A Three-Dimensional Forward and Inverse Method and System for DC Resistivity in Complex Terrain Based on Octree

Abstract

This invention relates to the field of engineering geophysical exploration technology, specifically to a three-dimensional forward and inverse modeling method and system for DC resistivity in complex terrain based on octrees. The method includes: establishing a target information sequence; constructing a three-dimensional geoelectric model based on an octree grid using the target information sequence, and locally refining the model near the surface and in the electrode neighborhood of the exploration area, and outputting the modeling results; distinguishing between underground active units located below the terrain surface and air units located above the terrain surface based on the modeling results, analyzing the underground active units and using the finite volume method to discretely solve the DC resistivity potential field control equation, obtaining the theoretical potential response corresponding to the electrode device, and obtaining the theoretical apparent resistivity response; constructing an inversion objective function, and using an inversion strategy to iteratively update the resistivity parameters of the three-dimensional geoelectric model; outputting the three-dimensional resistivity imaging results of the underground medium in the exploration area through the updated three-dimensional geoelectric model, and identifying adverse geological bodies.

Description

Technical Field

[0001] This invention relates to the field of engineering geophysical exploration technology, specifically to a three-dimensional forward and inverse method and system for DC resistivity modeling of complex terrain based on an octree. Background Technology

[0002] DC resistivity is a commonly used detection method in engineering geophysical exploration. By supplying power to the subsurface medium and observing the potential response, the spatial distribution of the subsurface medium's resistivity is obtained through inversion, thereby enabling the identification of adverse geological bodies such as water-bearing faults and karst caves. However, as engineering exploration targets have gradually expanded from regular sites to complex terrain areas such as mountains and reservoir banks, traditional DC resistivity forward and inverse methods are no longer sufficient to meet the demands of high-precision imaging, mainly facing the following two technical challenges: On the one hand, surface undulations significantly alter the distribution of underground electric fields. If the terrain boundaries are not accurately represented during forward modeling, the strong electrical differences between the air and the underground medium will amplify geometric errors and further transmit them to the observation response and inversion results, leading to the displacement of undesirable geological bodies, blurred boundaries, and even false anomalies. Therefore, to conduct high-precision three-dimensional DC resistivity forward and inversion modeling under complex terrain conditions, it is first necessary to establish a numerical model that can accurately characterize terrain undulations and electrode spatial locations. Existing three-dimensional forward modeling of DC resistivity typically uses regular hexahedral meshes or unstructured tetrahedral meshes. Regular hexahedral meshes are simple in structure and easy to calculate, but in complex terrain areas, it is often necessary to refine the mesh over a large area to better approximate the true boundary, resulting in a rapid increase in the number of meshes and the scale of unknown parameters, leading to high computational and storage costs. Although unstructured tetrahedral meshes have good adaptability to complex boundaries, their mesh generation process is more complex, element quality control is more difficult, and modeling efficiency and stability still have certain limitations in engineering applications. Therefore, how to balance the accuracy and efficiency of three-dimensional forward modeling of DC resistivity under complex terrain conditions remains a key technical challenge.

[0003] On the other hand, DC resistivity inversion is essentially a typical ill-posed problem. Because observational data is susceptible to noise, measurement point layout, topographic relief, and the complexity of underground structures, the inversion results are typically highly sensitive to the initial model, regularization form, and parameter selection. Especially in complex 3D terrain scenarios, directly performing inversion on a fine-grid global domain often results in problems such as an excessively large number of unknowns, high computational costs, and difficulties in iterative convergence; while using a coarser grid makes it difficult to guarantee the imaging accuracy of adverse geological bodies. Therefore, how to control the computational cost of inversion while ensuring accurate imaging of adverse geological bodies is another technical challenge that urgently needs to be addressed in 3D DC resistivity inversion of complex terrain.

[0004] In recent years, with the development of adaptive mesh technology and the concept of local refinement, octree meshes, with their hierarchical partitioning characteristics and multi-scale representation capabilities provided by local refinement, have gradually become an important technical means for numerical simulation of complex three-dimensional physical fields. This mesh can be locally refined at terrain boundaries, near electrode areas, and key areas of interest, while maintaining a relatively coarse scale in other non-critical spaces. This effectively controls the scale of unknowns while ensuring computational accuracy, demonstrating good application potential. However, existing research is mostly concentrated in specific fields such as electromagnetics, and integrated research on three-dimensional forward and inverse DC resistivity modeling under complex terrain conditions remains insufficient. In particular, systematic solutions are lacking in key areas such as geoelectric model construction methods applicable to complex terrains, stable and efficient forward modeling calculations based on non-uniform octree meshes, and improving the imaging quality of three-dimensional DC resistivity inversion by combining progressive mesh refinement techniques. Summary of the Invention

[0005] To address the technical problems of low forward modeling efficiency and insufficient inversion imaging accuracy in existing technologies for three-dimensional forward and inverse DC resistivity modeling under complex terrain conditions, the present invention aims to provide a three-dimensional forward and inverse DC resistivity modeling method for complex terrain based on an octree. The specific technical solution adopted is as follows: Collect topographic data, electrode layout information, and observation data of the detection area, and integrate them to establish a target information sequence; A three-dimensional geoelectric model based on an octree grid is constructed using the target information sequence, and local densification is performed near the surface and in the electrode neighborhood of the detection area. The modeling results are then output. Based on the modeling results, the underground active units located below the terrain surface and the air units located above the terrain surface are distinguished. The finite volume method is used to discretize the DC resistivity method potential field control equation of the underground active units, obtain the theoretical potential response corresponding to the electrode device, and obtain the theoretical apparent resistivity response. An inversion objective function is constructed by combining observational data with theoretical apparent resistivity response, and the resistivity parameters of the three-dimensional geoelectric model are iteratively updated using an inversion strategy. The updated three-dimensional geoelectric model outputs three-dimensional resistivity imaging results of the subsurface medium in the detection area and identifies adverse geological bodies.

[0006] Preferably, a three-dimensional geoelectric model based on an octree grid is constructed using the target information sequence, and local refinement is performed near the surface and in the electrode neighborhood of the detection area. The modeling results are output, including: Standard grid cells are established based on the detection area. Local densified areas that conform to the terrain undulations are set near the ground surface and distributed along the real terrain surface. The range of the local densified areas is determined by a preset depth range or a preset number of grid layers from the ground surface. A near-field densification zone is set up in the vicinity of the electrode with the actual spatial location of the electrode as the center. The range of the near-field densification zone is determined by the preset horizontal distance, vertical distance or preset number of grid layers around the electrode. The detection area is defined as the unencrypted area, excluding the local encrypted area and the near-field encrypted area. The unencrypted area is then divided into coarse grid cells.

[0007] Preferably, both the standard mesh element and the coarsened mesh element satisfy the adjacent scale transition constraint, specifically: Based on the adjacent grid cells of any shared surface in the local encrypted region, near-field encrypted region and unencrypted region in the detection area, the side length ratio does not exceed 2. When the local encrypted region has an adjacent relationship spanning two levels or more, the coarsened grid cells are gradually encrypted to form a transition region.

[0008] Preferably, the analysis of the underground active unit employs the finite volume method to discretize and solve the DC resistivity method potential field control equations, obtaining the theoretical potential response corresponding to the electrode device, specifically as follows: The control equations of the DC resistivity method potential field are discretized using a volume integral form, satisfying the current conservation relationship at the discretization level. Discretization operators are constructed to discretize the control equations of the DC resistivity method potential field into a sparse linear system of equations, and the theoretical potential response corresponding to the electrode device is obtained by solving the system.

[0009] Preferably, the theoretical potential response corresponding to the electrode device is calculated, specifically as follows: A direct method framework of one-time factorization and multiple back substitution is adopted for the sparse linear equation system. The PARDISO solver is used for reordering and factorization, and then reused to solve the point source field under different power supply conditions to obtain the theoretical potential response corresponding to the electrode device.

[0010] Preferably, the theoretical apparent resistivity response is obtained as follows: Based on the electrode device, the device coefficient is obtained, and combined with the theoretical potential response, the theoretical apparent resistivity response is determined. The corresponding calculation formula is as follows:

[0011]

[0012] in, This represents the theoretical apparent resistivity response; Indicates the device coefficient; , Both represent power supply electrodes; , All represent measuring electrodes; Indicates current; The measuring electrode indicates that the value is taken in a preset direction. and The potential difference; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance.

[0013] Preferably, an inversion objective function is constructed by combining observed data with the theoretical apparent resistivity response, and an inversion strategy is used to iteratively update the resistivity parameters of the three-dimensional geoelectric model, including: Based on the observed data and the theoretical apparent resistivity response, a data fitting term and a model regularization term are established respectively. The inversion objective function is constructed by combining the data fitting term and the model regularization term. The data fitting term is used to characterize the difference between the observed data and the theoretical apparent resistivity response. The model regularization term is used to constrain the spatial variation of resistivity in the three-dimensional geoelectric model. An inversion strategy combining variable Lp constraints and progressive mesh refinement is employed to iteratively update the resistivity parameters of the three-dimensional geoelectric model.

[0014] Preferably, the variable Lp constraint adopts the Ekblom differentiable approximation form; the progressive mesh refinement collaborative inversion strategy includes three stages, wherein, in the first stage, L2 constraint inversion is performed on the coarsened mesh cells, and inversion result one is output; in the second stage, the task requirement area in the detection area is defined as the target area, mesh refinement is performed on the target area based on inversion result one, and inversion result one is mapped to the refined mesh cells; in the third stage, the model regularization term is transitioned from L2 constraint to L1 constraint on the refined mesh cells.

[0015] To address the aforementioned technical problems, this invention further provides: a three-dimensional forward and inverse modeling system for DC resistivity of complex terrain based on an octree, the system comprising: The data acquisition module is used to: collect topographic data, electrode layout information and observation data of the detection area, and integrate them to establish a target information sequence; The geoelectric model construction module is used to: construct a three-dimensional geoelectric model based on an octree mesh using the target information sequence, and to perform local densification near the surface and electrode neighborhood of the detection area, and output the modeling results; The forward modeling module is used to: distinguish between underground active units located below the terrain surface and air units located above the terrain surface based on the modeling results; analyze the DC resistivity method potential field control equation of the underground active units; obtain the theoretical potential response corresponding to the electrode device; and obtain the theoretical apparent resistivity response. The inversion solution module is used to: construct an inversion objective function by combining observation data and theoretical apparent resistivity response, and iteratively update the resistivity parameters of the three-dimensional geoelectric model using an inversion strategy; The imaging output module is used to: output three-dimensional resistivity imaging results of the subsurface medium in the detection area through the updated three-dimensional geoelectric model, and identify adverse geological bodies.

[0016] To solve the above-mentioned technical problems, the present invention also provides: an electronic device, the device comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree as described in any of the preceding claims.

[0017] The present invention has the following beneficial effects: 1. Forward and inverse modeling is performed based on a 3D geoelectric model using an octree mesh. Local densification is applied near the surface and electrode neighborhoods of the detection area to output modeling results, balancing the accuracy of boundary representation in complex terrain with control of computational scale. Then, the finite volume method is used to discretize and solve the DC resistivity method potential field control equations for the differentiated underground active units. After analysis, the theoretical apparent resistivity response is determined, improving the efficiency of 3D forward modeling under complex terrain conditions. Furthermore, during the inversion objective function calculation, an inversion strategy is used to iteratively update the resistivity parameters of the 3D geoelectric model, improving the accuracy and engineering practicality of 3D imaging under complex terrain conditions.

[0018] 2. The three-dimensional forward and inverse modeling system and electronic device for DC resistivity of complex terrain based on octree provided by the present invention have the same beneficial effects as the three-dimensional forward and inverse modeling method for DC resistivity of complex terrain based on octree provided by the present invention, and will not be described in detail here. Attached Figure Description

[0019] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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 based on these drawings without creative effort.

[0020] Figure 1A flowchart illustrating the steps of a three-dimensional forward and inverse method for DC resistivity of complex terrain based on an octree, as provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the three-dimensional electrode layout and fault location of a three-dimensional forward and inverse method for DC resistivity of complex terrain based on an octree, provided in an embodiment of the present invention. Figure 3 A slice of a three-dimensional geoelectric model based on an octree grid, which is a method for three-dimensional forward and inverse retrieval of DC resistivity in complex terrain based on an octree, provided in an embodiment of the present invention. Figure 4 This is a schematic diagram showing the comparison before and after progressive mesh refinement of a three-dimensional forward and inverse octree-based method for DC resistivity of complex terrain. Figure 5 This is a slice of the three-dimensional inversion result of a three-dimensional forward and inverse 3D model of DC resistivity in complex terrain based on an octree, provided in an embodiment of the present invention. Detailed Implementation

[0021] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a three-dimensional forward and inverse method and system for DC resistivity of complex terrain based on an octree, as proposed by the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0022] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] The following description, in conjunction with the accompanying drawings, details the specific scheme of the three-dimensional forward and inverse modeling method and system for DC resistivity of complex terrain based on octree provided by this invention.

[0024] To better illustrate this, the entire method implementation process is based on the DC resistivity method's potential field control equation. A three-dimensional geoelectric model is constructed under complex terrain conditions, and combined with octree mesh forward modeling and progressive inversion imaging, the spatial distribution of subsurface resistivity is reconstructed. The DC resistivity method's potential field control equation refers to the mathematical and physical equations describing the potential distribution when DC current flows steadily in the subsurface medium. It is the theoretical foundation of DC resistivity exploration. By solving this equation, the influence of different subsurface structures on the potential field can be predicted, thereby inverting the subsurface resistivity distribution. The octree mesh is an adaptive meshing technique used for three-dimensional spatial discretization. It initially divides the entire detection area into a cube, i.e., the root node of the octree. Based on the complexity of the area or data requirements, each cube is recursively subdivided into eight smaller cubes of equal volume, i.e., child nodes, forming a tree-like hierarchical structure. Compared to traditional uniform meshes, the octree mesh can more efficiently handle the forward modeling calculations of large-scale three-dimensional geoelectric models, providing high-quality forward modeling data support for progressive inversion.

[0025] Please see Figure 1 The diagram illustrates a flowchart of a three-dimensional forward and inverse method for DC resistivity of complex terrain based on an octree, according to a first embodiment of the present invention. The method includes: Step S1: Collect topographic data, electrode layout information and observation data of the detection area, and integrate them to establish a target information sequence; Step S2: Construct a three-dimensional geoelectric model based on an octree grid using the target information sequence, and perform local densification near the surface and electrode neighborhood of the detection area, and output the modeling results; Step S3: Based on the modeling results, distinguish between underground active units located below the terrain surface and air units located above the terrain surface. Analyze the underground active units and use the finite volume method to discretize the DC resistivity method potential field control equation to obtain the theoretical potential response corresponding to the electrode device and obtain the theoretical apparent resistivity response. Step S4: Combine the observation data and theoretical apparent resistivity response to construct the inversion objective function, and use the inversion strategy to iteratively update the resistivity parameters of the three-dimensional geoelectric model; Step S5: Output the three-dimensional resistivity imaging results of the underground medium in the detection area through the updated three-dimensional geoelectric model, and identify adverse geological bodies.

[0026] Please see Figure 2As an optional implementation method, in this embodiment, a fault low-resistivity body is used as the target body to carry out numerical experiments to verify the three-dimensional forward and inverse modeling method of DC resistivity in complex terrain based on octree, and its ability to image adverse geological bodies in complex terrain conditions. Among them, the black dots are electrode positions, five survey lines are arranged in parallel, 32 electrodes are set in each survey line, the electrode spacing is 10 m, and the survey line spacing is 50 m. The fault is located in the middle of the survey line group, and its overall orientation is approximately orthogonal to the survey line direction. The corresponding data result values ​​are set according to the actual situation.

[0027] As explained, in step S1, the terrain data includes the surface elevation data of the detection area; the electrode layout information includes the spatial coordinates of the electrodes, the position of the survey lines, the electrode spacing and the survey line spacing; the observation data includes the measured potential difference data or apparent resistivity data corresponding to different power supply electrode pairs and measurement electrode pairs; and the terrain data, electrode layout information and observation data are integrated to establish a target information sequence.

[0028] Further, step S2 includes: Step S21: Establish standard grid units based on the detection area, and set up local densified areas that conform to the terrain undulations near the ground surface. These areas are distributed along the real terrain surface and the range of the local densified areas is determined by a preset depth range from the ground surface or a preset number of grid layers. That is, the division of local densified areas strictly follows the undulation shape and spatial orientation of the real terrain surface in the detection area. The spatial range and boundary of the local densified areas are determined by a preset depth range in the vertical direction from the ground surface or by a preset number of grid layers within the area.

[0029] Step S22: Set up a near-field densification region in the electrode neighborhood with the actual spatial location of the electrode as the center. The range of the near-field densification region is determined by the preset horizontal distance, vertical distance or preset number of grid layers around the electrode. That is, the near-field densification region is set based on the actual spatial coordinates of each electrode. Its core area usually extends outward from the specific physical location of each electrode. The size of this region is determined by the allowable horizontal extension distance and vertical extension depth around the electrode, or by the preset number of layers of the computational grid.

[0030] Step S23: Define the detection area as the unencrypted area, excluding the local encrypted area and the near-field encrypted area, and use coarse mesh cells to divide the unencrypted area.

[0031] In this embodiment, the standard grid cell and the coarse grid cell are relative concepts. By distinguishing the grid cell scale, the accuracy of the complex terrain boundary representation and the control of the computational scale are taken into account. That is, the boundary distortion or loss of key features due to the grid being too coarse is avoided. At the same time, the excessive amount of computation, low efficiency or even the inability to solve the problem due to the grid being too fine is avoided.

[0032] Furthermore, both standard and coarsened mesh elements satisfy adjacent scale transition constraints, specifically: Based on the adjacent grid cells of any shared surface in the local encrypted region, near-field encrypted region and unencrypted region in the detection area, the side length ratio does not exceed 2. When the local encrypted region has an adjacent relationship spanning two levels or more, the coarsened grid cells are gradually encrypted to form a transition region.

[0033] It can be noted that, in order to ensure the mesh quality of the mesh cells in the local and near-field encrypted regions, adjacent mesh cells satisfy the 2:1 scale transition constraint, that is, the ratio of the side lengths of adjacent mesh cells on any shared surface does not exceed 2.

[0034] Please see Figure 3 To better illustrate this, in the geoelectric model slice of the 3D geoelectric model based on an octree mesh, the near-surface layer is a cover layer with a thickness of approximately 10m and a resistivity of 200 Ω·cm. The overburden layer lies beneath a highly resistive bedrock with a resistivity of 2000 Ω·cm. The fault traverses the background medium in the form of a low-resistivity band with a resistivity of 20. It is located in the middle of the survey line group; the result values ​​in the entire schematic process can be specifically set according to the actual situation.

[0035] As explained, in step S3, after the three-dimensional geoelectric model is constructed, underground active units and air units are distinguished based on the modeling results. Underground active units refer to grid units located below the terrain surface that participate in the discretization solution of the underground medium potential field; air units refer to grid units located above the terrain surface that are used to characterize the boundaries of terrain undulations.

[0036] Further, in step S3, the underground active unit is analyzed by using the finite volume method to discretize and solve the DC resistivity method potential field control equation, and the theoretical potential response corresponding to the electrode device is obtained, specifically as follows: The control equations of the DC resistivity method potential field are discretized using a volume integral form, satisfying the current conservation relationship at the discretization level. Discretization operators are constructed to discretize the control equations of the DC resistivity method potential field into a sparse linear system of equations, and the theoretical potential response corresponding to the electrode device is obtained by solving the system.

[0037] As an optional implementation, the discrete operator includes a gradient operator, a divergence operator, and a coefficient matrix related to the element resistivity. The gradient operator is used to discretize the rate of change and direction of the scalar field in space. The divergence operator corresponds to the discrete representation of the source and sink characteristics of the vector field, reflecting the flux divergence or convergence behavior of the field. The coefficient matrix related to the element resistivity constructs the numerical correlation between the element properties and the electromagnetic field or current distribution, so as to support the solution framework for practical problems such as resistivity forward and inverse modeling and geoelectric modeling.

[0038] Furthermore, the theoretical potential response corresponding to the electrode device is calculated, specifically as follows: A direct method framework of one-time factorization and multiple back substitution is adopted for the sparse linear equation system. The PARDISO solver is used for reordering and factorization, and then reused to solve the point source field under different power supply conditions to obtain the theoretical potential response corresponding to the electrode device.

[0039] It is explained that the sparse linear equation system is a finite volume discrete equation system of the DC resistivity method potential field control equation on an octree grid, and its unknowns are the potential values ​​of each underground active unit.

[0040] Specifically, by discretizing the continuous governing equations into a sparse linear system of equations and combining boundary conditions and point source power supply conditions, a forward modeling solution is performed. Under the condition of a fixed mesh topology, discrete operators and index relationships related to the mesh topology are pre-computed and cached to reduce the overhead of repeated assembly. A direct method framework of one-time factorization and multiple back substitution is adopted for the sparse linear system of equations. The PARDISO (Parallel Direct Sparse Solver) solver is used for reordering and factorization, and reused for solving point source fields under different power supply conditions; repeated decomposition is avoided, thereby achieving fast and stable multi-point source field simulation.

[0041] Further, in step S3, the theoretical apparent resistivity response is obtained, specifically as follows: Based on the electrode device, the device coefficient is obtained, and combined with the theoretical potential response, the theoretical apparent resistivity response is determined. The corresponding calculation formula is as follows:

[0042]

[0043] in, This represents the theoretical apparent resistivity response; Indicates the device coefficient; , Both represent power supply electrodes; , All represent measuring electrodes; Indicates current; The measuring electrode indicates that the value is taken in a preset direction. and The potential difference; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance.

[0044] It can be noted that the power supply electrodes and measuring electrodes are usually arranged according to engineering requirements, including electrode coordinates, measuring line positions, electrode spacing, and measuring line spacing.

[0045] Further, step S4 includes: Step S41: Based on the observed data and the theoretical apparent resistivity response, establish a data fitting term and a model regularization term respectively. Combine the data fitting term and the model regularization term to construct the inversion objective function. The data fitting term is used to characterize the difference between the observed data and the theoretical apparent resistivity response; the model regularization term is used to constrain the spatial variation of resistivity in the three-dimensional geoelectric model.

[0046] Specifically, the corresponding calculation formula is:

[0047] in, Represents the inversion objective function; Represents the resistivity of a three-dimensional geoelectric model; Indicates the data fitting term; Represents the regularization parameter; This represents the regularization term of the model.

[0048] Step S42: The resistivity parameters of the three-dimensional geoelectric model are iteratively updated using an inversion strategy that combines variable Lp constraints with progressive mesh refinement.

[0049] Specifically, the variable Lp constraint adopts the Ekblom differentiable approximation form, and the corresponding calculation formula is as follows:

[0050] in, Represents the variable Lp constraint function; Indicates the terms to be constrained; Indicates constraints. , When, corresponding to the L1 norm constraint, When, it corresponds to the L2 norm constraint; The intermediate values ​​correspond to the transitional form between block constraints and smooth constraints; Represents the smoothing parameter, and To avoid It is not guideable.

[0051] Next, the data fitting term is used to characterize the difference between the observed data and the theoretical apparent resistivity response, and the corresponding calculation formula is:

[0052] in, Represents the observation data vector; This represents the total amount of observed data; Indicates the index of observation data; The data weight matrix is ​​obtained from the uncertainty of the observed data. This indicates forward modeling.

[0053] The model regularization term is used to constrain the spatial variation of resistivity in the three-dimensional geoelectric model, and the corresponding calculation formula is:

[0054] in, Indicates the number of grid cells; Indicates the grid cell index; Represents the model space constraint matrix; Represents the resistivity of a three-dimensional geoelectric model; This represents the reference resistivity model, which can be taken as a uniform background model when there is no external prior information.

[0055] Please see Figure 4 Furthermore, the variable Lp constraint adopts the Ekblom differentiable approximation form; the progressive mesh refinement collaborative inversion strategy includes three stages. In the first stage, L2 constraint inversion is performed on the coarsened mesh cells, and inversion result one is output. In the second stage, the task requirement area in the detection area is defined as the target area, and mesh refinement is performed on the target area based on inversion result one, and inversion result one is mapped to the refined mesh cells. In the third stage, the model regularization term is transitioned from L2 constraint to L1 constraint on the refined mesh cells.

[0056] It can be explained that the first stage outputs the inversion result to obtain a stable background layer and the initial position of the anomaly; the second stage refines the grid to improve the spatial resolution of the fault and its neighborhood; and finally, based on the third stage, the model gradually shifts from a relatively smooth expression to a more concentrated block expression.

[0057] Please see Figure 5 The explanation is as follows: In step S5, the three-dimensional resistivity imaging results of the underground medium in the detection area are output through the updated three-dimensional geoelectric model to more intuitively demonstrate that three-dimensional imaging and spatial identification of faults can be achieved under complex terrain conditions. Among them, the continuously distributed low resistivity anomaly zones in the imaging results are interpreted as unfavorable geological bodies corresponding to fault fracture zones, and their location and scale are determined according to their spatial extension range in multiple slices. Combining the spatial continuity, burial depth, scale and correspondence with the location of the survey line, unfavorable geological bodies such as faults, fracture zones, water-bearing anomaly areas or karst caves are identified.

[0058] Understandably, forward and inverse modeling based on an octree mesh is used for calculation. Local densification is applied near the surface and electrode neighborhoods of the detection area to output modeling results, balancing the accuracy of complex terrain boundary representation with computational scale control. Then, the finite volume method is used to discretize the DC resistivity method potential field control equations for the differentiated underground active units. After analysis, the theoretical apparent resistivity response is determined, improving the efficiency of 3D forward modeling under complex terrain conditions. In the process of solving the inverse objective function, an inverse strategy is used to iteratively update the resistivity parameters of the 3D geoelectric model, improving the accuracy and engineering practicality of 3D imaging under complex terrain conditions.

[0059] A second embodiment of the present invention provides a three-dimensional forward and inverse modeling system for DC resistivity of complex terrain based on an octree, the system comprising: The data acquisition module is used to: collect topographic data, electrode layout information and observation data of the detection area, and integrate them to establish a target information sequence; The geoelectric model construction module is used to: construct a three-dimensional geoelectric model based on an octree mesh using the target information sequence, and to perform local densification near the surface and electrode neighborhood of the detection area, and output the modeling results; The forward modeling module is used to: distinguish between underground active units located below the terrain surface and air units located above the terrain surface based on the modeling results; analyze the DC resistivity method potential field control equation of the underground active units; obtain the theoretical potential response corresponding to the electrode device; and obtain the theoretical apparent resistivity response. The inversion solution module is used to: construct an inversion objective function by combining observation data and theoretical apparent resistivity response, and iteratively update the resistivity parameters of the three-dimensional geoelectric model using an inversion strategy; The imaging output module is used to: output three-dimensional resistivity imaging results of the subsurface medium in the detection area through the updated three-dimensional geoelectric model, and identify adverse geological bodies.

[0060] Understandably, by integrating the data acquisition module, geoelectric model construction module, forward modeling solution module, inverse modeling solution module, and imaging output module, and integrating the octree-based three-dimensional forward and inverse modeling system for DC resistivity of complex terrain, the aforementioned embodiment of the method for three-dimensional forward and inverse modeling of DC resistivity of complex terrain, provided by the aforementioned embodiment, is automatically implemented to reconstruct the spatial distribution of underground resistivity, addressing the shortcomings of existing technologies.

[0061] The third embodiment of the present invention provides an electronic device, which includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree as described in any embodiment of the present invention.

[0062] When it is in operation, it needs to use a three-dimensional forward and inverse modeling method for DC resistivity of complex terrain based on octree. Therefore, whether the equipment and program data are integrated or different hardware is configured to produce a function with similar effect to that of the present invention, it is within the protection scope of the present invention. The equipment has the same beneficial effect as the aforementioned three-dimensional forward and inverse modeling method for DC resistivity of complex terrain based on octree, and will not be described in detail here.

[0063] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0064] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A three-dimensional forward and inverse method for DC resistivity in complex terrain based on octrees, characterized in that, The method includes: Collect topographic data, electrode layout information, and observation data of the detection area, and integrate them to establish a target information sequence; A three-dimensional geoelectric model based on an octree grid is constructed using the target information sequence, and local densification is performed near the surface and in the electrode neighborhood of the detection area. The modeling results are then output. Based on the modeling results, the underground active units located below the terrain surface and the air units located above the terrain surface are distinguished. The finite volume method is used to discretize the DC resistivity method potential field control equation of the underground active units, obtain the theoretical potential response corresponding to the electrode device, and obtain the theoretical apparent resistivity response. An inversion objective function is constructed by combining observed data with the theoretical apparent resistivity response. An inversion strategy is then used to iteratively update the resistivity parameters of the three-dimensional geoelectric model, including: Based on the observed data and the theoretical apparent resistivity response, a data fitting term and a model regularization term are established respectively. The inversion objective function is constructed by combining the data fitting term and the model regularization term. The data fitting term is used to characterize the difference between the observed data and the theoretical apparent resistivity response. The model regularization term is used to constrain the spatial variation of resistivity in the three-dimensional geoelectric model. An inversion strategy combining variable Lp constraints and progressive mesh refinement is adopted to iteratively update the resistivity parameters of the three-dimensional geoelectric model. The variable Lp constraint adopts the Ekblom differentiable approximation form; the progressive mesh refinement collaborative inversion strategy includes three stages, wherein, in the first stage, L2 constraint inversion is performed on the coarsened mesh cells, and inversion result one is output; in the second stage, the task requirement area in the detection area is defined as the target area, mesh refinement is performed on the target area based on inversion result one, and inversion result one is mapped to the refined mesh cells; in the third stage, the model regularization term is transitioned from L2 constraint to L1 constraint on the refined mesh cells; The updated three-dimensional geoelectric model outputs three-dimensional resistivity imaging results of the subsurface medium in the detection area and identifies adverse geological bodies.

2. The three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree as described in claim 1, characterized in that, A three-dimensional geoelectric model based on an octree mesh is constructed using the target information sequence, and local refinement is performed near the surface and in the electrode neighborhood of the detection area. The modeling results are output, including: Standard grid cells are established based on the detection area. Local densified areas that conform to the terrain undulations are set near the ground surface and distributed along the real terrain surface. The range of the local densified areas is determined by a preset depth range or a preset number of grid layers from the ground surface. A near-field densification zone is set up in the vicinity of the electrode with the actual spatial location of the electrode as the center. The range of the near-field densification zone is determined by the preset horizontal distance, vertical distance or preset number of grid layers around the electrode. The detection area is defined as the unencrypted area, excluding the local encrypted area and the near-field encrypted area. The unencrypted area is then divided into coarse grid cells.

3. The three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree according to claim 2, characterized in that, Both the standard mesh element and the coarsened mesh element satisfy the adjacent scale transition constraint, specifically: Based on the adjacent grid cells of any shared surface in the local encrypted region, near-field encrypted region and unencrypted region in the detection area, the side length ratio does not exceed 2. When the local encrypted region has an adjacent relationship spanning two levels or more, the coarsened grid cells are gradually encrypted to form a transition region.

4. The three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree according to claim 1, characterized in that, The analysis of underground active units employs the finite volume method to discretize and solve the DC resistivity method's potential field control equations, obtaining the theoretical potential response corresponding to the electrode device. Specifically: The control equations of the DC resistivity method potential field are discretized using a volume integral form, satisfying the current conservation relationship at the discretization level. Discretization operators are constructed to discretize the control equations of the DC resistivity method potential field into a sparse linear system of equations, and the theoretical potential response corresponding to the electrode device is obtained by solving the system.

5. The three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree according to claim 4, characterized in that, The theoretical potential response corresponding to the electrode device is obtained by calculation, specifically: A direct method framework of one-time factorization and multiple back substitution is adopted for the sparse linear equation system. The PARDISO solver is used for reordering and factorization, and then reused to solve the point source field under different power supply conditions to obtain the theoretical potential response corresponding to the electrode device.

6. The three-dimensional forward and inverse method for DC resistivity of complex terrain based on octree according to claim 4, characterized in that, The theoretical apparent resistivity response is obtained as follows: Based on the electrode device, the device coefficient is obtained, and combined with the theoretical potential response, the theoretical apparent resistivity response is determined. The corresponding calculation formula is as follows: in, This represents the theoretical apparent resistivity response; Indicates the device coefficient; , Both represent power supply electrodes; , All represent measuring electrodes; Indicates current; The measuring electrode indicates that the value is taken in a preset direction. and The potential difference; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance; Indicates the power supply electrode to measuring electrode The distance.

7. A three-dimensional forward and inverse modeling system for DC resistivity of complex terrain based on an octree, characterized in that, The system includes: The data acquisition module is used to: collect topographic data, electrode layout information and observation data of the detection area, and integrate them to establish a target information sequence; The geoelectric model construction module is used to: construct a three-dimensional geoelectric model based on an octree mesh using the target information sequence, and to perform local densification near the surface and electrode neighborhood of the detection area, and output the modeling results; The forward modeling module is used to: distinguish between underground active units located below the terrain surface and air units located above the terrain surface based on the modeling results; analyze the DC resistivity method potential field control equation of the underground active units; obtain the theoretical potential response corresponding to the electrode device; and obtain the theoretical apparent resistivity response. The inversion solution module is used to: construct an inversion objective function by combining observed data with the theoretical apparent resistivity response; and iteratively update the resistivity parameters of the three-dimensional geoelectric model using an inversion strategy, including: Based on the observed data and the theoretical apparent resistivity response, a data fitting term and a model regularization term are established respectively. The inversion objective function is constructed by combining the data fitting term and the model regularization term. The data fitting term is used to characterize the difference between the observed data and the theoretical apparent resistivity response. The model regularization term is used to constrain the spatial variation of resistivity in the three-dimensional geoelectric model. An inversion strategy combining variable Lp constraints and progressive mesh refinement is adopted to iteratively update the resistivity parameters of the three-dimensional geoelectric model. The variable Lp constraint adopts the Ekblom differentiable approximation form; the progressive mesh refinement collaborative inversion strategy includes three stages, wherein, in the first stage, L2 constraint inversion is performed on the coarsened mesh cells, and inversion result one is output; in the second stage, the task requirement area in the detection area is defined as the target area, mesh refinement is performed on the target area based on inversion result one, and inversion result one is mapped to the refined mesh cells; in the third stage, the model regularization term is transitioned from L2 constraint to L1 constraint on the refined mesh cells; The imaging output module is used to: output three-dimensional resistivity imaging results of the subsurface medium in the detection area through the updated three-dimensional geoelectric model, and identify adverse geological bodies.

8. An electronic device, characterized in that, The device includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the three-dimensional forward and inverse modeling method for DC resistivity of complex terrain based on octree as described in any one of claims 1 to 6.

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