Three-Dimensional Mineral Prospectivity Modeling with the Integration of Ore-Forming Computational Simulation in the Xiadian Gold Deposit, Eastern China

Abstract

Finding new, effective predictive variables for 3D mineral prospectivity modeling is both important and challenging. The 3D ore-forming numerical modeling quantitively characterizes the complex coupling-mineralization process of the structure, fluid, heat, and wall rock, which may be potential indicators for mineral exploration. We here conducted 3D mineral prospectivity modeling with the integration of ore-forming computational simulation information in the Xiadian orogenic gold deposit, China, to examine whether the simulation data input can improve the reliability of prospectivity modeling. First, we constructed the 3D models of the orebody and fault to extract the fault geometric features using spatial analysis, as they are always considered to be the crucial controls of gold distribution. Second, we performed 3D numerical modeling of the deformation–fluid–heat-coupling process of the structurally controlled hydrothermal Au system using the FLAC^3D platform. Finally, the fault-geometry features (buffer, dip, dip variation, and undulation) and the ore-formation-simulation indices (volume strain, shear strain, temperature variation, and fluid flux) were integrated using Bayesian decomposition modeling, which has a promising nonlinear model ability and a flexible variable-integration ability. The prospectivity modeling results demonstrated that the model generated by combining geometry and simulation variables achieved significantly higher AUC, precision, accuracy, Kappa, and F1 scores compared to other models using a single-predictor-variable dataset. This suggests that the joint use of geometry and simulation variables construct a comprehensive association between gold and its ore-controlling factors, thereby resulting in a highly reliable prospectivity model. Thus, the approach of 3D mineral prospectivity modeling aided by ore-forming numerical simulation proves to be more useful in guiding mineral exploration, especially in the condition of fewer variables. Based on the prospectivity modeling outcomes, we identified four gold targets at depth in the Xiadian district that warrant focused exploration efforts.

1. Introduction

Mineral exploration is a crucial, long-term endeavor for governments and society that requires sustainable mineral sources. The discovery of new mineral deposits or orebodies becomes increasingly challenging in the setting of extensive exploration at shallow depths [1]. This has led to a shift from 2D mineral prospectivity modeling (MPM) at a regional scale to 3D MPM at a mine scale. The 3D MPM is theoretically superior to 2D MPM because mineralization distribution occurs in a 3D space and is primarily controlled by the 3D features of the ore-controlling factors (e.g., intrusion, fold) [2,3,4,5]. However, compared with 2D MPM, which benefits from multiple-source data to generate predictor variables, such as geology, structure, remote sensing, and geochemistry exploration [6,7,8,9,10,11], 3D MPM often faces limitations in creating the variables, owing to the lack of robust information at depth related to technique and cost issues. How to obtain effective and high-quality prediction variables, especially at depth, to conduct 3D MPM is, thus, an ongoing focus.

The development of 3D-modeling methods has greatly contributed to the analysis of promising mineral reserves and locating potential mineralization. The joint interpretation of geological, geophysical, geochemical, and other data is usually used in the 3D modeling of deep-geology units [12,13,14]. Jointly using the geochemical and geophysical data, 3D models of the deep hydrothermal alteration zone can be constructed with machine learning using the spatial association of shallow geochemical anomalies and the deep alteration zone [15]. Using an objective interpretation method, the relationship between recovered physical properties and orebodies is able to be obtained via geophysical 2D and 3D inversions [16]. Inference modeling approaches using various geophysical data [17,18,19] have the capability to accurately reconstruct the deep architectures of geological objects by integrating geological–geophysical data and knowledge, thereby furnishing essential model support for the implementation of 3D MPM. Spatial analysis is an important tool to extract useful spatial ore-controlling information from 3D models. Existing methods have a laudable ability to capture the geological body spatial features, such as field analysis, shape analysis, and model projection [20,21,22,23,24,25]. The model spatial features are commonly selected as critical predictive variables for 3D MPM, which has already contributed to new resource discoveries [12,14,26,27,28,29,30]. Notably, mineral deposit formation involves complicated geodynamic processes in both space and time, in which magma and/or fluid flow, and its evolution and interaction with wall rocks, dominate the mineralization distribution [31,32,33,34,35]. While the spatial controls on mineralization are vital for exploration, the weak or insufficient representation of metallogenic geodynamic processes (e.g., volumetric strain, temperature variation) may reduce the reliability, accuracy, and confidence of prediction.

The ore-forming numerical modeling has greatly advanced our understanding of several geological processes (e.g., structure deformation, fluid flow) and their relation to ore deposit genesis [36,37,38,39,40,41,42,43,44]. For instance, Li et al. [38,45,46,47] employed computational modeling to uncover the influence of rock difference, dip variation, and strain localization on fluid flow patterns in the structural-controlled, unconformity-related uranium system in the Athabasca Basin, Canada. Additionally, numerical modeling can also simulate temporal–spatial metal precipitation or rock stress geodynamics to delineate the fluid pathways and traps to locate potential mineralization. For example, Liu et al. [13], Hu et al. [48], and Shan et al. [49] used the dilation space, mineralization rate, and/or geochemical interaction as ore proxies to find the favorable metal deposition location at depth. Ford et al. [50] and Wilson et al. [51] discussed the fault geometry controls on the rock deformation and fluid flow regular pattern and determined the mineralization exploration strategies in strike–slip fault fluid systems. Thus, ore-forming numerical modeling has the powerful ability to provide ore-predictive information in terms of the metallogenic geodynamic system. These data, together with model spatial features, are promising to enhance 3D mineral prospectivity models.

The Jiaodong Peninsula is the largest gold province of China, boasting more than 5000 tons of Au resources (Figure 1) [52]. Gold deposits in this region show similar geology and mineralization characteristics with orogenic gold deposits, of which the regional fault control orebody localizations are ubiquitous and lack the gold affinity for lithology [53,54,55,56,57,58,59,60,61,62]. In terms of relatively simple geological characteristics, these conditions provide an excellent study objective for performing 3D-model analysis and numerical modeling. However, few previous studies have conducted systematic and comprehensive research from spatial and temporal perspectives to investigate these gold deposits and guide deep exploration. Herein, we selected the Xiadian gold deposit as a case study to perform 3D MPM with the integration of ore-forming computational simulation information to examine the added geodynamic variables‘ effects on prediction results. This research aims to provide a new way to uncover more predictor variables for 3D MPM, gain new insights into the controls on gold mineralization, and identify mineral resources responsibly and efficiently.

The rest of this paper is structured as follows. Section 2 presents the geological background of the Xiadian deposit. In Section 3, we introduce the dataset used in the case study and describe the methodologies employed for 3D modeling, feature extraction, ore-forming simulation, and prospectivity modeling. In Section 4, we first detail the modeling and simulation outcomes and further discuss the differences between the three models based on different variable sets. Section 4 concludes by presenting the target appraisal facilitated by the prospectivity model. Finally, Section 5 summarizes the contributions made by this paper.

2. Geological Background

The giant Jiaodong gold province is located at the eastern margin of the North China Craton, east of the Tan-Lu Fault Zone (Figure 1). It consists of the Jiaobei Terrane to the northwest and the Sulu Ultra-High-Pressure Metamorphic Belt to the southeast, bounded by the Wulian–Yantai lithospheric fault. As a consequence of the subduction of the Paleo–Pacific plate, the Jiaodong Peninsula suffered extensive and intense magmatic activities and crustal deformation during the Mesozoic, accompanied by large-scale gold mineralization [52,62].

The Jiaobei Terrane endows most of the gold reserves of the Jiaodong Peninsula, with basement rocks primarily comprising the Neoarchean Jiaodong Group and the Paleoproterozoic Jingshan and Fenzishan Group (Figure 1). Mesozoic magmatism in the region is widely distributed and is mainly grouped into (1) Late Jurassic granitoid associated with partial melting of the lower crust including Longlong, Kunyushan, Luanjiahe, etc.; (2) Early Cretaceous granitoid genesis from crust–mantle interactions, represented by Guojialing granitoid [64]; and (3) widely intruded mafic–felsic dykes. The vast gold mineralization is principally manifested as auriferous–quartz vein type and disseminated-/stockwork-type, with a peak age of ~120 Ma [52].

The Xiadian gold deposit is located in the southern part of the Zhaoping regional detachment fault zone (Figure 1). There are different lithologies in the hanging wall and footwall of the Zhaoping fault (Figure 2), of which the former is dominated by the metamorphic rocks of the Jingshan Group and Jiaodong Group, and the other comprises Late Jurassic Linglong granite and a few metamorphic breccias.

At Xiadian, gold mineralization is spatially endowed predominantly in the footwall of the Zhaoping fault zone (Figure 3). The Zhaoping fault, marked by the dark fault gunge, is mainly NE- and NNE-striking, yet locally N-S striking, with variable dips between 35°–55° (average 45°). The fault underwent brittle–ductile deformation, with a several-meter-thick mylonite and alteration zone developed proximal to the fault [26,65]. During the mineralization period, the Zhaoping fault ordinary demonstrated a dextral strike-slip normal sense of movement, with NE-SW compression and NW-SE extension as the dominant tectonic regimes [54], reflecting vertical compressive and horizontal tensional stresses. The deformation of the Zhaoping fault controls the localization of hydrothermal alteration–mineralization showing that (1) the majority of gold orebodies are located in the footwall of the Zhaoping fault, (2) the hydrothermal alteration–mineralization zone is distributed along the fault (Figure 3a), and (3) the occurrence of orebodies is related to the fault geometry (Figure 3b).

Gold orebodies in the Xiadian district mainly include Nos. 2, 7, Daobeizhuangzi (DBZZ), and Jiangjiayao (JJY). They are dominantly lenticular, pillar, vein-like, and discontinuous, with a NE-plunging ore shoot extending ~1400 m with an average gold grade of 3.4 g/t. Gold mineralization at Xiadian is closely associated with quartz–pyrite–sericite alteration and shows the disseminated and stockwork characteristics, with minor auriferous quartz veins in the steeply brittle fractures. Gold is mostly observed as μm-scale electrum gains in the microcracks of sulfides, or as inclusion in sulfide minerals.

Previous geochronological studies recorded a mineralization age of ~120 Ma at Xiadian, comparable to most gold deposits within the Jiaodong Peninsula. This period occurred with the rollback of the Paleo–Pacific Plate, leading to a transformation in the tectonic regime of the Jiaodong Peninsula from regional compression to extension [54,64]. Companying with the geodynamic process, large-scale crustal thinning and tectonic–magmatic activities happened in the region. The metal source of the Mesozoic gold systems in the region has been suggested to be related to the overlying sediments of the subducting Paleo–Pacific Plate undergoing subduction-associated metamorphism [52,53]. The deep-source ore-forming fluids and metals flowed upward through lithospheric-scale and regional-scale faults to the economic portion (shallow crust, <10 km) of deposits [59,65] (Figure 4). At the shallow depths of Xiadian, these fluids migrated upward along the Zhaoping fault, exhibiting an oblique feature during the coupled normal and dextral strike-slip movement. Primary fluids were active near the fault, forming the disseminated gold mineralization related to sericite–pyrite–quartz alteration. In contrast, minor fluids flowed into the fractures distal to the fault, resulting in the formation of quartz sulfide veins [26]. The precipitation of gold was ultimately caused by pressure fluctuations and sulfidation [66].

3. Methods

The 3D mineral prospectivity modeling typically involves three main steps of 3D geological modeling, predictive variable generation, and variable integration [14,27,28,29,67,68]. The works and studies in the Xiadian gold deposit have well concluded the geological and mineral characteristics and demonstrated the gold mineralization-formation process and its controls (Figure 4), of which the Zhaoping fault, the critical ore-controlling object, plays a significant role in influencing ore fluid flow pathways and gold deposition happening. Therefore, from an empirical perspective, the most vital exploration criteria for gold exploration at Xiadian is identifying the spatial and genetic association between mineralization and the Zhaoping fault. Building upon the 3D geology modeling work, we employed spatial analysis to obtain the fault geometric features and numerical simulation to get the mineralization geodynamic information (such as volume strain and temperature variation), both prediction variables input into the prospectivity model. To balance the variable difference between geometry feature and simulation information during prospectivity modeling, we used a Bayesian decomposition modeling technique. Figure 5 presents the main steps undertaken in this study.

3.1. Dataset

The generation of predictive variables and the construction of the prospectivity model depend on critical geological models, including structure, lithology, gold orebody, and mineralization distribution. To this end, we collected a comprehensive dataset that can reflect the architecture and property information of the geological objects in the Xiadian deposit. This dataset includes one 1:10,000 surface geological map, 82 1:500 subsurface horizontal sections, 70 cross-sections, 392 drill holes, 74,515 gold assays (including ore and non-ore), 13 magnetotelluric (MT) sounding profiles, and one 1:200,000 Bouguer gravity anomaly measurement.

3.2. 3D Modeling and Feature Extraction

3D modeling of mineral deposits is a powerful tool for visualizing mineralization and its underlying controls. It serves as a data foundation for generating quantitative predictive variables that facilitate mineral exploration. Based on the exploration data, we used the implicit [69] and explicit modeling methods [14] to establish the geometrical wireframe models (i.e., triangular irregular network, TIN) of the Zhaoping fault and gold orebodies in the Xiadian district. To further enhance the accuracy of the fault model at depth, We adopted the level set method, as detailed in [19]. Specifically, we first established an initial model of the fault using geological data, and subsequently reconstructed its intricate architectures by updating the initial model with the MT and gravity anomaly data. The reliability of this fault model was further validated through preserved drillholes, encompassing fault features such as location, dip, and dip variation, confirming its accuracy and consistency. Detailed methodology of 3D modeling has been described in the literature [14,19].

In addition, the wireframe model of the gold orebodies was discretized into voxels for subsequent mineralization analysis. These voxels were further endowed with the properties relating to gold grade (Au) and gold amounts (AuMet) using the Kriging interpolation [70] based on the gold assay data.

Previous studies have demonstrated that spatial analysis effectively extracts geometric features associated with mineralization [20,22,24,25,27,29,71]. In this study, we carried out morphological analysis of the Zhaoping fault model and extracted four variables (gF, vF, waF and wbF;

Table 1. Model geometric feature and ore attribute description.

Variable	Definitions	Unit	Range/Mean
Au	Gold grade of one voxel	g/t	0~13.4/0.92
AuMet	Gold amounts of one voxel	g	0~303,532/7784
dF	Minimum distance to the Zhaoping fault	m	−416~113/−117
gF	Dip of the Zhaoping fault	°	8.8~89/47
vF	Dip variation of the Zhaoping fault in a 100 m buffer	°/100 m	−15.2~45.6/3.2
waF	Undulation relative to trending surface of the Zhaoping fault in a 180 m buffer	m	−164~96/−15.7
wbF	Undulation relative to trending surface of the Zhaoping fault in a 360 m buffer	m	−111~101/−13.5

) to comprehend their controls on the gold orebodies in the Xiadian deposit. Details methodologies of spatial analysis employed in this research, have been described in our previous work [14,26,27,72]. Furthermore, the distance analysis was performed to associate the gold orebody voxels with fault geometric variables. Specially, we calculated the minimum distance (dF) between the voxel and the fault TIN model and assigned the geometric variables of the nearest triangle to the voxel. In this way, the voxels were equipped with seven variables (Table 1), where Au and AuMet reflect the mineralization information, while the variables dF, gF, vF, waF and wbF represent the ore-controlling effect of the Zhaoping fault.

3.3. Ore-Forming Simulation

3.3.1. Numerical Method

Typically, the complex ore-forming process is considered to be thermal–hydraulic–mechanical–chemical coupling processes [37,44]. In a numerical simulation study, such processes can be approximated and characterized by a series of partial differential equations, including Darcy’s Law (describing fluid activities), Fourier’s Law (describing thermal convection), the Mohr–Coulomb constitutive model (describing the mechanical behavior of materials), and the mass and energy conservation equation (describing the coupled effects of the thermal–hydraulic–mechanical and chemical processes). These governing equations have been specifically reviewed in many prior studies [36,38,41,44,73,74,75,76], and further elaboration is beyond the scope of the study. The basic principle of numerical simulation is to discretize the geological body model of the study area into grids or elements. At each defined grid point, the partial differential equations are transformed into algebraic equations using the finite element method or the finite difference method. These equations are subsequently solved using a number of variable parameters as initial and boundary conditions (e.g., hydraulic potential, temperature, and pore pressure; [36,76,77]). This process can be carried out in a series of codes or commercial software.

Given the impracticality of universally simulating all relevant natural processes, it is necessary to choose the most appropriate software or codes related to numerical simulation, for specifically defined geological processes. In this study, the FLAC^3D 5.0 software (Fast Lagrangian Analysis of Continua in Three Dimensions [78], was employed. This powerful software allows for the simulation of fluid flow and heat transport in relation to tectonic deformation, and has been successfully applied to simulation in hydrothermal–structural coupling ore-forming systems [38,73,79]. FLAC^3D employs hexahedral elements for mesh discretization, which ensures good convergence and stability in the numerical calculations. In some scenarios with more complex geometries, polyhedral zones of other shapes (e.g., tetrahedral-shaped and pyramid zones) are deployed to create models. These discretizations can be performed in other software platforms such as SKUA-GOCAD 17 or ANSYS, and subsequently converted into a data format suitable for viewing and processing in FLAC^3D by computer programs. The mechanical, hydraulic and thermodynamic parameters of the materials such as density, permeability, porosity and conductivity are assigned to the zone, representing the nature of rocks in the actual ore-forming system. The simulation process in FLAC^3D proceeds through a cyclic iterative approach. During each iteration, FLAC^3D computes stress, strain, and other physical quantities for each element based on the selected constitutive model, initial and boundary conditions. It then updates nodal displacements and other variables according to results obtained from the execution of the previous cycle [80].

3.3.2. Model Setup

Previous researchers have generally concluded that fault zones and fractures are conduits for ore-forming fluid flow [81,82,83]. Refined architectures of the regional fault are essential, as the strain distribution and fluid migration occurs in fault zones [42,73]. Here we manually refined the Xiadian fault surface model constructed above to avoid the post-ore cutoff or deformation. A conceptual model (Figure 6), including the Xiadian fault zone, hanging wall (Jiaodong Group Precambrian metamorphic rocks), footwall (Linglong granite), and erosion cover, is necessary for ore-forming numerical modeling [47,49,84]. In this study, the dimensions of the overall model spanned 7 km horizontally and 10 km vertically. Before simulation, the meticulous mesh definition of these models was imperative to ensure accurate numerical results [44,85,86,87,88]. We used the tetrahedral elements for mesh discretization (Figure 6) via the software GoCAD 17, and converted to FLAC^3D tetrahedron-discretization model utilizing a new computer program [45]. This choice was motivated by the undulation features (see below models) generally displayed in the fault zone, which can lead to topological errors after refining the fault model using hexahedral meshes. Tetrahedral meshes, on the other hand, can be small or dense enough to adequately capture the geometric details of the fault model. For different units, meshes are distributed as uniformly as possible and their shape is generally similar as possible. As a result, the whole computational domain is simulated by 1,908,076 tetrahedral elements, including erosion (384,251 elements), fault zone (87,291 elements), footwall (704,938 elements) and hanging wall (731,596 elements). All units were treated as homogeneous porous zones, which are simplified respectively as the Jiaodong Group (hanging wall), Linglong granite (footwall), and fault damage zone with high permeability and low mechanical properties [82,89]. The specific mechanical, hydraulic and thermodynamic parameters of rocks are given in

Table 2. Numerical simulation parameters used in this study.

Property	Hanging Wall (Metamorphic Rocks)	Footwall (Granite)	Fault Zone
Density $(\mathrm{k}\mathrm{g}/{\mathrm{m}}^3)$	2.67	2.6	2.0
Bulk modulus ($\mathrm{P}\mathrm{a}$)	3.28	5.33	0.52
Shear modulus ($\mathrm{P}\mathrm{a}$)	0.56	0.32	0.031
Cohesion ($\mathrm{P}\mathrm{a}$)	8.9	33.6	16.9
Tensile strength (Pa)	3.77	5.16	2.97
Friction angle (°)	28	33	20
Dilation angle (°)	3.2	5.3	6.0
Porosity	0.29	0.19	0.4
Permeability (${\mathrm{m}}^2$)	2.09 × 10−11	1.81 × 10−11	1.00 × 10−10
Conductivity ($\mathrm{J}/\left(\mathrm{m}\mathrm{℃}\right)$)	2.63	3.05	4.0
Thermal expansion coefficient (°C−1)	5.40 × 10−6	6.70 × 10−6	6.70 × 10−6
Specific heat capacity ($\mathrm{J}/\left(\mathrm{k}\mathrm{g}\mathrm{℃}\right)$)	803	803	783

. These values are based on rock mechanical experiment data or related hand book and numerical simulation experiments in Jiaodong [49,84,90].

3.3.3. Initial and Boundary Conditions

According to the general model [91], the initial pore pressure was set as hydrostatic pressure in the Jiaodong Group and granite, and set as hydrostatic pressure with gradient variation in the fault zone, for the starting condition of the simulation. The initial temperature of the top surface was 25 °C and kept fixed, and the temperature gradient was 20 °C/km. The initial temperature of the top of the fault zone was set to 180 °C, a temperature range consistent with the gold mineralization [49,84,90].

Field geologic observations and published complications have concluded that the Xiadian gold deposit experienced a NW-SE extensional stress regime during the ore-forming period, and the fault zone underwent dextral strike-slip movement [26,54,92,93]. As such, this study set the NW-SE extensional stress regime as the boundary condition (Figure 6). This extensional stress was applied normally to the NW-SE direction boundaries vertically downward according to the gradient of 1.5 × 10⁴ N/m, with zero extensional stress at the top. The two NE-SW direction boundaries and the bottom boundary were all fixed.

3.4. 3D Prospectivity Modeling

The MPM task aims to resolve the complicated nonlinear relationships between the predictor and mineralization variables, ultimately establishing the quantitative association model. Currently, multivariate statistical and machine learning approaches have achieved significant results in MPM [7,11,15,67,94,95,96]. However, the predictor variables in this study contain two distinct types: geometry-related variables and simulation-related variables. Therefore, a hierarchical modeling approach is used to combine these two types of predictor variables and understand their contributions to MPM. The Bayesian decomposition modeling (BDM) is an MPM approach that integrates nonlinearity and interpretability [97]. More importantly, the BDM method can integrate multi-type variables using the “decomposition–integration” strategy. Thus, the BDM was applied to MPM in this study.

To integrate the two types of predictor variables, we realize MPM by two levels of BDM. At the bottom level, individual geometry- and simulation-related predictor variables are integrated to generate their distinctive feature representations. At the top level, we integrate geometry- and simulation-related feature representations and map them to ore-bearing probability.

Firstly, assuming that the geometry- and simulation-related variable sets are denoted as $E_g$ and $E_s$, respectively, the mineralization probability based on the Bayes’ rule can be expressed as:

$$P(Ore=1|E_g,E_s)=\frac{P\left(E_g,E_s|Ore=1\right)P\left(Ore=1\right)}{P\left(E_g,E_s\right)}.$$

(1)

According to the derivation in [97], Equation (1) can be formulated as:

$$P(Ore=1|E_g,E_s)=\frac{1}{1+\exp \left(-\left({\theta }_g{\varphi }_g\left(E_g\right)+{\theta }_s{\varphi }_s\left(E_s\right)+b\right)\right)},$$

(2)

where ${\theta }_g$ and ${\theta }_s$ are the relevant indices that express the correlation among the variable sets $E_g$ and $E_s$, while ${\varphi }_g\left(E_g\right)$, ${\varphi }_s\left(E_s\right)$ and $b$ represent the nonlinear mapping functions (NMFs) and the prior correction, respectively:

$$\left\{\begin{array}{l}{\varphi }_g\left(E_g\right)=\log \frac{P\left(Ore = 1|E_g\right)}{P\left(Ore = 0|E_g\right)}=\log \frac{P\left(Ore = 1|E_g\right)}{1-P\left(Ore = 1|E_g\right)}\\ {\varphi }_s\left(E_s\right)=\log \frac{P\left(Ore = 1|E_s\right)}{P\left(Ore = 0|E_s\right)}=\log \frac{P\left(Ore = 1|E_s\right)}{1-P\left(Ore = 1|E_s\right)}\\ b=\left(1-{\theta }_g-{\theta }_s\right)\log \frac{P\left(Ore = 1\right)}{P\left(Ore = 0\right)} \end{array}\right..$$

(3)

To model ${\varphi }_g\left(E_g\right)$ and ${\varphi }_s\left(E_s\right),$ we express the posteriors $P\left(Ore=1|E_g\right)$, and $P\left(Ore=1|E_s\right)$ with another level of BDM:

$$P(Ore=1|E_{\left(\cdot \right)})=\frac{1}{1+\exp \left(-\left({\sum }_{i=1}^n{\theta }_{\left(\cdot \right),i}^{\prime }{\varphi }_i\left(E_{\left(\cdot \right),i}\right)+b\prime \right)\right)}.$$

(4)

where $E_{\left(\cdot \right)}$ denotes $E_g$ or $E_s$, $E_{\left(\cdot \right),i}$ denotes $i$-th predictor variables in $E_{\left(\cdot \right)}$, ${\varphi }_i\left(E_{\left(\cdot \right),i}\right)$ is the nonlinear mapping function (NMF) for $E_{\left(\cdot \right),i}$ is quantified by local linear regression [98] as used in [40], ${\theta }_{\left(\cdot \right),i}^{\prime }$ is the corresponding regression coefficient.

After obtaining the estimation of the NMFs, we can learn the regression coefficients $\left\{{\theta }_g,{\theta }_s\right\}$ and ${\theta }_{\left(\cdot \right)}^{\prime }$, and the prior correction term $b$ and $b\prime$ in Equations (2) and (4) from the training data ${\left\{E_g^{\left(j\right)},E_s^{\left(j\right)};Y^{\left(j\right)}\right\}}_{j=1}^N$ and ${\left\{E_{\left(\cdot \right)}^{\left(j\right)};Y^{\left(j\right)}\right\}}_{j=1}^N$ in a maximum likelihood estimation fashion, which is converted to logistic regression problems:

$$\begin{gathered} \left\{{\theta }_g,{\theta }_s,b\right\}=\arg \underset{{\theta }_g,{\theta }_s,b}{\max }\sum _{j=1}^N\log P\left({Ore}^{\left(j\right)}|E_g^{\left(j\right)},E_s^{\left(j\right)};{\theta }_A,{\theta }_B,b\right). \\ \left\{{\theta }_{\left(\cdot \right)}^{\prime },b\prime \right\}=\arg \underset{{\theta }_{\left(\cdot \right)}^{\prime },b}{\max }\sum _{j=1}^N\log P\left({Ore}^{\left(j\right)}|E_{\left(\cdot \right)}^{\left(j\right)};{\theta }_{\left(\cdot \right)}^{\prime },b\prime \right). \end{gathered}$$

(5)

4. Results and Discussion

4.1. Model and Feature Visualization

The models show the gold orebodies in the Xiadian district are distributed unevenly, consisting of several Au enrichment segments, of which No. 7 is the largest gold orebody and others have a long-lensed feature (Figure 7a). The general dip of gold mineralization is weakly variable (~45°), but there is a notable increase in thickness at depths ranging from −500 m to −1300 m compared to the shallow and deep regions. Additionally, there are downward branches from the main gold zone at deep, displaying a gradual decrease in gold mineralization density. The statistics of Au grade of voxels, including drill holes, show the voxels of high Au grade (>4 g/t) occupy a small proportion and are distributed irregularly in the No. 5 and JJY orebodies. The majority of voxels exhibit low gold grades, ranging from 0 to 3 g/t (Figure 7b).

The Zhaoping fault model entirety presents the fault spatial features in a 3D view, making it easier to understand the mineralization location association with the fault geometry. The models reveal that the Zhaoping fault has many local undulations that company variations in both dip and strike (Figure 7c). These geometric features play a significant role in controlling ore body formation, particularly evident in the segments of the deep No. 7 and the shallow DBZZ, where both orebodies pinch out, and substantial transitions in fault shape (Figure 7c). On a larger scale, the boundaries of No. 7 orebodies are often characterized by fault dip or strike variations, while the areas near the inner parts of the orebodies show inconspicuous changes in geometry.

To better elucidate the complicated controls of fault geometry variation on mineralization, we present the orebody model with attributes of fault features and their quantitative correlation with gold mineralization (Figure 8 and Figure 9). The results highlight the models with a heterogeneous distribution of the effects of fault features (Figure 8) and the correlation is nonlinear (Figure 9). The distance between ore and fault generally ranges from 50 to −300 m, with a majority falling within −200 to 0 m, consistent with the footwall distribution characteristics. Overall, the No. 7 including high ore-bearing units is situated closer to the fault than (No. 2, JJY and DBZZ; Figure 8a and Figure 9a). Gold is widely distributed in the ranges of fault dip, but mostly in the dips from 30° to 60° (Figure 9b). The large fault dip occurs in the deep segments of JJY and DBZZ where ore branching occurs. The fault dip changes are generally variable near 0 with a SE-plunging distribution feature (Figure 8d and Figure 9c). The high degree (>10°) of dip variation is all positive, reaching up to 40°, which also influences the formation of high ore-bearing bodies. This means the fault from gentle to steep can promote the formation of high-grade ore, which supports the vein ore affinity to deep fractures. Notably, the locally consistent distribution of fault dip and orebodies (e.g., No. 7 center, JJY and DBZZ) well supports the model of fault geometry controls on gold (Figure 4). The presence of two scales of fault undulation reveals the main ore voxels are confined to areas with negative (convex parts; Figure 8e,f and Figure 9d,e), with no presence of very large fault undulations, which aligns with gentle feature observed (Figure 7c). Overall, the geometric features of the Zhaoping fault aptly reflect the structural controls on gold pattern of ore-forming model (Figure 4). Thus, they can be selected as predictive variables for gold prospectivity modeling.

4.2. Ore-Forming Simulation Results

The ore-forming computational simulation provides a series of parameters related to structure deformation, stress, heat, and fluid flow, which record the geodynamic conditions contributing to mineralization. Based on the proposed metallogenic model of the Xiadian and other Jiaodong gold deposits, we have chosen to focus on four critical parameters: volumetric strain, shear strain, temperature variation, and fluid divergence, to discuss the geodynamic controls on gold deposition (Figure 10). The reasons for selecting these parameters are (1) volumetric strain is related to the rock dilation or shrinkage and commonly used in understanding orebody localization in structure–hydrothermal systems, (2) shear strain reflects the shear or tensile failure degree in the strike-slip fault systems, which is relevant to the gold mineralization process, (3) temperature variation can impact the stability of gold complexes and consequently control gold deposition, and (4) fluid divergence denotes the ingress or egress of fluids in one voxel during ore-forming stage, which is crucial for understanding fluid movement during mineralization. The volumetric strain and shear strain are directly obtained by FLAC^3D, while temperature variation and fluid divergence are calculated using the Sobel operator. Here, the absolute values of temperature variation are used and the negative fluid divergence represents the fluid ingress into a voxel, while positive values represent fluid egress. Although all these indices are related to gold mineralization, we have singled out volumetric strain as a key indicator to validate the modeling results by following the strategies of previous studies [13,45,49,50,99,100]. This choice is driven by the fact that gold mineralization zones are always distinct to the surrounding rocks (non-mineralized areas) in the volumetric strain.

The simulation results show that the known gold orebodies in Xiadian are generally consistent with the distribution of high volumetric strain, moderate shear strain, high temperature variation, and negative fluid divergence (Figure 10). Specifically, a majority of Au-bearing voxels are concentrated within the volumetric strain range of 0.1% to 0.2%, and very minor units (shallow JJY) exhibit volumetric strain exceeding 0.2% (Figure 10a,b). This observation suggests that auriferous fluids tend to preferentially flow into areas characterized by relatively high dilation (permeability improved, tectonic stress releasing). But the low dilatation and extremely high dilatation may have limited ability of fluid transporting or trapping, respectively, resulting in the weak mineralization. This is also evidenced by the close association between thick gold orebodies and interval distribution of high and low dilatations in the No. 7 orebodies (Figure 10a). This distribution pattern of gold and volumetric strain underscores the combined influence of dilation and shrinkage as controlling factors in the ore-forming processes.

The shear strain presents a similar correlation with gold amounts as volumetric strain (Figure 10c,d). Most Au-bearing units have a shear strain from 0.01 to 0.02. Overall, the JJY and DBZZ have higher shear strain values than No. 2 and 7 orebodies, which is reflected in the bimodal distribution characteristic in Figure 10d. Notably, the areas of JJY and DBZZ occur the strike changes of the Zhaoping fault, displaying an eastward-bending feature (Figure 7c). Given that the Zhaoping fault underwent a dextral strike-slip deformation during the mineralization period, such variations in the strike would accelerate shear strain, resulting in a local, high strain accumulation. This may influence the distinct ore-shooting features at JJY (NE-plunging) and DBZZ (SE-plunging).

Temperature variation exhibits a noteworthy correlation with gold mineralization that most ore-bearing units occur the high temperature variations (Figure 10e) and the No. 7 orebody occurs slightly higher temperature changes than others. This suggests the gold deposition is at least partly influenced by temperature variation. However, we noticed that non-ore units can also undergo similar, high temperature changes (Figure 10e,f). Thus, gold-mineralization is most likely controlled by multiple factors at Xiadian, of which pressure fluctuation and water–rock interaction (i.e., sulfidation) have been recognized as important ore-forming mechanisms [57,63,65,66,101].

The fluid divergence records the fluid flow process in individual voxels. The voxels in the Xiadian gold deposits exhibit a wide range of fluid divergence and most of them (approximately 82%, 73 t) occur the ingress fluid flow (negative fluid divergence) (Figure 10g,h). Nevertheless, there are still some voxels with high gold contents and positive fluid divergence that appear to be irregularly distributed in space. We tentatively infer that while the fluid divergence indicates fluid flux characteristic, the orogenic gold deposit formed in an open structural–hydrothermal system in which fluid ingress and egress are common but not directly equivalent to gold precipitation or dissolution. Consequently, the relationship between fluid divergence and gold mineralization is complex.

In summary, the geodynamic indices of mineralization demonstrate a significant correlation with gold distribution and provide different controls on mineralization compared to fault geometry. Therefore, these indicators can be reasonably utilized as predictor variables for exploration.

4.3. Model Comparison

In this study, we conducted three experiments of prospectivity modeling using different sets of variables: (1) all variables, (2) only geometry variables, and (3) only geodynamic variables (simulation variables). To assess the impact of these variable sets on prospectivity modeling, we evaluated the regression and classification performance of three predictive models using various metrics. The regression model is conducted based on the gold amounts in each voxel.

Table 3. Performance comparisons of three regression models.

Models	MAE	MSE	RMSE	R	R2
all-variable model	2.74	41.60	6.45	0.92	0.85
geometry variable model	3.26	44.89	6.70	0.79	0.62
simulation variable model	4.44	65.44	8.09	0.74	0.55

Note: MAE, mean absolute error; MSE, mean squared error; RMSE, root mean squared error; R, correlation coefficient; R², coefficient of determination.

presents performance comparisons of these regression models, encompassing error metrics (MAE, MSE, and RMSE) and correlation metrics (R and R²). The outcomes indicate that the all-variable model displays the least error (MAE of 2.74, MSE of 41.60, and RMSE of 6.45) in contrast to the geometry and simulation variable models. In terms of correlation, the regression results of the all-variable model exhibit the highest significance (R of 0.92 and R² of 0.85) when compared to actual gold amounts. This is followed by the geometry variable model (R of 0.79 and R² of 0.62), whereas the simulation variable model shows the lowest significance (R of 0.74 and R² of 0.55).

In the assessment of classification performance, we used the receiver operating characteristic (ROC) curve [102], the area under the ROC curve (AUC), accuracy, precision, F1_score and kappa. The shape of the ROC curves reflects the predictive performance, and a curve that is convex towards the upper-left corner indicates better model performance. The AUC is a quantitative parameter of a ROC curve, similar to the other four metrics, where values closer to 1 indicate better model performance. Figure 11 illustrates the ROC curves and calculation of AUC, accuracy, precision, F1_score and kappa. Our findings reveal that the performance of the model incorporating all variable sets (red line) demonstrates significantly better performance than the two models based on individual variable sets, with the largest AUC (0.92), accuracy (0.85), precision (0.87), F1_source (0.87) and kappa (0.7; Figure 11). Besides, the geometry variable model (marked by the blue line) presents superior predictive capability than the simulation variable model (marked by the green line) but is not remarkable (AUC: 0.82 vs. 0.74; accuracy: 0.77 vs. 0.70; precision: 0.73 vs. 0.70; F1_source: 0.82 vs. 0.76; kappa: 0.50 vs. 0.38).

Furthermore, we used some reserved areas that are detected by drill holes to verify the generalization ability of three prospectivity modes (Figure 12). The results reveal that prospectivity models utilizing only single geometric or geodynamic variables yield the wrong prediction at depth (Figure 12; green arrow), while the model using all variables performs satisfactorily. These findings suggest that: (1) the geometry variables are more advantageous in indicating mineralization distribution compared to simulation variables; (2) the combination of the two variable sets dramatically enhances the model’s performance; in other words, the incorporation of simulation-related variables allows the prospectivity model to more comprehensively represent the quantitative associations between gold mineralization and its controls factors. This improvement is likely attributed to the input of key information about fluid flow and the ore-forming environment. Hence, we recommend using the 3D prospectivity model with joint geometric and geodynamic variables to identify potential gold mineralization at Xiadian.

4.4. Target Appraisal

Based on the prospectivity modeling results, we determined four gold exploration targets in the Xiadian gold deposit (Figure 12b), which may contribute to effective decision-making in next mineral exploration endeavors. Targets ① and ②, located in the depth of No. 7 orebody with elevations ranging from −1300 to −1700 m, are generally continuously along the known orebody. This is consistent with the common spatially continuous fluid flow pathways. Target ③ is sited in the deep regions of JJY and DBZZ, displaying the highest mineralization probability and the largest potential areas in all targets. It has an elevation of −2000 to −2500 m. The target contains some known mineralization determined by drill holes and is located to NE and SE stretching farther along the JJY and DBZZ orebodies. It mostly likely represents the branch of the known orebody. Target ④ with elevations of −2200 to −2500 m also has a very high mineralization potential. It is uncontinous with known mineralization or other prediction areas and likely presents a new, concealed gold enrichment zone, which existence possibility has been proven in other gold belts [56,103,104]. The details of target location are listed in the Table S1.

5. Conclusions

In this study, the 3D prospectivity modeling with incorporating spatial analysis data and ore-forming computational simulation data through Bayesian decomposition modeling was conducted in the Xiadian orogenic gold deposit. The results of spatial analysis of the ore-controlling Zhaoping fault find its significant influence on ore shooting or branching, which is primarily driven by variations in fault dip or strike. Most gold mineralization tends to concentrate in the convex areas of the fault zone. The numerical modeling results demonstrate that gold mineralization at Xiadian is closely linked to high rock permeability, but its localization is also influenced by the combination of dilation and shrinkage. Using multiple statistic examinations, this approach is proved to outperform traditional prospectivity modeling methods, likely due to the more systematic incorporation of predictor variables that encompass spatial and geodynamic ore controls information. The proposed 3D prospectivity modeling has successfully identified four gold targets in the Xiadian district. Among these targets, the depth of Jiangjiayao and Daobeizhuangzi orebodies exhibits the highest potential, likely indicating the presence of ore branching. Additionally, the No. 7 orebody at depth is anticipated to potentially host concealed gold mineralization.

While the 3D prospectivity modeling approach is promising to be applied in the mineral exploration of various deposits, it is still limited in the aspects that (1) there is no geochemical and geophysical data directly related to deep possible mineralization as prediction variables, and (2) the ore-forming simulation validation can be further improved to decrease the uncertainty and bias, like [86,87,88]. In the future, we will (1) contact the Xiadian gold mine to verify these targets by drillholes, (2) integrate the geochemical and geophysical variables into the prospectivity modeling using the Bayesian decomposition model and deep learning techniques, and (3) develop an automatic optimization method for ore-forming simulations to enhance result reliability.