Initial-Model-Guided 3D Long-Offset Transient Electromagnetic Inversion for Concealed Vein-Type Ore Body Identification

Abstract

Ore districts are important targets for deep mineral exploration. As exploration depths increase, exploration strategies are shifting from ore-body identification based mainly on existing metallogenic models toward refined characterization of subsurface structures and deep mineralization targets. Owing to its high sensitivity to low-resistivity targets, the long-offset transient electromagnetic method (LOTEM) is an important geophysical tool for mineral exploration. However, complex geological settings and electromagnetic interference in ore districts often reduce interpretation accuracy and increase inversion non-uniqueness. To address these challenges, this study proposes an initial-model-guided 3D LOTEM inversion strategy. Background resistivity trends and structural information are incorporated into initial-model construction to provide a better-informed starting model before inversion. Taking concealed vein-type ore bodies in the deep part of the Zhaoxian ore district, northwestern Jiaodong, as the target, an approximate 3D geoelectrical model was built by integrating geological data, borehole information, profile interpretations, and electrical-property constraints. Based on this model, LOTEM forward-response characteristics, inversion comparisons, recovery behavior, and quantitative target-identification metrics were analyzed. The results show that the layered alteration background modifies the response of low-resistivity vein-type targets and reduces the distinguishability between ore-body anomalies and background structural responses, thereby affecting inversion recovery. The structure-constrained initial model concentrates model updates near the target zone and significantly improves anomaly recovery. Sensitivity tests further indicate that one-dimensional electrical information mainly constrains the approximate position and resistivity level of the low-resistivity anomaly, whereas layer-interface information improves the spatial correspondence between the recovered anomaly, the layered background, and the ore-body extension direction. When both types of prior information are integrated, ore-body recovery is significantly enhanced. Under the synthetic-model conditions considered in this study, the initial-model optimization strategy improves the recovery of concealed vein-type low-resistivity targets in a layered alteration background and may inform subsequent LOTEM survey design and inversion interpretation in the Zhaoxian ore district.

1. Introduction

Ore districts are important targets for deep mineral exploration, particularly for greater-depth resources, blind targets, and lateral resource extension. Exploration strategies are accordingly shifting from conventional ore-body identification based mainly on metallogenic models toward integrated exploration and three-dimensional geological mapping. Such exploration increasingly relies on geophysical detection methods and on refined interpretation of three-dimensional subsurface structures, creating a strong demand for high-resolution three-dimensional electromagnetic exploration. Electromagnetic methods are highly sensitive to subsurface electrical-property contrasts and play an important role in deep ore-body detection, electrical-structural imaging, and integrated interpretation in ore districts [1,2,3,4]. As exploration targets move deeper, ore bodies become more deeply buried, anomaly amplitudes weaken, and the requirements for accurate target identification and three-dimensional structural interpretation become more stringent. For low-resistivity mineralized targets, electromagnetic methods generally provide favorable responses. However, low-resistivity anomalies may arise from multiple geological sources. Ore bodies, fault-fracture zones, alteration zones, and other conductive geological bodies containing groundwater or conductive minerals can produce similar or overlapping responses [5,6,7]. When targets are deeply buried, thin, and embedded in complex background electrical structures, conventional electromagnetic interpretation often suffers from diffuse anomaly boundaries, unstable continuity assessment, and poor discrimination between target-related anomalies and background responses.

The long-offset transient electromagnetic method (LOTEM) uses a grounded long-wire source to inject pulsed current into the subsurface and records the horizontal electric-field and vertical magnetic-field responses generated by induced eddy currents after current shut-off. Owing to its large depth of investigation and high sensitivity to low-resistivity anomalies, LOTEM has been widely applied to deep electrical-structure imaging, complex-structure interpretation, and mineral-resource exploration [8,9,10,11,12,13,14,15]. To improve interpretation capability under complex geoelectrical conditions, extensive studies have focused on three-dimensional forward modeling and inversion. Numerical methods, including finite-difference, finite-volume, and finite-element approaches, are widely used for three-dimensional transient electromagnetic simulations and provide essential support for response analysis in complex geoelectrical structures [16,17,18,19,20,21,22,23,24,25,26,27]. Among these, the unstructured tetrahedral-mesh vector finite-element method is particularly advantageous because it can flexibly represent complex geological boundaries and supports local mesh refinement near transmitters, receivers, and anomalous bodies. It is therefore well suited for 3D LOTEM forward modeling in structurally complex environments [19,23,25,26]. In inversion studies, research has mainly focused on gradient calculation, regularization constraints, and efficient iterative optimization for large-scale model-parameter problems. Because 3D transient electromagnetic inversion involves large numbers of model cells and time-channel data, explicit construction of the sensitivity matrix leads to high computational and memory costs. To address this, existing studies have improved inversion efficiency and stability by using adjoint methods for objective-function gradient calculation, combined with roughness constraints, reference-model constraints, and limited-memory BFGS-type optimization algorithms [19,26,28,29,30,31,32,33]. These developments provide an important algorithmic foundation for 3D LOTEM inversion under complex geoelectrical conditions.

In deep ore-district exploration, LOTEM responses are jointly controlled by target burial depth, ore-body geometry, and background electrical structure. When the subsurface medium changes from a simple background to a complex electrical system composed of faults, alteration zones, host rocks, and mineralized bodies, target and background responses become superimposed in the observed data. As a result, both the temporal characteristics and spatial distribution of the observed anomalies may change substantially. This response superposition is particularly important in the Zhaoxian ore district of northwestern Jiaodong, where deep concealed ore bodies are structurally controlled by faults and associated alteration zones. Located in an important segment of the Jiaojia gold belt, Zhaoxian has become a key area for recent deep mineral exploration. Previous studies indicate that deep ore bodies are closely associated with the Jiaojia fault and related structural alteration zones. The main ore bodies occur in pyrite–sericite–quartz altered cataclastic metamorphic and granitic rocks, are generally concordant with the main fracture plane, and exhibit vein-like geometry and downward-dipping extensions [34,35,36,37,38,39]. For such low-resistivity vein-type ore bodies, transient electromagnetic responses are strongly influenced by ore-body resistivity, thickness, dip angle, cover conditions, and the resistivity contrast with surrounding rocks [40,41,42,43]. In the Zhaoxian ore district, these target anomalies are commonly embedded in a complex host-rock and structural background. Consequently, observed LOTEM responses contain both local anomalies from the ore body and broader variations caused by surrounding geological structures. Conventional 3D inversion often uses a homogeneous half-space or simple layered model as the initial model, which provides only a limited representation of the true background electrical structure. When both background structures and target contribute to the response, inversion results may show diffuse boundaries, exaggerated anomaly extents, and poor discrimination between target-related and background-related anomalies. Geological and geophysical prior information can be integrated into electromagnetic inversion through reference-model regularization, structurally weighting, constrained inversion, and joint geological–geophysical inversion. Although these approaches improve inversion stability and geological consistency, they often require modification of the objective function, regularization terms, or coupling strategies. In contrast, this study focuses on optimizing the initial-model construction. The improved initial model serves only as the starting model for inversion, without changing the objective function, reference-model settings, or regularization framework. In this way, incorporating prior electrical and structural information provides a practical means of improving the model basis while preserving the standard inversion workflow.

Based on these considerations, this study investigates the identification of concealed vein-type ore bodies in the deep part of the Zhaoxian ore district, northwestern Jiaodong. Geological data, borehole information, profile interpretations, and electrical-property constraints are integrated to construct an approximate 3D geoelectrical model for LOTEM forward-response analysis. On this basis, inversion results obtained from different initial models are compared to examine the effect of the initial-model selection on inversion recovery. Additional initial models with varying degrees of prior-information completeness are then constructed to evaluate the respective roles of one-dimensional electrical information and layer-interface constraints in recovering concealed low-resistivity vein-type targets. Finally, ore-body identification performance is quantitatively assessed using recovery rate, recovery-center deviation, and dip-angle deviation. This study evaluates how initial-model optimization affects 3D LOTEM inversion under complex layered backgrounds, with particular emphasis on inversion recovery behavior and the quantitative characterization of concealed low-resistivity vein-type targets.

2. Construction of an Approximate 3D Geoelectrical Model for the Zhaoxian Ore District

The Zhaoxian ore district in northwestern Jiaodong is characterized by complex geological conditions and strong electromagnetic interference. LOTEM is expected to provide valuable information for detecting deep concealed vein-type ore bodies in this area. Before field application, however, it is necessary to evaluate both the response characteristics and inversion recovery capability of LOTEM for this type of target. To this end, an approximate 3D geoelectrical model of the Zhaoxian ore district was constructed by integrating available geological information. Based on this model, forward-response analysis and 3D inversion tests were carried out to assess the effectiveness of LOTEM in identifying deep concealed vein-type ore bodies from two perspectives: response characteristics and inversion recovery performance.

The Zhaoxian ore district is located in an important segment of the Jiaojia gold belt, where significant progress has been made in recent deep-drilling exploration [34,35,36,37,38,39]. Previous studies indicate that the main deep ore bodies in the northern Zhaoxian segment are hosted principally in pyrite–sericite–quartz altered cataclastic rocks and pyrite–sericite–quartz altered granitic cataclastic rocks. Their occurrence is generally consistent with the main fracture plane, and the ore bodies exhibit vein-like geometry with downward-dipping extensions. A clear spatial relationship exists among the ore-controlling fault, the altered cataclastic zone, the granitic host rocks, and the concealed ore bodies. Based on this geological framework, the approximate 3D geoelectrical model uses the fault-related alteration zone and its boundaries as the main structural control units. Their spatial distributions were constrained using geological maps, borehole data, integrated profile interpretations, and existing 3D geological models. The concealed vein-type ore body was defined from borehole and profile-interpretation data in the northern Zhaoxian segment to preserve its spatial correspondence with the main fracture plane of the Jiaojia fault and the associated alteration zone.

Figure 1 shows the approximate 3D geoelectrical model of the concealed vein-type ore body in the Zhaoxian ore district. The inclined zone in the central part of the model represents the fault-related alteration zone, and its upper and lower boundaries correspond to the electrical interfaces marking the transition from granitic host rocks to the alteration zone. The narrow blue body represents the concealed vein-type ore body. Together, these units define a 3D geological framework composed of the host-rock background, the fault-related alteration zone, and the concealed vein-type ore body. After defining the model geometry, resistivity values were assigned to each geoelectrical unit based on lithological and electrical-property information. The host-rock background is dominated by granitic rocks. The upper host-rock background, representing the integrated electrical characteristics of the shallow cover and granitic host rocks, was assigned a resistivity of 2000 Ω.m, whereas the deeper host-rock background, representing relatively intact deep granitic rocks, was assigned 2500 Ω.m. The resistivity of the alteration zone was determined according to previous studies of pyrite–sericite–quartz altered cataclastic rocks, pyrite–sericite–quartz altered granitic cataclastic rocks, and their relationship to deep ore bodies in the northern Zhaoxian segment [37,38,39]. Because these zones are affected by fracturing, hydrothermal alteration, and local enrichment of conductive minerals, their electrical properties are relatively complex. To represent the transition from the host rocks to the fault-related alteration zone, the alteration zone was assigned a resistivity of 1000 Ω.m, while the upper and lower boundary zones were set to 1500 Ω.m. These boundary zones represent the transitional electrical structure between the medium- to high-resistivity granitic host rocks and the relatively low-resistivity alteration zone. Considering the electrical contrast between the metallic ore body, the granitic host rocks, and the alteration background, the resistivity of the concealed vein-type ore body was set to 100 Ω.m.

Figure 1. Approximate 3D geoelectrical model of the concealed vein-type ore body in the Zhaoxian ore district: (a) overall 3D view; (b) vertical section showing the host-rock background, fault-related alteration zone, alteration-zone boundaries, and the concealed low-resistivity vein-type ore body. Different colors indicate different geoelectrical units.

In summary, publicly available geological data, borehole information, profile interpretations, and existing 3D geological models were integrated to define the spatial relationships among the host rock background, the fault-related alteration zone, the alteration-zone boundaries, and the concealed vein-type ore body. Resistivity values were then assigned based on lithological and electrical property information. An approximate geoelectrical model consisting of medium- to high-resistivity granitic host rocks, a relatively low-resistivity fault-related alteration zone, and a low-resistivity vein-type ore body is presented. The model provides the basis for subsequent LOTEM response analysis and evaluation of 3D inversion recovery performance.

3. 3D LOTEM Forward Modeling Method and Response-Characteristic Analysis

3.1. Time-Domain Forward Modeling Using the Unstructured Vector Finite-Element Method

In this study, LOTEM responses were calculated using a time-domain vector finite-element forward-modeling method based on unstructured tetrahedral meshes. Such meshes can flexibly represent rugged topography and irregular geological bodies, while allowing local refinement around transmitters, receivers, and target anomaly zones. They are therefore well suited for transient electromagnetic simulation of complex 3D geoelectrical models [19,23,25,26]. In the present formulation, the subsurface medium is assumed isotropic, with electrical conductivity represented by a scalar quantity. Starting from Maxwell’s equations and the constitutive relations and eliminating the magnetic field under the quasistatic approximation, the governing diffusion equation for the electric field is [19,23,25].

$$\nabla \times \left[{\displaystyle \frac{1}{{\mu }_0}}\nabla \times \mathbf{E}(\mathbf{r},t)\right]+\sigma {\displaystyle \frac{\partial E(r,t)}{\partial t}}+{\displaystyle \frac{\partial J_{\mathbf{s}}(r_{\mathbf{s}},t)}{\partial t}}=0$$

(1)

where $\partial J_{\mathbf{s}}(r_{\mathbf{s}},\mathbf{t})$ is the source current-density vector at time t and position r, σ is electrical conductivity, and ${\mu }_0$ is the magnetic permeability of free space.

The computational domain was discretized into unstructured tetrahedral elements. For the e-th element, the electric field was represented by the tangential electric fields on its six edges and the corresponding vector basis functions [19,23,25]:

$${\mathbf{E}}^e\left(\mathbf{r},t\right)={\displaystyle \sum _{i=1}^6{\mathbf{N}}_i^e}(\mathbf{r}){\mathbf{E}}_i^e(t)$$

(2)

where ${\mathbf{E}}^e\left(\mathbf{r},t\right)$ is the electric field degree of freedom on the i-th edge of the e-th element, and ${\mathbf{N}}_i^e\left(\mathbf{r}\right)$ is the vector interpolation basis function. Let the two end nodes of the i-th edge be denoted by i₁ and i₂, the edge length be $l_i^e$, and nodal scalar basis functions $L_{i_1}^e$ and $L_{i_2}^e$. The first-order Nédélec basis function, ensuring tangential continuity across element boundaries, is written as [44]:

$${\mathbf{N}}_i^e\left(\mathbf{r}\right)=(L_{i_1}^{\mathrm{e}}\nabla L_{i_2}^{\mathrm{e}}-L_{i_2}^{\mathrm{e}}\nabla L_{i_1}^{\mathrm{e}})l_i^{\mathrm{e}}$$

(3)

Applying the Galerkin weighted-residual method and assembling over all elements yields [19,23,25,26]:

$$\mathbf{K}\mathbf{E}\left(t\right)+\mathbf{M}{\displaystyle \frac{\partial \mathbf{E}\left(t\right)}{\partial t}}+{\mathbf{F}}_s\left(t\right)=\mathbf{0}$$

(4)

where K is the stiffness matrix, M is the mass matrix, and ${\mathbf{F}}_s\left(t\right)$ is the source-term vector. Their element forms are:

$$K_{i,j}^e={\displaystyle {\iiint }_{{\mathsf{\Omega }}_e}\frac{1}{{\mu }_0}\left[\nabla \times {\mathbf{N}}_i^e\left(\mathrm{r}\right)\right]}\cdot \left[\nabla \times {\mathbf{N}}_j^e\left(\mathrm{r}\right)\right]\mathrm{d}\mathsf{\Omega }$$

(5)

$$M_{i,j}^e={\displaystyle {\iiint }_{{\mathsf{\Omega }}_e}{\sigma }^e{\mathbf{N}}_i^e\left(\mathrm{r}\right)\cdot {\mathbf{N}}_j^e\left(\mathrm{r}\right)}\mathrm{d}\mathsf{\Omega }$$

(6)

$$F_{s,i}^e\left(t\right)={\displaystyle {\iiint }_{{\mathsf{\Omega }}_e}{\mathbf{N}}_i^e\left(\mathrm{r}\right)\cdot \frac{\partial {\mathbf{J}}_s\left({\mathbf{r}}_s,t\right)}{\partial t}}\mathrm{d}\mathsf{\Omega }$$

(7)

where ${\mathsf{\Omega }}_e$ denotes the domain of the e-th tetrahedral element and ${\sigma }^e$ is the electrical conductivity of this element.

For source treatment, the grounded long-wire source was approximated by segmented electric dipoles [19,23,25]. The source was divided into $N_s$ short wire segments. For the m-th dipole, with center position ${\mathbf{r}}_m$, unit direction vector ${\mathbf{p}}_m$, and length $\Delta l_m$, the source current density can then be expressed as:

$$J_s(\mathbf{r},\mathbf{t})=I\left(t\right){\displaystyle {\displaystyle \sum _{m=1}^{N_s}}{p}_m}\delta (r-r_m)\Delta l_m$$

(8)

where $\delta$ is the Dirac delta function. Substituting Equation (8) into Equation (7), the source term for the i-th edge in the e-th element can be written as:

$$F_{s,i}^e\left(t\right)={\displaystyle \frac{dI\left(t\right)}{dt}}{\displaystyle \sum _{m=1}^{N_s}{N}_i^e}\left({\mathbf{r}}_m\right)\cdot p_m\Delta l_m$$

(9)

For time discretization, an unconditionally stable second-order backward Euler scheme was adopted [19,23,25,26]:

$${\displaystyle \frac{\partial E\left(t_n\right)}{\partial t}}\approx {\displaystyle \frac{1}{\Delta t_n}}\left[{\displaystyle \frac{1+2k_n}{1+k_n}}\mathbf{E}\left(t_n\right)-\left(1+k_n\right)\mathbf{E}\left(t_{\left(n-1\right)}\right)+{\displaystyle \frac{k_n^2}{1+k_n}}\mathbf{E}\left(t_{\left(n-2\right)}\right)\right]$$

(10)

$${\displaystyle \frac{\partial {\mathbf{J}}_s\left({\mathbf{r}}_s,t_n\right)}{\partial t}}\approx {\displaystyle \frac{1}{\Delta t_n}}\left[{\displaystyle \frac{1+2k_n}{1+k_n}}\partial {\mathbf{J}}_s\left({\mathbf{r}}_s,t_n\right)-\left(1+k_n\right)\partial {\mathbf{J}}_s\left({\mathbf{r}}_s,t_{\left(n-1\right)}\right)+{\displaystyle \frac{k_n^2}{1+k_n}}\partial {\mathbf{J}}_s\left({\mathbf{r}}_s,t_{\left(n-2\right)}\right)\right]$$

(11)

where tn, tn−1, and tn−2 denote the n-th, (n−1)-th, and (n−2)-th time channels, respectively; $\Delta t$ is the current time step; and $\Delta t_n=k_n\Delta t_{\left(n-1\right)}$. Combining Equations (10) and (11) and substituting them into Equation (4) gives:

$$\left({\displaystyle \frac{1+2k_n}{1+k_n}}\mathbf{M}+\Delta t_n\mathbf{K}\right)\mathbf{E}\left(t_n\right)=\mathbf{M}\left[\left(1+k_n\right)\mathbf{E}\left(t_{\left(n-1\right)}\right)-{\displaystyle \frac{k_n^2}{1+k_n}}\mathbf{E}\left(t_{\left(n-2\right)}\right)\right]-\Delta t_n{\mathbf{F}}_s\left(t_n\right)$$

(12)

$$\Delta t_n{\mathbf{F}}_{s,i}^e\left(t_n\right)={\displaystyle \sum _{m=1}^{N_s}}{\mathbf{N}}_i^e\left({\mathbf{r}}_m\right)\cdot {\mathbf{p}}_m\Delta l_m\left[{\displaystyle \frac{1+2k_n}{1+k_n}}I\left(t_n\right)-\left(1+k_n\right)I\left(t_{n-1}\right)+{\displaystyle \frac{k_n^2}{1+k_n}}I\left(t_{n-2}\right)\right]$$

(13)

where $I_t$ denotes the current amplitude at time t, $\mathbf{p}$ denotes the current direction, and dl denotes the length of each electric-dipole segment.

For LOTEM, the transmitted waveform is typically a step-off waveform. The initial electric field corresponds to the direct-current electric field:

$$\mathbf{E}\left(\mathbf{r},0\right)={\mathbf{E}}_{\mathbf{D}\mathbf{C}}=-\nabla \phi$$

(14)

where $\phi$ is the electric potential satisfying:

$$-\nabla \cdot \left(\sigma \nabla \phi \right)=q_s$$

(15)

where $q_s$ is the source term. After discretizing Equation (15), the following linear system is obtained:

$${\mathbf{K}}_{\phi }\mathsf{\phi }={\mathbf{q}}_{\phi }$$

(16)

where ${\mathbf{K}}_{\phi }$ is the coefficient matrix, $\mathsf{\phi }$ is the nodal potential vector, and ${\mathbf{q}}_{\phi }$ is the source-term vector.

3.2. Model Response-Characteristic Analysis

To analyze the model response characteristics and the influence of background structures on LOTEM responses, a homogeneous half-space reference model was established for comparison with the approximate 3D geoelectrical model. As shown in Figure 2, Figure 2a represents the homogeneous half-space model, with a background resistivity of 2000 Ω.m, whereas Figure 2b represents the approximate geoelectrical model. In both models, the geometry and spatial position of the ore body are kept identical, allowing direct comparison of the influence of the layered alteration background on ore-body responses.

Figure 2. Schematic diagrams of the synthetic models: (a) homogeneous half-space model; (b) approximate geoelectrical model. The blue body denotes the concealed vein-type ore body.

The grounded long-wire source extends along the y-direction with a total length of 4000 m. A total of 378 receivers were distributed above and around the ore body, with a station spacing of 200 m. A step-off waveform was used for forward modeling, and the calculation time ranged from 0.0001 to 0.1 s, with 490 time channels. To investigate the response differences of concealed vein-type ore bodies under different background conditions, the Ey responses were calculated for both ore-bearing and ore-free cases in the homogeneous half-space model and the approximate geoelectrical model. The relative anomaly amplitude of the ore-body response is defined as: $\eta =\left|\left(E_y^{ore}-E_y^{\mathit{bg}}\right)/E_y^{\mathit{bg}}\right|$, where $E_y^{ore}$ is the Ey response of the ore-bearing model, and $E_y^{\mathit{bg}}$ is the Ey response of the ore-free model under the same background conditions.

According to the strike and burial depth of the ore body, three receivers at different spatial positions were selected along y = 0, with x = 1000 m, 2000 m, and 3000 m, respectively. These receivers were used to examine the influence of ore-body position on LOTEM responses. The results are shown in Figure 3. Figure 3(a1–c1) show that, even in the absence of the ore body, the background responses differ significantly among receiver locations. This indicates that the structural characteristics of the host-rock background and alteration zone strongly influence the LOTEM response. After the ore body is introduced, the background structure further modifies the expression of the ore-body anomaly in the total field. To compare the characteristics of the additional anomaly response, the time interval with the most pronounced relative variation, namely 0.001–0.01 s, was selected for further analysis.

Figure 3. Comparison of field-response decay curves and relative anomaly amplitudes at different receiver locations: (a1,a2) x = 1000 m; (b1,b2) x = 2000 m; (c1,c2) x = 3000 m. The upper row shows the Ey decay curves, and the lower row shows the corresponding relative anomaly amplitudes.

As shown in Figure 3(a2–c2), within the selected time interval, the relative anomaly amplitude generally increases at first and then gradually stabilizes. For the same receiver location, the relative anomaly amplitude of the approximate geoelectrical model is consistently lower than that of the homogeneous half-space model, particularly during the rising stage. In terms of both amplitude and variation pattern, the low-resistivity ore body can still produce a recognizable additional response under the complex background. However, the fault-related alteration zone, alteration-zone boundaries, and host-rock background weaken the expression of the ore-body anomaly in the total response.

To further explain the mechanism responsible for this difference, the electric-field distribution and current-density vectors on the vertical y-z section were analyzed. Figure 4 shows the Ey distribution and current-density vectors at different times. The left column corresponds to the homogeneous half-space model, and the right column to the approximate geoelectrical model. The selected times are 0.1 ms, 1 ms, and 10 ms. The results show that, under different model conditions, the response variation caused by the ore body evolves from a local perturbation to broader spatial diffusion. In the approximate geoelectrical model, the coupled effects of the ore body, the fault-related alteration zone, and the alteration-zone boundaries are more pronounced.

Figure 4. Comparison of Ey distributions and current-density vectors on the vertical y–z section at different times: (a1–a3) homogeneous half-space model at 0.1 ms, 1 ms, and 10 ms, respectively; (b1–b3) approximate geoelectrical model at 0.1 ms, 1 ms, and 10 ms, respectively. Black arrows denote current-density vectors, blue lines outline the ore body, and red lines indicate alteration-zone boundaries.

At 0.1 ms, a local anomaly appears near the ore body in the homogeneous half-space model. The current-density vectors are deflected around the ore body, and the response variation is mainly confined to the ore body and its boundaries. In the approximate geoelectrical model, the variation in the Ey distribution extends toward the upper and lower background interfaces, and the current paths are redistributed around the fault-related alteration zone and its boundaries. This indicates that even at early times, the ore body response is influenced by the background interfaces and alteration-zone structure. At 1 ms, the differences between the two models become more pronounced. In the homogeneous half-space model, clear current deflection and rotation develop beneath the ore body, while the response remains concentrated around the low-resistivity target. In the approximate geoelectrical model, in addition to the ore body response, continuous variations develop along the upper and lower boundaries of the alteration zone. The regions above and below the ore body, together with the adjacent background interfaces, jointly control current redistribution. At this stage, the anomalous response is governed by the combined effect of the ore body, the alteration zone, and its boundaries. At 10 ms, the overall field distribution becomes smoother, and the current-density vectors evolve toward large-scale diffusion. In the homogeneous half-space model, the response variations remain localized near the ore body. In contrast, the approximate geoelectrical model shows broader coupled response variations develop between the ore body and the surrounding background structure. This indicates that the influence of the background structure persists into later times. This observation is consistent with Figure 3, where the relative anomaly amplitude of the approximate geoelectrical model is consistently lower than that of the homogeneous half-space model. The layered alteration background therefore weakens the ore-body anomaly.

In summary, concealed vein-type ore bodies can still generate recognizable additional LOTEM responses. As the receiver position shifts from deeper to shallower parts of the ore body, the relative anomaly amplitude increases, indicating that LOTEM has the basic capability to detect this type of low-resistivity target. However, in the approximate geoelectrical model, the alteration zone modifies the current distribution around the ore body. As a result, the target anomaly evolves from a localized perturbation in a homogeneous background into a coupled response controlled by both the ore body and the background structure, reducing the distinguishability between ore-body anomalies and background structural responses.

4. 3D LOTEM Inversion Method and Synthetic Example Analysis

4.1. 3D LOTEM Inversion Algorithm and Initial-Model Optimization Strategy

This study adopts a 3D LOTEM inversion method based on limited-memory BFGS (L-BFGS) algorithm. The L-BFGS method approximates the action of the inverse Hessian matrix using a limited number of stored gradients and model-update vectors, thereby avoiding the explicit construction and storage of a large-scale Hessian matrix. It is therefore well suited for 3D inversion problems involving a large number of model parameters [19,26,28,29,30,31,32,33].

The inversion objective function consists of a data-misfit term and a model-regularization term:

$$\varphi (\mathbf{m})={\varphi }_d(\mathbf{m})+\lambda {\varphi }_m(\mathbf{m})={\mathbf{W}}_d{({\mathbf{d}}_{obs}-{\mathbf{d}}_{pre})}_2^2+\lambda \parallel {\mathbf{W}}_m(\mathbf{m}-{\mathbf{m}}_{ref}){\parallel }_2^2$$

(17)

where ${\varphi }_d\left(\mathbf{m}\right)$ is the data-misfit term, ${\varphi }_m\left(\mathbf{m}\right)$ is the model-regularization term, $\lambda$ is the regularization factor, $\mathbf{m}$ is an Nm-dimensional model vector, ${\mathbf{N}}_m$ is the number of model parameters, ${\mathbf{m}}_{ref}$ is the reference model, ${\mathbf{d}}_{obs}$ is the N-dimensional observed-data vector, ${\mathbf{d}}_{pre}$ is the predicted-data vector, ${\mathbf{W}}_d$ is the data-error weighting matrix, and ${\mathbf{W}}_m$ is the roughness matrix.

Taking the derivative of Equation (17) with respect to the model parameter m gives the objective function gradient:

$$\mathbf{g}\left(\mathbf{m}\right)=-2J^{\mathrm{T}}{W}_{\mathbf{d}}^{\mathrm{T}}{W}_{\mathbf{d}}\left[d_{\mathrm{obs}}-d\left(m\right)\right]+2\lambda {\mathbf{W}}_{\mathbf{m}}^{\mathrm{T}}{\mathbf{W}}_{\mathbf{m}}\left(m-m_{\mathrm{ref}}\right)$$

(18)

where $\mathbf{J}$ is the sensitivity matrix. In 3D LOTEM inversion, explicit construction of the full sensitivity matrix requires substantial computational cost and memory. Therefore, the adjoint method is used for gradient calculation. The discretized forward equation is written as:

$$A\left(m\right)E=b$$

(19)

Differentiating Equation (19) with respect to $\mathbf{m}$ gives:

$${\displaystyle \frac{\partial E}{\partial m}}=-A^{-1}{\displaystyle \frac{\partial A}{\partial m}}E$$

(20)

The observed data are obtained by interpolating the electric field:

$$d\left(m\right)=QE$$

(21)

where $\mathbf{Q}$ is the interpolation operator. Defining the weighted data residual as:

$$r={\mathbf{W}}_{\mathbf{d}}^{\mathrm{T}}{\mathbf{W}}_{\mathbf{d}}\left[{\mathbf{d}}_{\mathrm{obs}}-\mathbf{d}\left(m\right)\right]$$

(22)

The adjoint equation is:

$${\mathbf{A}}^{\mathrm{T}}\mathbf{u}={\mathbf{Q}}^{\mathrm{T}}\mathbf{r}$$

(23)

Thus, the gradient of the data-misfit term can be computed from the adjoint field and the forward electric field without explicitly storing the sensitivity matrix. Combined with the regularization term, the gradient becomes:

$$\mathbf{g}\left(\mathbf{m}\right)=2G^{\mathrm{T}}u+2\lambda W_{\mathbf{m}}^{\mathrm{T}}{W}_{\mathbf{m}}\left(m-m_{\mathrm{ref}}\right)$$

(24)

where $\mathbf{G}$ denotes the model-derivative term formed by the derivative of the system matrix with respect to the model parameters and the forward electric field.

This study adopts a roughness constraint based on neighboring-cell relationships. For the i-th inversion cell and its neighboring cell j, the roughness matrix is defined as:

$${\mathbf{W}}_m(i,j)=\left\{\begin{array}{ll}-\sqrt{{\displaystyle \frac{V_i{V}_{ij}}{V_{max}{\displaystyle {\sum }_{k=1}^N{V}_{ik}}}}}/{\mathbf{r}}_{ij}& \hspace{1em}\hspace{1em}i\ne j\\ -{\displaystyle \sum _{j=1}^N{\mathbf{W}}_m(i,j)}& \hspace{1em}i=j\\ 0& \mathit{else}\end{array}\right.$$

(25)

where $N_i$ is the number of neighboring cells of the i-th inversion cell, $V_i$ is the volume of the i-th cell, $V_{ij}$ is the volume of the j-th neighboring cell, $V_{\mathit{max}}$ is the maximum cell volume in the inversion domain, and ${\mathbf{r}}_{ij}$ is the distance between the centers of the cells i and j.

To ensure physically reasonable inversion results, the resistivity range of resistivity values in the inversion domain was first estimated from geological information. The model parameters were then transformed logarithmically, and lower and upper bounds were imposed on each parameter. The constrained parameter of the k-th inversion cell is expressed as:

$$m_{k^{\prime }}=\ln \left({\displaystyle \frac{\ln (m_k/a_k)}{\ln (b_k/m_k)}}\right), a_k<m_k<b_k$$

(26)

where $m_k$ is the model parameter of the k-th inversion cell, and $a_k$ and $b_k$ are the corresponding lower and upper bounds.

The updated model parameter is obtained as:

$$m_k=\exp \left[{\displaystyle \frac{\ln (a_k)+\ln (b_k\left)\exp \right(m_k^{\prime })}{1+\exp (m_k^{\prime })}}\right]$$

(27)

After this transformation, the bounded optimization problem is converted into an unconstrained optimization problem. In the L-BFGS framework, the inverse Hessian matrix is approximated using the current gradient and gradient-variation information. The search direction is written as:

$${\mathbf{p}}^{\left(n\right)}=-{\mathbf{H}}_n{\mathbf{g}}^{\prime }\left({{\mathbf{m}}^{\prime }}^{\left(n\right)}\right)$$

(28)

where ${\mathbf{H}}_n$ is the inverse-Hessian approximation and ${\mathbf{g}}^{\prime }$ is the gradient in the transformed parameter space. The model is updated as:

$${{\mathbf{m}}^{\prime }}^{(n+1)}={{\mathbf{m}}^{\prime }}^{\left(n\right)}+{\alpha }_n{\mathbf{p}}^{\left(n\right)}$$

(29)

where ${\alpha }_n$ is the line-search step length. Through the parameter transformations in Equations (26) and (27), the updated resistivity model automatically satisfies the prescribed lower and upper bounds at each iteration.

For nonlinear problems such as 3D inversion, the initial model serves as the starting point for model updating and therefore strongly influences the early update direction and the subsequent recovery process [45,46]. Constructing a reasonable initial model is thus important for reducing inversion non-uniqueness and improving solution stability. It should be noted that the initial-model optimization in this study is implemented only through the construction of the starting model. The objective function, reference model, and regularization form remain unchanged.

In this study, the prior information used for initial-model construction is divided into two categories: electrical information and structural information. Electrical information includes station-wise 1D inversion results, existing electromagnetic interpretations, borehole resistivity data, and other geophysical data reflecting background resistivity variations. These data mainly constrain the vertical resistivity trend. Structural information includes regional geological data, borehole information, seismic horizon interpretations, geological cross-sections, and existing 3D geological models. These data mainly constrain the spatial boundaries and internal continuity of geological units.

In the synthetic examples, the electrical prior information is derived from station-wise 1D inversion results, whereas the structural prior information is represented by the layer interfaces in the approximate geoelectrical model. These two types of prior information are jointly used to construct the structure-constrained initial model.

Let $m^{1\mathrm{D}}$ denote the set of station-wise 1D inversion results, $\mathcal{S}$ the structural prior information defined by layer interfaces and alteration-zone boundaries, and $\mathcal{T}$ the reference resistivity trends within different structural units. The structure-constrained initial model is expressed as:

$$m^0={\mathcal{M}}_{\mathrm{SC}}\left[m^{1\mathrm{D}},\mathcal{S},\mathcal{T}\right]$$

(30)

where ${\mathcal{M}}_{\mathrm{SC}}$ is the structure-constrained mapping operator and $m^0$ is the optimized initial model used for 3D inversion.

First, the inversion domain is divided into $L$ structural units according to the layer-interface information:

$$\mathsf{\Omega }={\displaystyle \underset{l=1}{\overset{L}{\cup }}{\mathsf{\Omega }}_l}, {\mathsf{\Omega }}_l\cap {\mathsf{\Omega }}_k=\varnothing (l\ne k)$$

(31)

where $\mathsf{\Omega }$ is the entire inversion domain and ${\mathsf{\Omega }}_l$ is the spatial subdomain of the l-th structural unit. To constrain the spatial boundaries of structural units during 3D mapping and restrict the assignment of electrical-property trends, a structural indicator function is introduced:

$${\chi }_l(r)=\left\{\begin{array}{ll}1,\hfill & r\in {\mathsf{\Omega }}_l,\hfill \\ 0,\hfill & r\notin {\mathsf{\Omega }}_l.\hfill \end{array}\right.$$

(32)

The station-wise 1D inversion results are first smoothed laterally to suppress local jumps between adjacent stations and extract a more stable background resistivity trend. For the j-th station, the smoothed 1D result is:

$${\widehat{m}}_j^{1D}(z)={\displaystyle \frac{{\displaystyle \sum _{k\in N_s(j)}{G}_{jk}}{m}_k^{1D}(z)}{{\displaystyle \sum _{k\in N_s(j)}{G}_{jk}}}}$$

(33)

where $m_k^{1D}(z)$ is the 1D inversion result at the k-th station, $N_s$ is the set of neighboring stations of station j, and $G$ is the Gaussian weight:

$$G_{jk}=\exp \left(-{\displaystyle \frac{d_{jk}^2}{2{\sigma }_s^2}}\right)$$

(34)

where $d_{jk}$ is the horizontal distance between stations j and k, and ${\sigma }_s$ is the smoothing scale.

The smoothed 1D results are corrected using structural-unit information. For the depth interval $Z_{j,l}$ corresponding to the l-th structural unit at the j-th station, the following local constrained objective function is constructed:

$$\begin{array}{l}{\mathcal{J}}_{j,l}={\displaystyle \sum _{z_q\in Z_{j,l}}{\left[m_{j,l}(z_q)-{\widehat{m}}_j^{1D}(z_q)\right]}^2}+{\mu }_l{\displaystyle \sum _{z_q\in Z_{j,l}}{\left[m_{j,l}(z_q)-T_{j,l}(z_q)\right]}^2}\\ +{\nu }_l{\displaystyle \sum _{z_q\in Z_{j,l}}{\displaystyle \sum _{z_p\in N_l(z_q)}{\beta }_{qp}}}{\left[m_{j,l}(z_q)-m_{j,l}(z_p)\right]}^2\end{array}$$

(35)

where ${\mu }_l$ and $v_l$ are the weighting coefficients for the reference-trend constraint and the intra-layer smoothing constraint, respectively. $N_l\left(z_q\right)$ denotes the neighboring depth points belonging to the same structural unit as $z_q$, and ${\beta }_{qp}$ is the normalized distance weight. The three terms in Equation (35) constrain the smoothed 1D resistivity trend of the structural unit and the intra-layer continuity, respectively.

The reference electrical-property trend function $T_{j,l}$ is defined as a linear trend within the depth interval Zj,l corresponding to the l-th structural unit at the j-th station:

$$T_{j,l}(z)=a_{j,l}z+b_{j,l}, z\in Z_{j,l}$$

(36)

where $a_{j,l}$ and $b_{j,l}$ are the trend coefficients of the l-th structural unit at the j-th station. The normalized distance weight is defined as:

$${\beta }_{qp}={\displaystyle \frac{|z_q-z_p{|}^{-2}}{{\displaystyle \sum _{z_k\in N_l(z_q)}|}{z}_q-z_k{|}^{-2}}}$$

(37)

The layer-constrained 1D electrical result is then obtained by minimizing the local objective function:

$${\tilde{m}}_{j,l}^{lc}(z)=\arg {\min }_{m_{j,l}}{\mathcal{J}}_{j,l}, z\in Z_{j,l}$$

(38)

For the i-th cell in the 3D inversion mesh, the initial-model parameter is obtained by interpolating the layer-constrained 1D resistivity results from nearby stations:

$$m_i^0={\displaystyle {\displaystyle \sum _{l=1}^L}{\chi }_l}(r_i){\displaystyle {\displaystyle \sum _{j=1}^{N_s}}{w}_{ij}}{\tilde{m}}_{j,l}^{lc}(z_i)$$

(39)

where $r_i$ is the center coordinate of the i-th 3D inversion cell. In this study, the nearest four stations are used for interpolation. The interpolation weights are defined using a normalized inverse-distance-squared scheme:

$$w_{ij}={\displaystyle \frac{d_{ij}^{-2}}{{\displaystyle \sum _{k=1}^{N_s}{d}_{ik}^{-2}}}}$$

(40)

The final structure-constrained initial model is expressed as:

$$m^0={\left[m_1^0,m_2^0,\cdots ,m_{N_m}^0\right]}^{\mathrm{T}}$$

(41)

Compared with a homogeneous half-space initial model, the structure-constrained initial model incorporates prior information on background resistivity trends, structural-interface geometry, and intra-layer continuity before inversion begins. This reduces the burden of recovering the background structure during the early inversion stage and allows subsequent model updates to focus more effectively on the target anomaly and its surrounding region.

4.2. Inversion Validation Using the Homogeneous Background Model

Before analyzing the effects of the layered alteration background and different initial models, an inversion test was first carried out using the homogeneous half-space model. To simulate observational errors, 5% random noise was added to the synthetic forward responses. The same data-error weighting matrix and noise level were used in all inversion cases to ensure comparability under different initial-model conditions. This provides a baseline validation of the 3D LOTEM inversion workflow under a simple background setting.

As shown by the RMS convergence curve in Figure 5, the RMS decreases from an initial value of 4.35 to 0.98 after 18 iterations, indicating that an acceptable level of data fitting is achieved in this synthetic test.

Figure 5. RMS variation curve with iteration number.

The 3D inversion results for the homogeneous half-space model are shown in Figure 6. The recovered low-resistivity anomaly generally corresponds to the spatial position of the true ore body. From the perspective of ore-body recovery, under a simple background structure and a clear resistivity contrast between the target and the surrounding rocks, the 3D LOTEM inversion method adopted in this study can effectively recover the approximate position, dipping trend, and spatial distribution of the concealed vein-type low-resistivity body.

Figure 6. Three-dimensional inversion results of the concealed vein-type ore body in the homogeneous background model: (a1,b1) true model; (a2,b2) corresponding recovered results.

The recovered anomaly still shows a certain degree of diffusion relative to the true ore body. Nevertheless, it remains distributed along the extension direction of the target and preserves the overall dipping spatial trend of the ore body. These results provide a baseline reference for evaluating inversion performance under more complex background conditions and different initial-model strategies.

4.3. Comparison of Inversion Results for the Approximate Geoelectrical Model

The forward-modeling analysis indicates that concealed vein-type ore bodies can generate recognizable LOTEM responses. However, under a layered alteration background, the separation between the ore-body anomaly response and background structural responses is reduced. In subsequent 3D inversion, when both the background structure and the target anomaly jointly affect the observed data, a conventional homogeneous initial model must simultaneously account for background-structure adjustment and target-anomaly recovery. As a result, the inversion may produce diffuse anomaly boundaries, enlarged anomaly extents, and poor separation between the target anomaly and the background structure. To address this issue, inversion results obtained using a homogeneous half-space initial model are compared with those obtained using a structure-constrained initial model.

To ensure that the comparison reflects only the influence of the initial model, all inversion cases under the approximate geoelectrical model use the same survey geometry, synthetic data, time channels, inversion mesh, objective function, model-parameter bounds, L-BFGS workflow, and stopping criteria. Only the initial model differs. During inversion, an adaptive regularization factor is used to balance the data-misfit term and the model-constraint terms, and the same regularization-update strategy is applied in all cases. The inversion is terminated when the RMS reaches an acceptable level or when its reduction becomes slow after multiple iterations.

Under the approximate geoelectrical model, 3D inversion was first performed using the homogeneous half-space initial model. The RMS convergence curve is shown in Figure 7, where the RMS decreases from an initial value of 9.06 to 0.98 after 48 iterations.

Figure 7. RMS convergence curve versus iteration number for the inversion using the homogeneous half-space initial model.

The corresponding 3D inversion result is shown in Figure 8. A low-resistivity anomaly is recovered near the true ore body, indicating a general spatial correspondence with the target zone. However, compared with the true model, the recovered result still shows clear differences in anomaly geometry, boundary definition, and background-structure representation. Although the anomaly occurs near the ore body, it does not form a narrow, well-defined vein-like geometry. Instead, the anomaly boundary spreads outward around the target, making accurate delineation of the ore body difficult. The expected inclined extension and local continuity expected of the vein-type ore body are also not clearly recovered. In addition, the low-resistivity distribution remains relatively diffuse, and the spatial relationship between the anomaly and the alteration zone is not clearly distinguishable. These results indicate that, under the homogeneous half-space initial model, the inversion can recover a low-resistivity anomaly near the target zone, but its ability to resolve the ore-body boundaries, geometry, dip direction, and anomaly concentration is limited.

Figure 8. Three-dimensional inversion results under the homogeneous half-space initial model: (a1,b1) true model; (a2,b2) corresponding recovered results.

From the perspective of response superposition between the ore-body anomaly and the background structure, the low-resistivity ore body produces a detectable response in the target zone and its surrounding region. However, background structure also contributes to the low-resistivity recovery during inversion, resulting in an enlarged anomaly extent. For deep concealed vein-type ore bodies in the Zhaoxian ore district, the low-resistivity target commonly occurs within or near the fault-related alteration zone. Therefore, the alteration zone and its boundaries are important geological constraints for evaluating whether a recovered low-resistivity anomaly has metallogenic significance. In the inversion result obtained using the homogeneous half-space initial model, the low-resistivity anomaly is partially merged with the adjacent dipping background zone, while the alteration-zone boundaries remain poorly resolved. This increases the uncertainty of the geological interpretation.

To address these limitations, the proposed initial-model optimization strategy was applied to construct a structure-constrained initial model. The construction process and the final structure-constrained initial model are shown in Figure 9.

Figure 9. Construction process and final structure-constrained initial model: (a) 1D inversion results at different stations and the corresponding layer-constraint curves; and (b) the structure-constrained initial model constructed from the 1D resistivity trends and layer interface information. The color scale in panel (b) represents the resistivity distribution of the structure-constrained initial model.

In Figure 9a, the solid lines represent the 1D inversion results at different stations for the case without the concealed vein-type low-resistivity ore body, whereas the dashed lines represent the corresponding layer-constrained curves used to define the background structure. The 1D inversion results reflect the resistivity variation with depth, but lateral fluctuations and local jumps occur between adjacent stations. By introducing layer information, the electrical boundaries are constrained while the overall 1D resistivity trends are preserved. Figure 9b shows the structure-constrained initial model constructed under the joint guidance of the 1D inversion results and layer information. Compared with the homogeneous half-space initial model, this model exhibits clearer electrical zonation and structural characteristics. The host-rock background and alteration zone are preliminarily represented, providing a more reasonable starting model for subsequent inversion.

Figure 10 shows the RMS convergence curve for the inversion using the structure-constrained initial model. The RMS decreases from an initial value of 8.33 to 0.99 after 30 iterations.

Figure 10. RMS convergence curve versus iteration number for the inversion using the structure-constrained initial model.

Figure 11 presents the 3D inversion result obtained using the structure-constrained initial model. Compared with the true model, the recovered result forms a clear low-resistivity anomaly near the concealed vein-type ore body. The anomaly center shows good spatial correspondence with the true ore body. The recovered anomaly extends along the dipping background zone, and its overall position, extension direction, and dip trend are generally consistent with those of the target. These results indicate that the structure-constrained initial model provides a more suitable starting model for recovering the target anomaly under a layered alteration background.

Figure 11. Three-dimensional inversion results using the structure-constrained initial model: (a1,b1) true model; and (a2,b2) corresponding recovered results.

Compared with the inversion result obtained using the homogeneous half-space initial model, the structure-constrained initial model mainly improves the spatial concentration and structural correspondence of the recovered low-resistivity anomaly. The anomaly center is more focused near the target, and its extension into non-target background regions is reduced. The recovered anomaly also shows better continuity along the ore-body extension direction, allowing the vein-like geometry and dip trend of the target to be more clearly expressed. Because the structure-constrained initial model incorporates background interfaces and alteration-zone geometry before inversion, the spatial relationship between the recovered anomaly and the alteration zone is also better defined.

4.4. Analysis of the Inversion Recovery Process

To further analyze how initial-model optimization affects target recovery, the inversion recovery processes under the two initial-model strategies were compared. Figure 12 shows the RMS convergence curves for both inversions. For the inversion using the homogeneous half-space initial model, the RMS starts from a relatively high initial value, decreases continuously during the early stage, and then enters a prolonged slow-decrease stage before gradually approaching convergence. In contrast, the inversion using the structure-constrained initial model shows a faster early stage decrease, reaches a low RMS level earlier, and enters a stable-stage decrease within fewer iterations. Although both inversions ultimately achieve an acceptable level of data fitting, their convergence paths differ significantly. This indicates that initial-model optimization mainly affects the model-updating process and recovery behavior during inversion, rather than only the final data-fitting level.

Figure 12. Comparison of RMS convergence curves under different initial-model conditions.

According to the decay behavior and inflection points of the RMS curves, the inversion process was divided into three stages: rapid decrease, slow decrease, and low-value convergence. For the homogeneous half-space initial model, these three stages correspond to iterations 1–13, 14–39, and 40–48, respectively. For the structure-constrained initial model, they correspond to iterations 1–7, 8–18, and 19–30, respectively. The stage boundaries are marked by colored dashed lines in Figure 12.

Based on this classification, the first two stages were selected for cumulative model-update analysis. Iteration interval I corresponds to the rapid-decrease stage and is used to analyze the spatial distribution of model updates during the early inversion stage. Iteration interval II corresponds to the slow-decrease stage and is used to examine changes in the model-update region after the RMS reduction becomes less pronounced.

For the i-th inversion cell, the model-update intensity between iterations $k_a$ and $k_b$ is defined as:

$$U_i(k_a,k_b)=\left|\ln {\rho }_i^{(k_b)}-\ln {\rho }_i^{(k_a)}\right|$$

(42)

To facilitate comparison between different initial-model schemes, the model-update intensity is normalized as:

$$U_{N,i}^{(s)}={\displaystyle \frac{U_i^{(s)}(k_a,k_b)}{{\max }_i{U}_i^{(s)}(k_a,k_b)}}, \mathit{s}\in \{\mathrm{uni},\mathrm{sc}\}$$

(43)

where s denotes the initial model type, with uni representing the homogeneous half-space initial model and sc the structure-constrained model.

Figure 13 shows the normalized cumulative model-update intensity distributions during iteration interval I under the two initial-model conditions. Figure 13(a1,a2) correspond to the homogeneous half-space initial model. The model updates are strongly distributed in the shallow background, near the dipping background zone, and within the target zone. This indicates that, during the early inversion stage, the model updates must simultaneously account for both background-structure adjustment and target-anomaly recovery. In contrast, Figure 13(b1,b2) show the results obtained using the structure-constrained initial model. The cumulative updates are mainly concentrated around the ore body and its neighboring region, forming a belt-like distribution along the target body. The update intensity in the shallow background and near the layer-interface regions is significantly reduced. This indicates that the structure-constrained initial model provides more reasonable background resistivity trends and structural boundaries before inversion, allowing the early-stage updates to focus more effectively on the target zone and its surroundings.

Figure 13. Normalized cumulative model-update intensity distributions during iteration interval I under different initial-model conditions: (a1,a2) homogeneous half-space initial model; and (b1,b2) structure-constrained initial model.

Figure 14 shows the normalized cumulative model-update intensity distributions during iteration interval II. Figure 14(a1,a2) correspond to the homogeneous half-space initial model. In this interval, the cumulative updates remain concentrated in the shallow background and near the alteration-zone region, and the update range is still relatively broad. This indicates that, after entering the middle-to-late inversion stage under the homogeneous initial-model condition, the inversion must continue adjusting the background structure. As a result, part of the response difference associated with the background structure may be incorporated into the low-resistivity recovery near the target. This overlap between target-anomaly recovery and background-structure adjustment enlarges the low-resistivity anomaly and reduces the separation between the target body and the surrounding background structure.

Figure 14. Normalized cumulative model-update intensity distributions during iteration interval II under different initial-model conditions: (a1,a2) homogeneous half-space initial model; and (b1,b2) structure-constrained initial model.

In contrast, the structure-constrained initial-model results shown in Figure 14(b1,b2) exhibit a further reduction in the spatial range of cumulative updates. Updates in the shallow background and broad layer-interface regions are weakened, whereas the main updates are concentrated in the local region near the target body and along its extension direction. This indicates that, once the background resistivity trend and structural information are incorporated into the initial model, the inversion no longer needs to devote a large proportion of model updates to broad background adjustment. The subsequent recovery process can therefore focus more effectively on refining the low-resistivity anomaly in the target region.

Overall, initial-model optimization mainly affects the spatial distribution of model updates. The homogeneous half-space initial model lacks background structural information, so the inversion must adjust the background structure and recover the target anomaly simultaneously. As a result, background-related response differences may be partly mapped into the target-neighboring region, enlarging the recovered low-resistivity anomaly and reducing its separation from the surrounding background structure. In contrast, the structure-constrained initial model incorporates background resistivity trends and structural information before inversion. This reduces the need for broad background adjustment and concentrates subsequent updates around the target region.

4.5. Prior-Information Completeness Sensitivity Test

The comparison above shows that the complete structure-constrained initial model provides a more suitable starting model for inversion under the synthetic-model conditions considered in this study. However, in practical exploration, prior information is often incomplete or uncertain. Electrical information may be spatially sparse, and layer-interface information may be unavailable, only partially available, or affected by interpretation uncertainty. To evaluate the dependence of inversion recovery on prior information completeness, two additional initial models were constructed under incomplete prior-information conditions.

The first model is a no-layer-constrained one-dimensional electrical initial model. It was constructed from station-wise 1D inversion results with lateral smoothing, but without layer-interface or alteration-zone boundary information. It therefore mainly reflects the background resistivity trend inferred from 1D inversion results, without explicit structural guidance. The second model is a layer-constrained limited electrical-information initial model. In this case, only limited 1D electrical information was used to define the basic resistivity trend, while layer-interface and alteration-zone boundary information were introduced to guide the spatial organization of resistivity. This model was designed to test the role of structural guidance when the electrical prior information is incomplete.

All inversion settings in these sensitivity tests were kept identical to those used in the previous comparison, including the survey geometry, synthetic data, time channels, inversion mesh, objective function, model-parameter bounds, L-BFGS workflow, regularization-update strategy, and stopping criteria. Only the initial model was changed. Thus, differences in the inversion results mainly reflect the influence of prior-information completeness on the recovery process.

Figure 15 shows the two initial models constructed under incomplete prior-information conditions. Figure 15a shows the no-layer-constrained one-dimensional electrical initial model. This model preserves the general resistivity variation trend derived from the 1D inversion results, but its resistivity distribution is relatively smooth and lacks clear correspondence with layer interfaces and alteration-zone boundaries. Figure 15b shows the layer-constrained limited electrical-information initial model. Compared with Figure 15a, this model exhibits clearer structural zoning and better spatial correspondence with the layered background, although the electrical information used to define the resistivity trend remains limited.

Figure 15. Initial models constructed under different prior-information conditions. (a) No-layer-constrained one-dimensional electrical initial model. (b) Layer-constrained initial model with limited electrical-information.

Figure 16 compares the corresponding inversion results. Under the no-layer-constrained one-dimensional electrical initial model, the center of the recovered low-resistivity anomaly shows general spatial correspondence with the true ore body. This indicates that one-dimensional electrical information can provide useful constraints on the approximate position and resistivity level of the low-resistivity anomaly. However, the recovered anomaly is relatively thick and tends to form a local block-like low-resistivity accumulation. The slender vein-like geometry along the layer direction is not well recovered, and the spatial relationship between the low-resistivity anomaly, the layered background, and the alteration zone remains unclear. Under the layer-constrained initial model with limited electrical information, the extension direction of the recovered low-resistivity anomaly is more consistent with the layer interfaces and the spatial relationship of the alteration zone. The overall anomaly morphology is closer to the inclined extension of the true ore body. However, because the electrical information used to construct this initial model remains limited, the recovered anomaly still shows a certain spatial offset and relatively diffuse boundaries.

Figure 16. Comparison of inversion results under different levels of prior-information completeness. (a1) No-layer-constrained one-dimensional electrical initial model; (a2,a3) corresponding inversion results. (b1) Layer-constrained initial model with limited electrical-information; (b2,b3) corresponding inversion results.

These results indicate that electrical information and structural information play different roles in initial-model construction. Electrical information constrains the approximate position and resistivity characteristics of the low-resistivity anomaly, whereas layer-interface information improves the spatial correspondence between the recovered anomaly, the layered background, the alteration zone, and the ore-body extension direction. Consequently, the layer-constrained initial model with limited electrical information performs better than the no-layer-constrained 1D electrical initial model in recovering the anomaly extension direction and its relationship with the layered background. However, because the electrical information remains incomplete, boundary diffusion and local recovery errors are still present. These results suggest that both electrical and structural information are required to construct a favorable initial model for stable target recovery.

4.6. Quantitative Evaluation of Ore-Body Identification Under Different Initial-Model Conditions

The inversion-result comparisons and recovery-process analysis above show that low-resistivity anomalies can be recovered near the true ore-body region under different initial-model conditions. However, the continuity, concentration, spatial correspondence, and dipping geometry of the recovered anomalies differ significantly among the four initial-model schemes. To further evaluate the ore-body identification under these conditions, low-resistivity candidate anomaly zones were first extracted from the inversion results, and their correspondence with the true ore-body region was then quantitatively analyzed.

To compare the spatial distribution of low-resistivity anomalies, the candidate anomaly zone, $A_{\mathrm{low}}$, was extracted from each inversion result using the threshold $A_{\mathrm{low}}=\lfloor \left.i\right|1.5\le m_i\le 2.5\rfloor$ where mi denotes the model parameter of the i-th inversion cell. Figure 17 shows the extracted low-resistivity candidate anomaly zones under the four initial-model conditions. Under the homogeneous half-space initial model, the low-resistivity anomaly is spatially close to the true ore-body region, but its distribution is relatively fragmented and its continuity along the ore-body extension direction is weak. Under the no-layer-constrained one-dimensional electrical initial model, the main low-resistivity anomaly is closer to the true ore body, but the recovered body is relatively thick, and the vein-like extension characteristic is not sufficiently expressed. Under the layer-constrained initial model with limited electrical information, the continuity of the low-resistivity anomaly along the ore-body direction is improved, but the anomaly boundaries remain diffuse and a certain spatial offset is still present. Under the complete structure-constrained initial model, the low-resistivity anomaly forms a relatively continuous belt-like distribution, with clear spatial correspondence to the true ore-body geometry.

Figure 17. Extracted low-resistivity candidate anomaly zones under different initial-model conditions: (a) homogeneous half-space initial model; (b) no-layer-constrained one-dimensional electrical initial model; (c) layer-constrained initial model with limited electrical information; and (d) complete structure-constrained initial model. The blue areas denote extracted low-resistivity candidate anomaly zones, and the red line indicates the reference ore-body geometry.

The global low-resistivity candidate anomaly zone $A_{\mathrm{low}}$ provides a visual comparison of the low-resistivity distribution, but it is not directly used as the final object for quantitative evaluation. To reduce the influence of non-target low-resistivity anomalies outside the true ore-body region, the true ore-body region, $M$, was used as the spatial reference. The recovered low-resistivity cells within the true ore-body region are defined as:

$$A_M=A_{\mathrm{low}}\cap M$$

(44)

where $A_M$ represents the set of cells within the true ore-body region that are recovered as low-resistivity anomaly cells. Based on $A_M$, the ore-body identification effect under different initial-model conditions was evaluated using the ore-body-region recovery rate, recovery-center deviation, recovered dip angle, and dip-angle deviation.

The ore-body-region recovery rate is defined as:

$$R_M={\displaystyle \frac{{\displaystyle \sum _{i\in M}{V}_i}{I}_i}{{\displaystyle \sum _{i\in M}{V}_i}}}$$

(45)

where $V_i$ is the volume of the i-th cell within the true ore-body region, and $I_i=1$ if the i-th cell belongs to the low-resistivity candidate anomaly zone; otherwise, $I_i=0$. This metric reflects the proportion of the true ore-body region recovered as a low-resistivity anomaly.

The recovery center is calculated as the volume-weighted average of the recovered low-resistivity cells within AM:

$$r_R={\displaystyle \frac{{\displaystyle \sum _{i\in M}{V}_i}{I}_i{r}_i}{{\displaystyle \sum _{i\in M}{V}_i}{I}_i}}$$

(46)

where $r_i$ is the center coordinate of the i-th recovered low-resistivity cell. The recovery-center deviation is defined as the distance between the recovered center and the volume center of the true ore body:

$$D_c=‖r_R-r_M‖$$

(47)

where $r_M$ is the volume center of the true ore-body region.

Because the target ore body in this study has a clear inclined extension, the main dip direction of the recovered low-resistivity cells was further calculated from their spatial distribution and compared with that of the true ore body. The dip-angle deviation is defined as:

$$\Delta \theta =\left|{\theta }_R-{\theta }_M\right|$$

(48)

where ${\theta }_R$ is the recovered dip angle of the low-resistivity anomaly, and ${\theta }_M$ is the true dip angle of the ore body.

Table 1 summarizes the quantitative evaluation results under different initial-model conditions. As shown in Table 1, all inversion cases reach final RMS values close to 1, indicating broadly comparable data-fitting levels. However, the ore-body recovery metrics differ significantly among the four initial-model conditions. The homogeneous half-space initial model has the lowest recovery rate and a relatively large dip-angle deviation, indicating that data fitting alone is insufficient to ensure accurate recovery of the spatial morphology of a concealed vein-type ore body. Compared with the model, the no-layer-constrained one-dimensional electrical initial model improves the approximate positioning of the low-resistivity anomaly and increases the ore-body-region recovery rate. However, its recovered dip angle still differs substantially from that of the true ore body, indicating that one-dimensional electrical information alone provides limited control on the inclined extension geometry of the vein-type target. The layer-constrained initial model with limited electrical information improves the recovered extension direction and structural correspondence of the low-resistivity anomaly. Its dip-angle deviation is smaller than those of the homogeneous half-space and no-layer-constrained initial models. However, because the electrical information used to construct this model is limited, the recovery center still shows a relatively large spatial offset.

Table 1. Quantitative evaluation of ore-body identification performance under different initial-model conditions.

Initial Model	RMS	Iterations	Recovery Rate	Recovery-Center Deviation (m)	Recovered Dip Angle (°)	Dip-Angle Deviation (°)
Homogeneous half-space initial model	9.06–0.98	48	0.394	171.08	6.74	10.42
No-layer-constrained one-dimensional electrical initial model	9.42–0.97	52	0.498	83.62	8.06	9.10
Layer-constrained limited electrical-information initial model	8.18–0.98	44	0.615	183.66	18.09	0.93
Complete structure-constrained initial model	8.33–0.99	30	0.781	42.08	18.05	0.89

The complete structure-constrained initial model provides the most balanced recovery among the four cases, with a higher recovery rate, smaller recovery-center deviation, smaller dip-angle deviation, and fewer iterations. These results indicate that, under the synthetic-model conditions considered in this study, combining electrical and structural information provides a more favorable initial model for recovering the spatial position and dipping geometry of concealed vein-type low-resistivity targets.

5. Discussion

This study focuses on how initial-model construction influences 3D LOTEM inversion results. The structure-constrained initial model was used only as the starting model, while the objective-function form, reference-model setting, and regularization form remained unchanged across all comparison cases. Therefore, the differences among the inversion results mainly reflect the influence of background resistivity trends and structural-interface information on the model-updating process. For concealed vein-type low-resistivity targets in a layered alteration background, a better-informed starting model can reduce broad background adjustment and improve the separation between target-related anomalies and background-related responses.

The prior-information completeness sensitivity test further shows that electrical and structural information play different roles in initial-model construction. One-dimensional electrical information mainly constrains the approximate resistivity level and general position of the low-resistivity anomaly. However, when layer-interface information is absent, the recovered anomaly tends to be relatively thick, and the vein-like dipping geometry is not clearly expressed. In contrast, layer-interface information and alteration-zone boundaries help organize the resistivity distribution in 3D space and improve the correspondence between the recovered anomaly, the layered background, and the ore-body extension direction. However, if electrical information is limited, the recovered anomaly may still show spatial offset and boundary diffusion. These results indicate that electrical and structural information are complementary in constructing a favorable initial model.

In practical mineral exploration, the prior information used for initial-model construction may come from multiple sources. Borehole resistivity measurements, station-wise 1D inversion results, and electromagnetic interpretation results can provide constraints on background electrical-property trends. Regional geological interpretations, drilling information, geological cross-sections, seismic horizon interpretations, and 3D geological model can constrain layer interfaces, alteration-zone boundaries, and structural continuity. However, these data may differ in spatial coverage, resolution, and reliability. Therefore, the construction of a structure-constrained initial model should account for data quality, target scale, and geological plausibility. For ore districts with relatively abundant prior information, this strategy can transform existing geological and geophysical knowledge into a more reliable model basis for 3D inversion. For areas where prior information is uncertain or incomplete, comparison among multiple initial models and prior-information sensitivity tests are needed to evaluate the stability of inversion interpretations.

This validation is based on synthetic-model conditions. Synthetic models allow full control of the true model, survey geometry, noise level, and inversion parameters, which is useful for isolating the influence of the initial model on inversion recovery. However, actual LOTEM field data are affected by more complex factors, including observational noise, receiver-position errors, source-geometry uncertainty, near-surface heterogeneity, topographic effects, and possible inconsistencies in geological constraints. These factors can increase the non-uniqueness and uncertainty of inversion interpretation. Therefore, the results of this study should be regarded as a synthetic feasibility analysis rather than a direct demonstration of reliable ore-body identification in real ore districts.

Several limitations should also be noted. First, the present forward-modeling and inversion framework assumes an isotropic electrical medium. In real geological settings, anisotropy may affect transient electromagnetic responses and inversion recovery, especially in layered or strongly deformed formations. Second, this study does not provide a formal uncertainty estimate for the recovered target geometry. Future uncertainty analysis based on stochastic perturbations of initial models, structural interfaces, background resistivity values, and ore-body geometry could be used to evaluate the robustness of the recovered anomalies. Third, effects such as induced polarization, layer-interface errors, background-resistivity errors, ore-body scale variation, and more complex near-surface inhomogeneity were not fully considered in the present synthetic tests. These factors should be incorporated in future studies to further assess the applicability of the structure-constrained initial-model strategy under realistic exploration conditions.

Overall, the synthetic examples in this study show that initial-model optimization can improve the recovery of concealed vein-type low-resistivity targets under a layered alteration background. The improvement is mainly reflected in the spatial concentration of model updates, the correspondence between recovered anomalies and the structural background, and the recovery of target morphology. However, the practical effectiveness of this strategy depends on the quality and completeness of prior electrical and structural information. Future work should combine real LOTEM field data, multi-source geological constraints, and multi-scenario initial-model testing to further evaluate its applicability in mineral exploration.

6. Conclusions

This study investigated the influence of initial-model optimization on 3D LOTEM inversion for concealed vein-type low-resistivity targets under a layered alteration background. An approximate 3D geoelectrical model of the Zhaoxian ore district was constructed by integrating geological data, borehole information, profile interpretations, and electrical-property knowledge. Based on this model, LOTEM forward-response characteristics, inversion-result comparisons, recovery-process behavior, prior-information completeness sensitivity tests, and quantitative ore-body identification metrics were analyzed. Under the synthetic-model conditions considered in this study, the following conclusions can be drawn.

• The layered alteration background modifies the response characteristics of concealed vein-type low-resistivity targets. Compared with the homogeneous half-space model, the approximate geoelectrical model produces a stronger coupling between ore-body responses and background structural responses. This reduces the distinguishability between target anomalies and background responses and increases the difficulty of recovering a narrow vein-type target by inversion.
• The initial model has an important influence on the inversion recovery process. Under the homogeneous half-space initial model, the inversion can recover a low-resistivity anomaly near the true ore-body region, but the recovered anomaly is relatively diffuse, with unclear boundaries and poorly expressed dipping vein-like geometry. In contrast, the structure-constrained initial model provides a more reasonable background basis before inversion, reduces broad background adjustment during the early inversion stage, and concentrates subsequent model updates near the target region.
• The prior-information completeness sensitivity test shows that electrical and structural information play complementary roles in initial-model construction. One-dimensional electrical information mainly constrains the approximate position and resistivity level of the low-resistivity anomaly, whereas layer-interface information improves the spatial correspondence between the recovered anomaly, the layered background, the alteration zone, and the ore-body extension direction. When both types of information are incorporated, the recovery of concealed vein-type targets are improved.
• The quantitative evaluation shows that similar final RMS values can be achieved under different initial-model conditions, but comparable data-fitting levels do not necessarily imply comparable model-recovery quality. Compared with the homogeneous half-space initial model and the two incomplete-prior initial models, the complete structure-constrained initial model shows better overall performance in terms of ore-body-region recovery, recovery-center deviation, dip-angle recovery, and iteration efficiency. This further demonstrates that a better-informed initial model can improve the spatial recovery of concealed vein-type low-resistivity targets under the synthetic-model conditions considered in this study.

Overall, the results suggest that incorporating background resistivity trends and structural information into the initial model can improve the recovery of concealed vein-type low-resistivity targets in a layered alteration background. The proposed initial-model optimization strategy may provide useful guidance for LOTEM survey design and inversion interpretation in the Zhaoxian ore district. Further validation using real LOTEM field data and multi-source geological constraints is needed to evaluate its practical applicability under more realistic exploration conditions.