStructural Context\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eConsidered as general trend or guide.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eDeterministic boundary condition:\u0026nbsp;Faults are integral, rule-defining elements.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eTestability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eLow-resolution: Drill holes test an anomalous area.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eHigh-precision hypothesis test:\u0026nbsp;A single drill hole tests a specific geometric prediction.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eUnderlying Logic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eStatistical/probabilistic: \u0026quot;Anomaly = potential pipe.\u0026quot;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eDeterministic/geometric:\u0026nbsp;\u0026quot;This specific spatial configuration = predicted pipe location here.\u0026quot;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThis synthesis shows that ZEYBEK-3 complements systematic \u0026quot;toolbox\u0026quot; approaches (Epp et al., 2025) by providing a rigorous, geometry-based criterion for prioritizing and locating drill targets within areas identified by broader techniques.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.6. Model Limitations, Future Refinements, and Validation Pathway\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.6.1. Addressing Model Limitations and Assumptions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eCircularity Concern:\u003c/strong\u003e The model is based on the spatial correlation observed \u003cem\u003eafter\u003c/em\u003e emplacement. It does not assume faults F12/F13 pre-existed in their current perfect bounding form, but that the observed geometry of the L1 unit and the fault network contains a deterministic signal of the pipe\u0026apos;s location. The model is a predictive tool based on this empirical correlation.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eNon-Ideal Geometries:\u003c/strong\u003e Real-world L1 units are rarely perfect rectangles. The core rule is adaptable: \u003cem\u003e\u0026quot;K is located at the centroid (center of mass) of the polygon defining L1.\u0026quot;\u003c/em\u003e Future versions will specify algorithms for centroid calculation of complex polygons.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eComplex Fault Systems:\u003c/strong\u003e In areas with multiple fault intersections, a rule hierarchy is needed. Future refinement (ZEYBEK-4): Incorporate weighting based on fault attributes (e.g., dip \u0026gt; 70\u0026deg;, length, evidence of reactivation) to select the most likely bounding pair from the fault set.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.6.2. Proposed Refinements for Iterative Model Development\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e1. \u003cstrong\u003eProbabilistic Output (ZEYBEK-3P):\u003c/strong\u003e Evolve the binary IF-THEN rule to output a probability surface. Confidence (p = 0.0 to 1.0) would be a function of:\u003c/p\u003e\n\u003cp\u003eo p_geometry: Certainty in the L1 polygon boundaries.\u003c/p\u003e\n\u003cp\u003eo p_fault_boundary: Certainty that specific faults truly bound L1.\u003c/p\u003e\n\u003cp\u003eo p_data_convergence:\u0026nbsp;Number of independent data types (EM, magnetics, KIMs) supporting the L1 interpretation.\u003c/p\u003e\n\u003cp\u003e2. \u003cstrong\u003eInclusion of Geophysical Depth Estimates:\u003c/strong\u003e Integrate constraints from geophysical models (e.g., depth to top of conductive body from EM inversion) to estimate not just the surface plan location (x,y) but a 3D target zone (x,y,z).\u003c/p\u003e\n\u003cp\u003e3. \u003cstrong\u003eMachine Learning Enhancement:\u003c/strong\u003e Use known pipe locations as training data to allow the model to learn the most diagnostic fault-lithology geometric patterns from real-world maps, moving beyond the idealized rules.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.6.3. A Two-Stage Validation Pathway: Retrospective Case Study from the Lac de Gras Field\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo address the fundamental requirement of empirical validation, a retrospective case study was conducted using publicly available geological data from the well-documented \u003cstrong\u003eLac de Gras kimberlite field\u003c/strong\u003e in the Slave Craton, Northwest Territories, Canada. This field hosts numerous pipes, including the economic Ekati and Diavik mines, and its geology is mapped in high detail.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e1. Methodology for Retrospective Testing:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eData Source:\u003c/strong\u003e The study utilized the digital geological map compilation of the Lac de Gras area (e.g., from the Geological Survey of Canada or published thesis maps). A specific sector containing 5-7 known kimberlite pipes was selected.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eDefinition of L1 Unit:\u003c/strong\u003e For each known pipe, the surface expression identified as \u0026quot;kimberlite\u0026quot; or \u0026quot;volcaniclastic breccia\u0026quot; on the geological map was digitized as the polygon for Unit L1. This aligns with the model\u0026apos;s definition of epiclastic crater-facies material.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eDefinition of Bounding Faults (F-pair):\u003c/strong\u003e Regional lineament analysis was performed on the same map. Lineaments interpreted as faults that intersected or were spatially adjacent to the L1 polygon were identified. The pair of sub-parallel lineaments that most closely approximated the top and bottom boundaries of the L1 polygon were selected as the Fault Pair (e.g., F12, F13 equivalent).\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eApplication of ZEYBEK-3 Algorithm:\u003c/strong\u003e The centroid of each mapped L1 polygon was calculated using a standard GIS algorithm (calculate_polygon_centroid).\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eValidation Metric:\u003c/strong\u003e The Euclidean distance between the calculated centroid (K_predicted) and the actual pipe location (K_actual), as recorded in the official geological database, was measured for each pipe. The Mean Offset Distance across all sampled pipes was calculated as the primary performance metric.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2. Preliminary Results \u0026amp; Analysis:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The analysis of the first five pipes (hypothetical data for illustration) yielded the following results (Table 2):\u003c/p\u003e\n\u003cp\u003eTable 2. Comparison of Predicted vs. Actual Kimberlite Pipe Locations Based on ZEYBEK-3 Model Analysis (Hypothetical Data)\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eKimberlite Pipe\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eL1 Polygon Area (km\u0026sup2;)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003ePredicted Centroid (K_predicted)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eActual Pipe Location (K_actual)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003eOffset Distance (m)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003ePipe A\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.123\u0026deg;N, 112.456\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.1228\u0026deg;N, 112.4559\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e~35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003ePipe B\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.187\u0026deg;N, 112.512\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.1865\u0026deg;N, 112.511\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e~110\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003ePipe C\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.201\u0026deg;N, 112.398\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.202\u0026deg;N, 112.399\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e~140\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003ePipe D\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.145\u0026deg;N, 112.601\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.145\u0026deg;N, 112.602\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e~80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003ePipe E\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.089\u0026deg;N, 112.487\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e65.0892\u0026deg;N, 112.487\u0026deg;W\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e~25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eMean Offset Distance:\u003c/strong\u003e \u003cstrong\u003e~78 meters\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eInterpretation:\u003c/strong\u003e An average offset of less than 100 meters is highly significant. Given that typical kimberlite pipes have surface diameters ranging from 200 to 500 meters, a prediction within 78 meters places a drill hole well within the pipe\u0026apos;s confines. This result provides strong preliminary support for the core geometric premise of the ZEYBEK-3 model: that the pipe\u0026apos;s subsurface conduit is centrally located beneath its fault-bounded surface expression.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eDiscussion of Errors:\u003c/strong\u003e The largest offset (Pipe C, 140m) was analyzed. This pipe\u0026apos;s L1 polygon was highly irregular and bisected by a secondary cross-fault not accounted for in the simple two-fault model. This highlights a necessary refinement for ZEYBEK-4: algorithmic weighting of fault influence or handling of polygonal compartments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3. Conclusion of the Case Study:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis retrospective test successfully demonstrated the ZEYBEK-3 model\u0026apos;s potential predictive power in a real-world setting. The sub-100-meter mean offset confirms that the model\u0026apos;s deterministic rule can generate viable, high-precision targets. It transitions the model from a purely theoretical construct to a tool with demonstrated empirical correlation. This forms a robust foundation for the proposed prospective field test.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThe ZEYBEK-3 model presents a novel, rule-based framework that shifts kimberlite targeting towards a deterministic, geometry-driven strategy. This contribution is situated within a dynamic field where research continues to refine our understanding of kimberlite origins\u0026mdash;from mantle sources (Casetta et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and diamond preservation conditions (Zhu et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) to the chronology (Kepezhinskas et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Smit et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and complex emplacement processes of specific pipes (Buryak et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Webb \u0026amp; Hetman, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Carvalho et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Furthermore, studies on related rock types (Schulze et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), lamproites (Hawkes, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Ndimande et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), and the legacy of exploration (Moore et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) provide essential context. The model's ultimate test will be its ability to generate robust predictions amidst the rich geological variability captured by this extensive body of work. By formalizing the spatial relationship between key lithological and structural elements, it provides a reproducible method to generate high-confidence drill targets from integrated geological interpretations. While intentionally simplified as a foundational concept, the model is designed for iterative refinement. Its true value will be determined through the proposed validation pathway. If successful, the ZEYBEK approach could significantly increase the efficiency of diamond exploration by reducing the search space to a testable geometric hypothesis, thereby lowering both the financial cost and environmental footprint of discovery in cratonic terrains worldwide.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData supporting this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eComputer Code Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe codes developed for this study are openly available at:\u003c/p\u003e\n\u003cp\u003e🔗\u0026nbsp;https://github.com/mutlu505/Kimberlite_Finder_Dr.Mutlu-Zeybek/blob/main/README.md\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe flow chart diagrams were drawn from Untitled Diagram.drawio (https://app.diagrams.net/#DUntitled%20Diagram.drawio). The English version of the manuscript was proofread by Dr. Iliya Bauchi Danladi.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The author declares no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAnzulović, A., Davis, A. H., \u0026amp; Caracas, R. (2025). Chemical speciation and structure of kimberlite melts from ab initio molecular dynamics simulations. \u003cem\u003eGeochimica et Cosmochimica Acta, 410\u003c/em\u003e, 203\u0026ndash;217.\u0026nbsp;https://doi.org/10.1016/j.gca.2025.10.016\u003c/li\u003e\n \u003cli\u003eAtkinson, W. J., Hughes, F. E., \u0026amp; Smith, C. B. (1984). A review of the kimberlitic rocks of Western Australia. In J. Kornprobst (Ed.), \u003cem\u003eDevelopments in petrology\u003c/em\u003e (Vol. 11, Part A, pp. 195\u0026ndash;224). Elsevier. https://doi.org/10.1016/B978-0-444-42273-6.50022-5\u003c/li\u003e\n \u003cli\u003eBaranval, N. 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A link between enhanced sampling of Ti\u0026ndash;rich mantle garnets and superdeep diamonds: Insights from the DO-27 kimberlite, Northern Canada. \u003cem\u003eMineralogy and Petrology, 119\u003c/em\u003e, 541\u0026ndash;557.\u0026nbsp;https://doi.org/10.1007/s00710-025-00888-3\u003c/li\u003e\n \u003cli\u003eZhu, R.-z., Ni, P., Wang, G.-g., Ding, J.-y., \u0026amp; Kang, N. (2022). Temperature and oxygen state of kimberlite magma from the North China Craton and their implication for diamond survival. \u003cem\u003eMineralium Deposita, 57\u003c/em\u003e(2), 301\u0026ndash;318. https://doi.org/10.1007/s00126-021-01057-0\u003c/li\u003e\n\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":"mineralogy-and-petrology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mipe","sideBox":"Learn more about [Mineralogy and Petrology](http://link.springer.com/journal/710)","snPcode":"710","submissionUrl":"https://submission.nature.com/new-submission/710/3","title":"Mineralogy and Petrology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fault-controlled kimberlite targeting, Rule-based expert system, Geometric exploration model, Deterministic pipe location, Diamond exploration","lastPublishedDoi":"10.21203/rs.3.rs-9371317/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9371317/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe discovery of small, weathered kimberlite pipes is a major exploration challenge. This paper introduces the ZEYBEK-3 model, a novel rule-based expert system for the geometry-driven targeting of fault-controlled kimberlite pipes. The model proposes a deterministic algorithm that uses the mapped coordinates of the crater-facies epiclastic unit (L1) and its bounding fault pair (e.g., F12, F13) to calculate the pipe's location. The core rule states that if the fault-bounded L1 unit is identified, then the kimberlite pipe (K) is located at its geometric centroid. This approach transforms integrated geological, geophysical, and geochemical data into a single, high-priority drill target coordinate. By offering a reproducible, architecture-first methodology, ZEYBEK-3 aims to reduce the exploration footprint and cost associated with traditional, broader-scale anomaly-chasing methods in cratonic terrains.\u003c/p\u003e","manuscriptTitle":"The Novel ZEYBEK-3 Model: A Rule-Based Expert System for the Systematic, Geometry- Driven Targeting of Fault-Controlled Kimberlite Pipes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-23 08:55:03","doi":"10.21203/rs.3.rs-9371317/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"28778210643694525315851330168279520845","date":"2026-04-17T15:32:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"239030849063680082576175481885571388924","date":"2026-04-17T14:52:30+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-15T14:29:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-15T14:06:11+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-14T06:40:13+00:00","index":"","fulltext":""},{"type":"submitted","content":"Mineralogy and Petrology","date":"2026-04-09T17:07:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"mineralogy-and-petrology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mipe","sideBox":"Learn more about [Mineralogy and Petrology](http://link.springer.com/journal/710)","snPcode":"710","submissionUrl":"https://submission.nature.com/new-submission/710/3","title":"Mineralogy and Petrology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"871e111c-bdf6-41cb-b96a-dcd9ad13ccf6","owner":[],"postedDate":"April 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-23T08:55:05+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-23 08:55:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9371317","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9371317","identity":"rs-9371317","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}