Method for detecting hidden goaf based on borehole multi-source constraint electrical method inversion

Abstract

The application discloses a method for detecting hidden goaf by electrical method inversion based on borehole multi-source constraint, and belongs to the technical field of cross of geophysical exploration and mine safety monitoring. The method comprises the following steps: obtaining borehole point cloud data to construct a cavity model; constructing a gradient weight matrix as a geometric constraint by using a model geometric boundary, setting a resistivity threshold according to a filling state and locking as a physical property constraint; constructing a target function containing data fitting, smoothing, priori and geometric terms, adopting adaptive regularization and local grid encryption for joint inversion to generate a resistivity three-dimensional model; based on spatial consistency level evaluation, combining D-S evidence theory to fuse a decision circle to delineate a goaf boundary, and dynamically adjusting a constraint weight to form a closed loop; and further migrating the optimal resistivity threshold to a non-borehole survey line. The application quantifies the borehole information into double quantitative constraints, reduces the positioning error from 5-10 meters to within 1 meter, reduces the volume error from + / - 8% to + / - 3%, and improves the convergence speed by more than 40%.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of geophysical exploration and mine safety monitoring, and specifically relates to a method for detecting hidden voids based on borehole multi-source constrained electrical inversion. Background Technology

[0002] Existing technologies for detecting hidden voids in open-pit coal mines have the following key shortcomings that urgently need to be addressed: High-density electrical resistivity inversion suffers from significant ambiguity: traditional high-density electrical resistivity inversion heavily relies on empirical initial models. Due to the relatively limited resistivity difference between concealed voids and intact surrounding rock, coupled with the influence of volume effects, the inversion process is prone to misinterpreting low-resistivity anomalies as water-bearing concealed voids or water-rich fracture zones, and high-resistivity anomalies as interbedded rock or surrounding rock. This results in severe ambiguity in the inversion results, making it difficult to accurately characterize the boundary morphology and three-dimensional spatial distribution of concealed voids.

[0003] Insufficient boundary delineation accuracy poses significant safety risks: Open-pit coal mining demands extremely high precision in locating the boundaries of concealed voids. Traditional inversion algorithms smooth out sharp resistivity boundaries, often resulting in a deviation of 5–10 meters or even more between the delineated boundary and the actual location. This deviation significantly increases the risk of catastrophic geological accidents such as slope instability and equipment collapse, posing a serious threat to personnel and equipment safety and the continued operation of the mine.

[0004] Insufficient utilization of prior borehole information and a disconnect between detection and inversion processes: While 3D laser scanning or sonar detection of boreholes can obtain centimeter-level precision in the geometry and filling status of empty areas, traditional methods only use this information as an independent single-point verification, failing to deeply integrate the high-precision geometric and physical property information contained within into the inversion modeling process. The accuracy of borehole detection is insufficient to quantitatively constrain electrical inference, resulting in the ineffective utilization of valuable known information.

[0005] Interpretive experience is difficult to transfer across survey lines, relying heavily on subjective human judgment: Traditional methods cannot automatically and quantitatively transfer physical property knowledge obtained from a known borehole control survey line to the inversion of other borehole-free survey lines within the same work area. The interpretation process heavily depends on human experience, resulting in low efficiency and high subjectivity, making it difficult to achieve intelligent transitions from accurate detection in the area surrounding the borehole to accurate detection across the entire survey area. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for detecting hidden voids based on borehole multi-source constrained electrical inversion.

[0007] The technical solution adopted in this invention is: a method for detecting hidden voids based on borehole multi-source constrained electrical inversion, the key technical points of which include: Three-dimensional point cloud data of the inner wall of the concealed void area is obtained by embedding a three-dimensional laser scanner or sonar detector in the borehole; a high-density resistivity measurement network is deployed on the ground to collect apparent resistivity data; and the borehole detection data and electrical resistivity data are spatially registered based on a unified coordinate system. A three-dimensional solid model of the cavity is constructed based on the three-dimensional point cloud data and discretized into an inversion mesh; a gradient weight matrix is ​​constructed using the geometric boundary information of the three-dimensional solid model of the cavity as a geometric constraint; a resistivity threshold for the corresponding cavity region is set according to the cavity filling state and the resistivity parameter of the region is locked as a physical property constraint. An objective function containing data fitting terms, model smoothing constraints, prior model constraints, and geometric constraints is constructed to iteratively invert high-density electrical resistivity data and generate a three-dimensional resistivity model that incorporates the cavity morphology. During the inversion process, residual-driven adaptive regularization parameter adjustment and resistivity gradient-driven local mesh refinement are adopted. The spatial consistency between the resistivity abrupt change interface in the resistivity 3D model and the boundary of the cavity 3D solid model is evaluated, and a fusion decision is made in combination with DS evidence theory to delineate the boundary of the hidden void area. The weights of the prior model constraint terms or geometric constraint terms in the objective function are dynamically adjusted according to the evaluation results, and the inversion is re-executed to form a "inversion-verification-optimization" closed loop. On the convergent inversion model of the borehole control survey line, the optimal resistivity anomaly threshold is extracted through dynamic statistical analysis and intelligent iteration. This threshold is then used as a strong physical property constraint and applied to the inversion of other non-brillhole control survey lines in the same work area, realizing cross-survey line knowledge transfer.

[0008] In the above scheme, the elements of the cavity boundary grid cells in the gradient weight matrix are set to one, and the elements of the non-boundary grid cells are set to zero; the geometric constraint term is composed of the product of the gradient weight coefficient, the gradient weight matrix and the resistivity gradient vector.

[0009] In the above scheme, the physical property constraints are specifically as follows: for dry cavities, the resistivity is forced to be greater than a preset high-resistivity threshold and iterative updates are prohibited; for water-filled cavities, the resistivity is forced to be less than a preset low-resistivity threshold and iterative updates are prohibited; a weak constraint region is set within a preset distance outside the boundary of the cavity's three-dimensional solid model, limiting the resistivity of this region to a set percentage range of the surrounding rock background value.

[0010] In the above scheme, the inversion objective function consists of the sum of the following four terms: the first term is the data fitting term, which measures the weighted difference between the observed data and the theoretical data of the forward simulation; the second term is the model smoothing constraint term, which is used to maintain the overall smoothness of the inversion model; the third term is the prior model constraint term, which is used to force the prior constraint region in the inversion result not to deviate from the prior geological model constructed based on the cavity three-dimensional solid model; and the fourth term is the geometric constraint term, which is used to strengthen the resistivity abrupt change characteristics of the cavity boundary.

[0011] In the above scheme, the model smoothing constraint term includes a regularization parameter, which adopts a residual-driven dynamic adjustment strategy: the regularization parameter of the next iteration is adjusted according to the regularization parameter of the previous iteration and the ratio of the data residual norms of the two iterations.

[0012] In the above scheme, during the joint inversion process, an adaptive local mesh refinement driven by resistivity gradient is adopted: the resistivity gradient value of each mesh cell is calculated in real time; when the resistivity gradient value of a certain region is greater than a preset threshold, and the spatial distance of the region from the boundary of the cavity three-dimensional solid model is less than a preset outward expansion distance, the mesh size of the region is halved; the above refinement process is repeated until the local mesh reaches the preset minimum size.

[0013] In the above scheme, the spatial consistency assessment includes: calculating the average spatial distance between the resistivity abrupt change interface and the boundary of the cavity three-dimensional solid model; classifying the average distance into excellent, good, and poor grades; dynamically adjusting the weights of the prior model constraint terms or the coefficients of the geometric constraint terms in the objective function based on the assessment results; and re-performing the joint inversion based on the adjusted weights or coefficients.

[0014] In the above scheme, the DS evidence theory fusion decision is specifically as follows: Constructing a high-density electrical resistivity evidence source: taking the spatial location of the resistivity abrupt change interface in the resistivity three-dimensional model as the first proposition, and assigning a first basic probability mass to this proposition; Constructing a borehole model evidence source: taking the spatial location of the boundary of the cavity three-dimensional solid model as the second proposition, and assigning a second basic probability mass to this proposition; Combining all propositions of the above two evidence sources, and calculating the joint probability mass of each combined proposition; When the joint probability mass of a certain spatial location being determined as the boundary of a hidden void is greater than or equal to a preset confidence threshold, the location is finally confirmed as the boundary of a hidden void.

[0015] The above scheme also includes terrain correction of high-density electrical resistivity tomography data: the three-dimensional spatial coordinates of the ground electrodes are obtained through the global navigation satellite system, and the influence of terrain undulations on the electric field distribution is eliminated based on the finite element forward modeling algorithm, so that the spatial registration error between the electrical resistivity data and the borehole model is controlled within a preset range.

[0016] In the above scheme, the resistivity threshold intelligent iterative picking adopts dynamic threshold calculation, and the final obtained optimal threshold is used as a strong physical property constraint to force the abnormal area in the borehole-free survey line inversion to meet the condition that the resistivity is greater than or less than the threshold.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention transforms high-precision borehole point cloud data into dual geometric-physical property quantification constraints, overcoming the shortcomings of traditional methods where borehole information is only used for qualitative reference and cannot be quantitatively integrated into the inversion. For the first time, this invention utilizes the cavity geometry and filling state obtained from 3D laser scanning or sonar detection of the borehole to directly construct resistivity locking rules (physical property constraints) and boundary gradient weight matrices (geometric constraints) in the inversion mesh. Thus, prior information is no longer merely a decoration for post-inversion verification, but becomes a mandatory indicator participating in iterative calculations, significantly reducing the ambiguity of high-density electrical resistivity tomography (EDS) inversion and lowering the cavity boundary positioning error from 5–10 meters in conventional methods to less than 1 meter.

[0018] 2. By explicitly introducing geometric and prior model constraint terms into the inversion objective function and combining them with adaptive local mesh refinement, the limitations of traditional smooth constraints in blurring cavity boundaries are overcome. A resistivity abrupt change at the cavity boundary is forced through the gradient weight matrix, while resistivity gradient-driven mesh refinement is performed only near the prior model boundary, significantly improving boundary resolution. Experiments show that when the refined mesh size reaches 0.2 meters, the volume estimation error can be reduced from ±8% to ±3%, and the convergence speed is improved by more than 40% compared to traditional methods, achieving accurate characterization of complex cavities (such as multi-layered cavities and inclined fracture zones).

[0019] 3. A dynamic closed-loop verification system based on the fusion of spatial coincidence quantification and DS evidence theory was established, solving the reliability defect of traditional inversion methods that are "one-time calculations without self-checking." By calculating the average distance between the resistivity abrupt change interface and the borehole model boundary, and combining the probability of electrical anomalies with the probability of borehole presence for joint judgment, the constraint weights are automatically adjusted and the inversion is re-performed based on the evaluation results, forming an adaptive loop of "inversion-verification-optimization." Examples show that the coincidence between the cavity boundary and the borehole model can reach 94.5%–95.82%, and the subsequent drilling verification error is less than 0.8 meters, ensuring the robustness and engineering credibility of the detection results.

[0020] 4. An innovative intelligent iterative acquisition and cross-surveyline migration mechanism for resistivity thresholds is introduced, enabling knowledge transfer from "single-point accuracy" to "full-area reliability." This invention automatically extracts the optimal resistivity anomaly threshold through dynamic statistical formulas on the convergent inversion model of borehole control surveys, and applies it as a strong physical property constraint to the inversion of other borehole-free control surveys within the same work area. Engineering examples show that after migration, the anomaly area of ​​borehole-free surveys is intelligently optimized and reduced by 14%–44%, effectively eliminating a large number of false anomalies, and subsequent verification shows a high degree of consistency between borehole exposure and prediction results. This method efficiently and quantitatively extends the physical property knowledge of "known points" to "unknown areas," significantly reducing the subjectivity and workload of manual interpretation.

[0021] 5. By achieving centimeter-level spatial registration between borehole laser / sonar detection and ground high-density electrical resistivity methods through GNSS terrain correction, this invention establishes a collaborative application chain for multi-source heterogeneous data. This invention enables deep fusion of fine underground point clouds and wide-area ground resistivity data under a unified coordinate reference, avoiding constraint failures caused by spatial misalignment. This improvement not only enhances the realism of the initial inversion model but also provides directly applicable high-precision three-dimensional distribution maps of open-pit coal mine stripping and blasting operations, reducing geological safety risks such as slope instability and equipment collapse from the source. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0023] Figure 1 This is a flowchart of the electrical inversion method for detecting goaf based on borehole multi-source detection constraints in an embodiment of the present invention; Figure 2 This is a flowchart of the intelligent feedback inversion technology in an embodiment of the present invention; Figure 3 This is a schematic diagram of the DS evidence theory fusion results in an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the traditional electrical inversion method with the method of the present invention for identifying the hidden void boundary in an embodiment of the present invention, wherein (a) is a schematic diagram of the traditional electrical inversion method for identifying the hidden void boundary; and (b) is a schematic diagram of the hidden void boundary identification. Detailed Implementation

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the following description is provided in conjunction with the accompanying drawings. Figures 1-4 The present invention will be further described in detail below with reference to specific embodiments.

[0025] The electrical inversion method for detecting goaf areas based on borehole multi-source detection constraints used in this embodiment includes the following steps: Step 1: Collaborative acquisition and spatial synchronization of multi-source data.

[0026] In traditional detection of concealed voids in open-pit coal mines, while borehole data (such as laser scanning) can acquire high-precision information about the local voids, it cannot cover the entire void area; and while ground-based high-density electrical resistivity tomography (EDS) can provide a wide range of resistivity distributions, its inversion results are highly ambiguous. Therefore, this embodiment uses borehole laser / sonar to acquire the precise geometry inside the void (as the "true value" for subsequent constraints), and simultaneously uses ground-based high-density EDS to acquire the resistivity response. GNSS terrain correction is then used to achieve centimeter-level spatial registration of the two types of data, laying the foundation for subsequently converting the high-precision borehole information into inversion constraints.

[0027] S1.1: 3D Detection Inside the Borehole: Vertical or inclined boreholes (diameter ≥ 75mm) are drilled in the target area. An explosion-proof borehole laser scanner (scanning accuracy ≤ 1mm) is lowered into the borehole, performing a 360° circular scan every 0.5 meters to acquire point cloud data of the inner wall of the concealed cavity, with a point cloud density ≥ 500 points / square meter. Features of suspended objects inside the cavity are marked. If the borehole is filled with water or mud, a borehole sonar (2MHz main frequency, ranging accuracy ≤ 2mm) is used, employing a spiral lifting mode (lifting speed 0.1m / s) to collect echo signals, acquiring 360 echo signals per revolution to construct an underwater cavity model. For partially filled cavities, laser and sonar data are fused, and a complete cavity model is formed using a point cloud stitching algorithm.

[0028] S1.2 High-density electrical resistivity tomography (ERT) data acquisition: High-density ERT lines are laid out along a direction perpendicular to the target body, using Wenner or dipole devices, with an electrode spacing of 2–5 meters and a line length ≥300 meters, covering an area of ​​at least 50 meters around the borehole. Simultaneously, GNSS terrain correction is performed to measure the three-dimensional coordinates (X, Y, Z) of each electrode point.

[0029] S1.3 Spatial Registration: Using the surface electrode coordinates measured by GNSS as a reference, the borehole detection data is converted to the same spatial coordinate system to eliminate the influence of terrain undulations on the electric field distribution and ensure that the spatial registration error between the borehole cavity model and the electrical survey line is ≤5 cm.

[0030] Step 2: Construction of the prior geological model and quantification of constraints.

[0031] This embodiment first discretizes the continuous cavity surface model into a three-dimensional mesh compatible with electrical resistivity inversion meshes. Then, it assigns a defined resistivity threshold based on the cavity filling state (dry or water-filled) and explicitly locks rules prohibiting updates. Simultaneously, to prevent numerical oscillations at the cavity boundaries due to excessive property jumps during inversion, a weakly constrained transition zone is set at the periphery. Furthermore, mesh refinement is applied near the cavity boundaries to ensure accurate capture of boundary details. In this way, the borehole information becomes a quantitative index system of "rigid hard constraints + flexible transition zone + local refinement".

[0032] S2.1 Cavity Model Discretization and Local Encryption.

[0033] Import the borehole point cloud data obtained in step 1 into 3D modeling software to construct a triangular mesh surface model of the cavity and convert it into a solid model. Then, divide the underground space into a 3D mesh, with an initial background mesh size of 2 m × 2 m × 2 m. Locally refine the mesh cells occupied by the cavity solid model and the mesh within a 0.5-meter radius of the boundary, resulting in a mesh size of 0.5 m × 0.5 m × 0.5 m to ensure fine depiction of boundary details.

[0034] S2.2 Setting of material property constraint rules.

[0035] Based on the cavity filling state identified by borehole laser scanning or sonar detection, the following physical property constraint rules are set: For dry cavities: the resistivity of their grid cells is forced to be fixed to be greater than 4000 Ω·m and locked during the inversion process, prohibiting any iterative updates; For water-filled cavities: the resistivity of their grid cells is forced to be fixed to less than 50 Ω·m, and is also locked, prohibiting iterative updates; For the grid extending 0.5–21 meters beyond the cavity boundary (referred to as the weakly constrained transition zone): resistivity is allowed to fluctuate within ±20% of the surrounding rock background value to avoid excessive boundary smoothing; the surrounding rock background value is obtained through unconstrained inversion of the neighborhood or regional geological data; using the geometric boundary information of the cavity 3D solid model, a boundary gradient weight matrix Wg is constructed. Elements corresponding to the cavity boundary grid cells are set to 1, and elements of non-boundary grid cells are set to 0. This forced abrupt change in resistivity at the cavity boundary overcomes the fuzzing effect of traditional smoothing constraints on the boundary.

[0036] For the background region (the region far from the cavity): no physical property constraints are imposed, allowing free updates during inversion.

[0037] Step 3: Intelligent constraint joint inversion.

[0038] Traditional high-density electrical resistivity tomography (EDS) inversion uses smoothing constraints, tending to smooth sharp physical property interfaces into gradual transitions, resulting in severe blurring of cavity boundaries. This embodiment aims to address the issue of simultaneously using the prior information constructed in step 2 to force the cavity region to conform to the actual resistivity while maintaining boundary clarity. This embodiment explicitly adds two new constraints to the objective function: a prior model constraint term (forcing the resistivity of the cavity and transition region to not deviate from the prior value) and a geometric constraint term (strengthening abrupt changes through the boundary gradient weight matrix) to achieve the above objectives. Simultaneously, through residual-driven adaptive regularization parameter adjustment and resistivity gradient-triggered local mesh refinement, a differentiated inversion strategy is achieved, characterized by strong constraints in the prior region, high resolution in the boundary region, and smooth and stable background region.

[0039] S3.1 Construction of the inverse objective function.

[0040] The prior geological model obtained in step 2 (discrete grid + property locking rules + weakly constrained transition zone) is introduced into the objective function to construct the following optimization problem: (1) The meanings of each term in the formula are as follows: Here, d represents the data fitting term, and d is the observed data vector. Forward modeling operator, and theoretical data obtained from electrical forward modeling simulation; For the data weight matrix, high-quality, low-noise data points can be given higher weights; For model smoothing constraints, For regularization parameters, For model roughness operators; As a priori model constraint term, it forces the inversion results not to deviate from the prior model in the region Ω (i.e., the "cavity + weak constraint transition zone" defined in step 2). This is crucial for quantitatively integrating high-precision borehole information into the inversion process. Prior geological model Data is obtained and models are built by three-dimensional laser scanning or sonar detection inside the borehole.

[0041] For geometric constraint terms: η is the gradient weight coefficient (initially taken as 10¹ to 10²), Wg is the boundary gradient weight matrix (based on the cavity boundary in step 2, the weights of the boundary mesh elements are set to 1, and those of the non-boundary elements are set to 0), and ∇m is the resistivity gradient vector. This term directly forces a sudden change in resistivity at the cavity boundary, overcoming the fuzziness effect of traditional smooth constraints on the boundary.

[0042] S3.2 Finite element forward modeling calculation.

[0043] Solve the control equations using software or a custom acceleration algorithm: (2) In the formula: The dielectric conductivity; I represents the potential distribution; I represents the injected current. It is the Dirac function; This indicates the power supply location.

[0044] Boundary conditions: The ground surface is set as a free surface, and the bottom and sides of the model are set as infinite boundaries to reduce boundary effects.

[0045] S3.3 Inversion Iteration and Model Update.

[0046] The step size α is determined by the Armijo criterion and adaptively determined by the Wolfe-Powell condition, which avoids iterative oscillations and improves the convergence speed by 30%.

[0047] Adaptive regularization parameter tuning: Dynamically updated, the formula is: (3) In the formula: The data residual for the k-th iteration; When the residual decreases When the residual decreases, the residual increases. This design prioritizes data fitting in the early stages of the inversion process while maintaining model smoothness in later stages.

[0048] Iteration termination condition: The iteration terminates when any of the following conditions are met: Relative residual change rate: <10⁻⁴; Model variation norm: <10⁻³; Maximum number of iterations: 100.

[0049] S3.4 Adaptive Grid Encryption.

[0050] Real-time detection of resistivity gradient during the inversion process: (4) Encryption trigger condition: When the resistivity gradient value of a certain region is greater than the preset threshold (500Ω·m / m in this embodiment), and the distance of the region from the boundary of the cavity model in step 2 is less than 0.5 m, local mesh encryption is performed.

[0051] Encryption termination condition: The local mesh size is minimized to 0.2m to avoid excessive encryption leading to a surge in computational load. This strategy only increases resolution near the prior boundary, avoiding the computational burden of global encryption.

[0052] After the inversion is completed, a three-dimensional resistivity model with integrated cavity morphology is obtained. This model will be used for dynamic verification and feedback in step 4.

[0053] Step 4: Decision-level integration and dynamic verification feedback.

[0054] This step addresses how to determine the reliability of the inversion result obtained in step 3, and how to automatically improve it when reliability is insufficient. This embodiment employs a two-level verification process: the first level is spatial coincidence quantification (directly comparing the distance between the resistivity abrupt change interface and the borehole model boundary from step 2); the second level is decision-level fusion using DS evidence theory (integrating the electrical anomaly probability and the borehole existence probability). If the evaluation result is "poor," the system automatically increases the weight of the prior constraint term λ2 or the geometric constraint coefficient η, returning to step 3 for re-inversion, forming a closed loop of "inversion, verification, adjustment, and re-inversion." This ensures the robustness and reliability of the final result.

[0055] S4.1 Spatial overlap metric quantification.

[0056] Calculate the average distance D between the resistivity abrupt change interface obtained in step 3 and the borehole model boundary in step 2: If D < 0.3m, the overlap is considered excellent; If 0.3m ≤ D < 0.5m, it is considered good; If D ≥ 0.5m, it is a difference.

[0057] S4.2 DS Evidence Theory Integration Judgment.

[0058] Construct two sources of evidence: Evidence 1 (High-density electrical resistivity method): Based on the three-dimensional resistivity model obtained from step 3, calculate the probability of resistivity anomaly in the cavity region. For example, the probability that the air-filled cavity ρ > 4000Ω·m; Evidence 2 is based on borehole laser scanning and sonar: The probability of cavity existence is calculated using the borehole point cloud data from step 1. For example, the proportion of laser point cloud cavities.

[0059] DS Evidence Theory Fusion Formula: (5) In the formula: This is the basic probability assignment function after combination; and The basic probability assignment function for the two evidence sources: high-density electrical resistivity and borehole three-dimensional laser scanning and sonar detection; To sum ∑, we require that the summation be performed only on those proposition pairs (B, C) where the intersection of B and C is exactly equal to A; K is the conflict coefficient, representing the total conflict between the two sources of evidence. When If the value is greater than 0.8, the result is considered reliable; otherwise, an adjustment mechanism is triggered (such as increasing the weight of electrical resistivity data or re-examining the borehole model). S4.3 Results Output and Volume Error Assessment.

[0060] Volume error assessment formula: Error = ×100% (6) When the mesh size is reduced from 1 m to 0.2 m, the volume error can be reduced from ±8% to ±3%.

[0061] 3D visualization: Output a 3D resistivity model that integrates the cavity morphology, generating representative slices along the major axis, minor axis, and vertical direction of the concealed cavity, and labeling resistivity values ​​and cavity boundary coordinates. During the simulation, the spatial overlap between the resistivity abrupt change interface and the borehole laser model is compared. If the deviation is >10%, the constraint weights are adaptively adjusted. Finally, the boundary of the concealed cavity is delineated, and the positioning error is reduced from 5–10 m in conventional methods to <1 m, with a convergence speed improvement of over 40%.

[0062] Steps 1-4 above effectively constrain electrical inversion using high-precision borehole information, overcoming the fundamental shortcomings of traditional methods such as strong ambiguity and blurred boundaries. This method is suitable for the precise detection of complex, concealed voids (such as multi-layered cavities and inclined fracture zones).

[0063] Step 5: Intelligent iterative picking of resistivity threshold and cross-test line migration application.

[0064] This embodiment aims to address how to automatically and quantitatively transfer resistivity anomaly characteristics learned from known borehole control survey lines to other survey lines without borehole control, thereby extending "single-point precision" knowledge to "reliable detection across the entire area." This embodiment employs a two-level transfer strategy: the first level uses dynamic statistical iteration to intelligently select the optimal resistivity anomaly threshold τ on the convergent inversion model of the borehole control survey lines (adaptively capturing the electrical boundary between the void and the surrounding rock using a combination formula of mean and standard deviation); the second level applies this threshold as a strong physical property constraint to the inversion objective function of the borehole-free survey lines, guiding the anomaly regions to satisfy the learned resistivity characteristics. If the transferred inversion results significantly contradict subsequent verification borehole findings (e.g., a large deviation between the predicted void location and the actual location), the system automatically triggers a threshold correction mechanism—returning to step 5.1, expanding the statistical range or adjusting the α coefficient based on the original known void area, re-extracting the threshold, and transferring again, forming a closed-loop iteration of "learning—transfer—verification—correction." This ensures that the transfer of knowledge from known areas to unknown areas is highly reliable and adaptive, significantly reducing the subjective bias of human experience interpretation.

[0065] S5.1 Resistivity Threshold Intelligent Pickup On the borehole control survey line, based on the converged strongly constrained inversion model, within the known void area precisely defined by the borehole laser / sonar model, the optimal resistivity anomaly threshold is extracted through intelligent iteration using dynamic statistical analysis. The dynamic threshold calculation formula is: In the formula: τ (k) μ is the high-resistivity anomaly threshold for the k-th iteration; (k) σ is the mean resistivity of the current model; (k) τ represents the standard deviation of the resistivity of the current model; α is an empirical coefficient, typically taken as 1.5–2.0, used to control the sensitivity of anomaly identification. Through multiple iterations, a resistivity threshold τ that can optimally distinguish between voids and surrounding rock is finally obtained.

[0066] S5.2 Cross-line migration application.

[0067] This threshold τ is used as a strong physical property constraint and applied to the inversion of other control survey lines without boreholes within the same work area. Specific procedures are as follows: A physical property constraint term is added to the new inversion objective function to force the predicted anomalous regions to satisfy the condition that resistivity ρ>τ for high-resistivity void regions or ρ<τ for low-resistivity water-filled void regions.

[0068] Re-execute the intelligent constraint inversion in step 3 so that the inversion results of the borehole-free survey line can inherit the learned resistivity characteristics.

[0069] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for detecting hidden voids based on borehole multi-source constrained electrical resistivity tomography (EDT), characterized in that, include: Three-dimensional point cloud data of the inner wall of the concealed void area is obtained by embedding a three-dimensional laser scanner or sonar detector in the borehole; a high-density resistivity measurement network is deployed on the ground to collect apparent resistivity data; and the borehole detection data and electrical resistivity data are spatially registered based on a unified coordinate system. A three-dimensional solid model of the cavity is constructed based on the three-dimensional point cloud data and discretized into an inversion mesh; a gradient weight matrix is ​​constructed using the geometric boundary information of the three-dimensional solid model of the cavity as a geometric constraint; a resistivity threshold for the corresponding cavity region is set according to the cavity filling state and the resistivity parameter of the region is locked as a physical property constraint. An objective function containing data fitting terms, model smoothing constraints, prior model constraints, and geometric constraints is constructed to iteratively invert high-density electrical resistivity data and generate a three-dimensional resistivity model that incorporates the cavity morphology. During the inversion process, residual-driven adaptive regularization parameter adjustment and resistivity gradient-driven local mesh refinement are adopted. The spatial consistency between the resistivity abrupt change interface in the resistivity 3D model and the boundary of the cavity 3D solid model is evaluated, and a fusion decision is made in combination with DS evidence theory to delineate the boundary of the hidden void area. The weights of the prior model constraint terms or geometric constraint terms in the objective function are dynamically adjusted according to the evaluation results, and the inversion is re-executed to form a "inversion-verification-optimization" closed loop. On the convergent inversion model of the borehole control survey line, the optimal resistivity anomaly threshold is extracted through dynamic statistical analysis and intelligent iteration. This threshold is then used as a strong physical property constraint and applied to the inversion of other non-brillhole control survey lines in the same work area, realizing cross-survey line knowledge transfer.

2. The method for detecting hidden voids based on borehole multi-source constrained electrical resistivity tomography inversion as described in claim 1, characterized in that, In the gradient weight matrix, the elements corresponding to the cavity boundary grid cells are set to one, and the elements of the non-boundary grid cells are set to zero; the geometric constraint term is composed of the product of the gradient weight coefficient, the gradient weight matrix, and the resistivity gradient vector.

3. The method for detecting hidden voids based on borehole multi-source constrained electrical inversion as described in claim 1, characterized in that, The specific physical property constraints are as follows: for dry cavities, the resistivity is forced to be greater than a preset high-resistivity threshold and iterative updates are prohibited; for water-filled cavities, the resistivity is forced to be less than a preset low-resistivity threshold and iterative updates are prohibited; a weak constraint region is set within a preset distance outside the boundary of the cavity's three-dimensional solid model, limiting the resistivity of this region to a set percentage range of the surrounding rock background value.

4. The method for detecting hidden voids based on borehole multi-source constrained electrical inversion as described in claim 1, characterized in that, The inversion objective function consists of the sum of the following four terms: the first term is the data fitting term, which measures the weighted difference between the observed data and the theoretical data of the forward simulation; the second term is the model smoothing constraint term, which is used to maintain the overall smoothness of the inversion model; The third term is the prior model constraint term, which is used to force the prior constraint region in the inversion result to not deviate from the prior geological model constructed based on the cavity three-dimensional solid model; the fourth term is the geometric constraint term, which is used to strengthen the resistivity abrupt change characteristics of the cavity boundary.

5. The method for detecting hidden voids based on borehole multi-source constrained electrical inversion as described in claim 3, characterized in that, The model smoothing constraint term includes a regularization parameter, which adopts a residual-driven dynamic adjustment strategy: the regularization parameter of the next iteration is adjusted based on the regularization parameter of the previous iteration and the ratio of the data residual norms of the two iterations.

6. The method for detecting hidden voids based on borehole multi-source constrained electrical resistivity tomography inversion as described in claim 1, characterized in that, In the joint inversion process, an adaptive local mesh refinement driven by resistivity gradient is adopted: the resistivity gradient value of each mesh cell is calculated in real time; when the resistivity gradient value of a certain region is greater than a preset threshold, and the spatial distance of the region from the boundary of the cavity three-dimensional solid model is less than a preset outward expansion distance, the mesh size of the region is halved; the above refinement process is repeated until the local mesh reaches the preset minimum size.

7. The method for detecting hidden voids based on borehole multi-source constrained electrical inversion as described in claim 1, characterized in that, The spatial consistency assessment includes: calculating the average spatial distance between the resistivity abrupt change interface and the boundary of the cavity three-dimensional solid model; classifying the average distance into excellent, good, and poor grades; dynamically adjusting the weights of the prior model constraint terms or the coefficients of the geometric constraint terms in the objective function based on the assessment results; and re-performing the joint inversion based on the adjusted weights or coefficients.

8. The method for detecting hidden voids based on borehole multi-source constrained electrical inversion as described in claim 1, characterized in that, The DS evidence theory fusion decision is specifically as follows: Constructing a high-density electrical resistivity evidence source: taking the spatial location of the resistivity abrupt change interface in the resistivity three-dimensional model as the first proposition, and assigning a first basic probability mass to this proposition; Constructing a borehole model evidence source: taking the spatial location of the boundary of the cavity three-dimensional solid model as the second proposition, and assigning a second basic probability mass to this proposition; Combining all propositions of the above two evidence sources, and calculating the joint probability mass of each combined proposition; When the joint probability mass of a certain spatial location being determined as the boundary of a hidden void is greater than or equal to a preset confidence threshold, the location is finally confirmed as the boundary of a hidden void.

9. The method for detecting hidden voids based on borehole multi-source constrained electrical inversion as described in claim 1, characterized in that, It also includes terrain correction for high-density electrical resistivity tomography (ERT) data: the three-dimensional spatial coordinates of the ground electrodes are obtained through the Global Navigation Satellite System, and the influence of terrain undulations on the electric field distribution is eliminated based on the finite element forward modeling algorithm, so that the spatial registration error between the ERT data and the borehole model is controlled within a preset range.

10. The method for detecting hidden voids based on borehole multi-source constrained electrical resistivity tomography inversion as described in claim 1, characterized in that, The aforementioned intelligent iterative picking of resistivity threshold uses dynamic threshold calculation, and the final optimal threshold is used as a strong physical property constraint to force abnormal areas in the borehole-free survey line inversion to meet the condition that the resistivity is greater than or less than the threshold.

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