Electrical Source Semi-Airborne Transient Electromagnetic Complex Terrain FDTD 3D Forward Modeling Method and System

Abstract

This invention discloses a three-dimensional forward modeling method and system for complex terrain using semi-airborne transient electromagnetic (FDTD) with electrical sources, belonging to the field of transient electromagnetic forward modeling technology. The method includes the following steps: constructing a forward model and meshing it; constructing a surface model of the forward model and meshing it; processing the meshed information of the forward model and surface model using the BEDS-FDTD method, wherein conformal mesh technology is used to determine the spatial location attributes of the model based on the meshed information, and the equivalent conductivity is further calculated; arbitrarily complex shaped excitation sources are applied to the forward model based on the interpolation basis function idea; and the three-dimensional forward modeling result is obtained through iterative calculation of the forward electromagnetic field. This invention aims to achieve refined modeling and calculation of anomalies in arbitrarily complex terrain using transient electromagnetic FDTD methods, and to flexibly apply arbitrarily complex excitation sources during the forward modeling process.

Description

Technical Field

[0001] This invention relates to the field of transient electromagnetic forward modeling technology, and in particular to a three-dimensional forward modeling method and system for complex terrain using electrical source semi-airborne transient electromagnetic FDTD. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] The Semi-Airborne Transient Electromagnetic Method (SATEM) is a method that deploys high-power transmitting equipment on the ground and uses a receiving system mounted on a flight platform to achieve large-area scanning data acquisition. SATEM combines the advantages of the Airborne Transient Electromagnetic Method (ATEM) and the Transient Electromagnetic Method (TEM), and has the advantages of large detection depth, ease of construction, and high efficiency, making it very suitable for observation in complex terrain areas.

[0004] Transient electromagnetic three-dimensional numerical simulation is the foundation and tool for studying the response law of underground media. Commonly used numerical simulation methods include integral equation method (IE), finite difference method (FD), finite element method (FE), and finite volume method (FV). Among them, the finite-difference time-domain (FDTD) method has the advantages of simple mesh generation and high computational efficiency, and is widely used. However, when the traditional FDTD method simulates underground curved surface targets with regular hexahedral mesh, it cannot fit the surface boundary well, resulting in a large step error. Moreover, this error increases with the increase of mesh size. Therefore, it is particularly important to achieve fine detection of curved surface targets.

[0005] Furthermore, in the transient electromagnetic three-dimensional forward modeling process, there are two main methods for loading the excitation source: The first method treats the shallow surface as a homogeneous medium and incorporates the analytical solution of the homogeneous half-space as an initial condition into the iterative equations of FDTD. However, this method assumes a horizontal surface, limiting the simulation of undulating terrain. The second method introduces a current source into the Maxwell equations and loads the excitation source onto the Yee cell. However, this method imposes restrictions on the shape and position of the source, requiring the excitation source to be loaded onto the edges of the Yee cell. Neither of these methods can construct an excitation source that varies with the terrain, causing the simulation results to deviate from reality.

[0006] In summary, in the forward modeling process of the semi-airborne transient electromagnetic method for electric sources, how to achieve accurate fitting of curved surface boundaries and flexible loading of excitation sources in complex terrain has become an urgent problem to be solved by existing technologies. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the present invention aims to provide a three-dimensional forward modeling method and system for FDTD (Fluid Dynamics Theory) of complex terrain using a semi-airborne transient electromagnetic method. This method aims to achieve refined modeling and calculation of anomalies in any complex terrain using transient electromagnetic FDTD methods, as well as flexible application of any complex excitation source during the forward modeling process.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0009] The first aspect of this invention provides a three-dimensional forward modeling method for complex terrain using electrical source semi-airborne transient electromagnetic FDTD, comprising the following steps:

[0010] A forward model is constructed based on the terrain information of the target area, and the forward model is then meshed.

[0011] Construct the surface model of the forward model based on the model size of the meshed model, and then mesh the surface model.

[0012] The BEDS-FDTD method (Backward Euler Direct Splitting Finite-Difference Time-Domain) is used to process the information after meshing the forward model and the surface model. Specifically, conformal mesh technology is used to determine the spatial location attributes of the model based on the information after meshing, and the equivalent conductivity is further calculated. Based on the idea of ​​interpolation basis function, an excitation source of arbitrary complex shape is applied to the forward model.

[0013] The three-dimensional forward modeling results are obtained through iterative calculations of the forward electromagnetic field.

[0014] Furthermore, the target area includes the core area of ​​the transmitter and receiver measurement points, as well as the extended area to prevent boundary interference.

[0015] Furthermore, the forward model is meshed using Yee meshes. The core region is meshed using a uniform mesh, while the extended regions outside the core region are meshed using a non-uniform mesh that is expanded according to a set scaling factor.

[0016] Furthermore, the surface model includes an air layer, a formation, and an anomaly. The surface model is divided using a triangular mesh. By modifying the surface normal direction, the normal directions of the air layer, formation, and anomaly are made to point inward. When an anomaly is contained in the formation, the formation normal points inward, and the anomaly surface normal points outward.

[0017] Furthermore, using conformal mesh technology to determine the spatial location attributes of the model based on the information after mesh partitioning, the specific steps for further calculating the equivalent conductivity are as follows:

[0018] Ray tracing technology is used to calculate the nesting relationship between the forward model mesh and the surface model mesh to determine the spatial location attributes of the model.

[0019] Based on the spatial location attributes of the model, the equivalent conductivity of complex interfaces is calculated using the linear weighted average method.

[0020] Furthermore, based on the spatial location attributes of the model, the specific steps for calculating the equivalent conductivity of complex interfaces using the linear weighted average method are as follows:

[0021] Assume that the surface model mesh is divided into two spaces, each filled with a medium with different electrical parameters;

[0022] The equivalent conductivity is calculated by weighted average of the lengths of the edges containing different media.

[0023] Furthermore, the specific steps for applying arbitrarily complex shape excitation sources to the forward model based on the interpolation basis function idea are as follows:

[0024] Calculate and sort the intersection points of the line source segment with the Yee mesh surface;

[0025] Line source segments are divided based on the calculated intersection points;

[0026] Based on the idea of ​​interpolation basis functions, the midpoint of the line source segment is mapped by combining the spatial distribution of the electric field in the Yee grid.

[0027] A second aspect of the present invention provides a system for a three-dimensional forward modeling method for complex terrain using electrical source semi-airborne transient electromagnetic FDTD, comprising:

[0028] The forward model module is configured to construct a forward model based on the terrain information of the target area and to perform mesh subdivision on the forward model;

[0029] The surface model module is configured to construct the surface model of the forward model based on the meshed model size, and to mesh the surface model.

[0030] The Finite-Difference Time-Domain (FDTD) method module is configured to process the information after meshing the forward model and the surface model using the BEDS-FDTD method. Specifically, it uses conformal mesh technology to determine the spatial location attributes of the model based on the information after meshing, and further calculates the equivalent conductivity. Based on the idea of ​​interpolation basis functions, it applies excitation sources of arbitrary complex shapes to the forward model.

[0031] The iterative calculation module is configured to obtain three-dimensional forward modeling results through iterative calculation of the forward electromagnetic field.

[0032] A third aspect of the present invention provides a computer-readable storage medium storing a computer program adapted to be loaded by a processor and to execute steps in the FDTD three-dimensional forward modeling method for electrically sourced semi-airborne transient electromagnetic complex terrain as described in the first aspect of the present invention.

[0033] A fourth aspect of the present invention provides a computer device comprising:

[0034] A processor, adapted to execute computer programs;

[0035] A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the FDTD three-dimensional forward modeling method for electrical source semi-airborne transient electromagnetic complex terrain as described in the first aspect of the present invention.

[0036] The above one or more technical solutions have the following beneficial effects:

[0037] This invention discloses a three-dimensional forward modeling method and system for semi-airborne transient electromagnetic complex terrain using FDTD (Functional Directive Testing) with electrical sources. It introduces conformal mesh technology into the BEDS-FDTD method, proposing a modeling and calculation method for three-dimensional curved surface targets. Regarding the application of excitation sources, based on the interpolation basis function concept in the vector finite element method, excitation sources of arbitrary shapes are mapped onto the FDTD mesh, thereby enabling the application of arbitrary excitation sources under real-world conditions. Ultimately, this achieves forward numerical simulation of arbitrary electrical source application in semi-airborne transient electromagnetic complex terrain using FDTD three-dimensional forward modeling.

[0038] This invention introduces conformal mesh technology into the BEDS-FDTD fast 3D forward modeling method, uses two sets of meshes for calculation, and introduces ray tracing technology to realize the relationship between the two sets of meshes. It proposes to calculate the equivalent conductivity of the edges intersecting with complex interfaces based on the idea of ​​linear weighted averaging, which effectively improves the adaptability to complex terrain and irregular anomalies in the forward modeling process, realizes the fine modeling and calculation of arbitrarily complex terrain and anomalies, and improves the accuracy of simulation results.

[0039] Regarding the application of excitation sources, this invention proposes a method for applying arbitrary complex curve sources in transient electromagnetic FDTD three-dimensional forward modeling based on the interpolation basis function concept in the vector finite element method. This method can flexibly apply arbitrary complex excitation sources, enhancing the simulation capability for real complex geological structures and diverse excitation sources. This makes the numerical simulation results closer to the actual engineering situation, providing a more reliable theoretical basis and technical support for engineering applications.

[0040] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of this application 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 this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a flowchart of the FDTD three-dimensional forward modeling method for electrical source semi-airborne transient electromagnetic complex terrain in Embodiment 1 of the present invention;

[0043] Figure 2 In Embodiment 1 of the present invention, the target body surface divides the Yee cell into two spatial front views;

[0044] Figure 3 In Embodiment 1 of the present invention, the target body surface divides the Yee cell into two spatial side views;

[0045] Figure 4 This is a schematic diagram of the edge numbering of the Yee grid unit in Embodiment 1 of the present invention;

[0046] Figure 5 This is a schematic diagram of the uniform half-space model and the triangular mesh partitioning in Embodiment 1 of the present invention, wherein (a) is a schematic diagram of the core region of the uniform half-space model, and (b) is a schematic diagram of the triangular mesh partitioning.

[0047] Figure 6 This is a schematic diagram of the XOY plane excitation source and receiving measurement point in Embodiment 1 of the present invention;

[0048] Figure 7The above are comparison charts of the numerical and analytical solutions of BEDS-FDTD in Embodiment 1 of the present invention. (a) is a comparison chart with the measurement point (-150, 0, -50), (b) is a comparison chart with the measurement point (0, 0, -50), (c) is a comparison chart with the measurement point (100, -100, -50), and (d) is a comparison chart with the measurement point (200, 130, -50). Detailed Implementation

[0049] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, 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.

[0050] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0051] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0052] Example 1:

[0053] Embodiment 1 of the present invention provides a three-dimensional forward modeling method for FDTD (Fluid Dynamics Theory) of complex terrain with electrical sources and semi-airborne transient electromagnetic characteristics, such as... Figure 1 As shown, it includes the following steps:

[0054] Step 1: Construct a forward model based on the terrain information of the target area, and then perform grid subdivision on the forward model.

[0055] In this embodiment, the target area has complex terrain, namely irregular natural terrain obtained through field measurements or remote sensing data, characterized by arbitrary elevation undulations. The target area is determined based on engineering requirements, and includes the core area of ​​the transmitter and receiver measurement points, as well as an extended area to prevent boundary interference.

[0056] The forward model is meshed using Yee meshes. The core region is meshed using a uniform mesh, while the extended regions outside the core region are meshed using a non-uniform mesh that is expanded according to a set scaling factor.

[0057] After meshing, record the overall dimensions of the forward model, the expansion coefficients of adjacent meshes, the coordinates of the center point, and the coordinates of the eight corner points. The eight corner points refer to the eight geometric vertices of the three-dimensional Yee cell. The spatial rules for its electromagnetic field components are as follows: the electric field component is located at the midpoint of the edge of the Yee mesh cell, and the magnetic field component is located at the center of the face of the Yee mesh.

[0058] Step 2: Construct the surface model of the forward model based on the model size of the meshed model, and mesh the surface model.

[0059] The surface model comprises an air layer, a ground layer, and an anomaly. It is meshed using triangular facets. By modifying the surface normal direction, the normals of the air layer, ground layer, and anomaly are aligned inwards. When an anomaly is present within a ground layer, the ground layer normal points inwards, while the anomaly surface normal points outwards. Since the air layer, ground layer, and anomaly all form a closed surface, "inside" refers to the interior of this closed surface.

[0060] The model is meshed using triangular facets. After meshing, the number of triangular facet nodes, the number of elements, the XYZ coordinates of each node, and the element information are output for each model. The element information includes the element number and the node numbers contained in the element.

[0061] Step 3: Process the information after meshing the forward model and surface model using the BEDS-FDTD method.

[0062] This embodiment introduces conformal mesh technology into the BEDS-FDTD method, proposing a modeling and calculation method for three-dimensional curved surface targets. After the two sets of mesh models are established, the triangular element information files of the air layer, the strata, and the anomaly, as well as the emission source, receiver point information, model conductivity information, and Yee mesh subdivision size information are imported into the BEDS-FDTD method.

[0063] Step 3.1: Use conformal mesh technology to determine the spatial location attributes of the model based on the information after mesh partitioning, and further calculate the equivalent conductivity.

[0064] Step 3.1.1: Use ray tracing technology to calculate the nesting relationship between the forward model mesh and the surface model mesh, and determine the spatial location attributes of the model.

[0065] Specifically, each grid line of the Yee mesh is regarded as a ray emanating from the model boundary. The positional relationship between the ray and the triangular mesh of the undulating terrain or the surface of the anomalous body is determined in the Cartesian coordinate system, thereby obtaining the spatial position of different line segments and thus realizing the fine depiction of complex structures.

[0066] More specifically, the determination of "entry point" and "exit point" is mainly based on the inner product. Taking a ray along the X-direction as an example, its direction vector is (1,0,0). The inner product between the ray and the normal vector of the triangular element is calculated. If the inner product is less than 0, meaning the projection of the triangular element's normal vector onto the ray's direction vector is negative, then the intersection of the triangular element and the X-direction ray is the entry point. If the inner product is greater than 0, meaning the projection of the triangular element's normal vector onto the ray's direction vector is positive, then the intersection of the triangular element and the X-direction ray is the exit point. In forward modeling, the computational domain is typically divided into three parts: the air layer, the background ground, and the anomaly. For each medium region, the region between the ray's "entry point" and "exit point" is assigned the inherent physical properties of that medium; however, at the surface boundary, conformal processing with the physical properties of the adjacent medium is required.

[0067] Since the intersection process between each triangle element and the ray is independent and does not interfere with each other, parallel techniques such as OpenMP or OpenACC can be added to achieve fast intersection. This ray tracing method is the minimum storage ray-triangle intersection algorithm proposed by Thomas Möller et al. in 1997, which will not be elaborated here.

[0068] Step 3.1.2: Based on the spatial location attributes of the model, calculate the equivalent conductivity of the complex interface using the linear weighted average method.

[0069] Step 3.1.2.1: Assume that the surface model mesh is divided into two spaces, each filled with a medium with different electrical parameters.

[0070] Once the spatial location attributes of the model are determined, the equivalent conductivity of the edges intersecting with the interface of the complex medium is calculated using the concept of linear weighted averaging. For example... Figure 2 and Figure 3 As shown, it is assumed that the target body surface after triangular element subdivision divides the Yee cell into two spaces, which are filled by two media with different electrical parameters, namely medium 1 and medium 2.

[0071] In this embodiment, a complex medium interface refers to an interface with a curved shape, such as the surface of a terrain or an anomaly. Since the Yee mesh is an approximate subdivision of a curved surface, conformal processing is introduced to handle the conductivity of the curved surface. For non-curved interfaces, the cell contains only a single medium, and its conductivity does not require additional processing.

[0072] Step 3.1.2.2: Calculate the equivalent conductivity based on the weighted average of the lengths of the edges containing different media.

[0073] Since the electric field is located at the center of the cell edge, the equivalent conductivity is calculated by the weighted average of the lengths of the edges where different media are located, as shown in formulas (1) to (4).

[0074] (1),

[0075] (2),

[0076] (3),

[0077] (4).

[0078] In the formula, and These represent different electrical conductivities. Let A, B, C, and D represent the equivalent conductivity at points A, B, C, and D, respectively. , These represent the lengths of the grid edges in the Z and X directions, respectively. , , , These represent the lengths at which different media intersect with the edge.

[0079] By substituting the above-mentioned edge equivalent conductivity into the electric field iteration equations of the BEDS-FDTD method, namely formulas (23) and (24), the conformal mesh technology for complex terrain and anomalous bodies can be completed.

[0080] Step 3.2: Apply excitation sources of arbitrary complex shapes to the forward model based on the idea of ​​interpolation basis functions.

[0081] In this embodiment, the application of excitation sources of arbitrary complex shapes is based on the interpolation basis function concept in the vector finite element method. The edge numbering of the Yee mesh elements is as follows: Figure 4 As shown.

[0082] Step 3.2.1: Calculate and sort the intersection points of the line source segment and the Yee mesh surface.

[0083] First, the coordinate data of any wire source node is read, and all intersection points between the wire source and the Yee mesh element surface are calculated. These intersection points are then sorted according to their distance from the starting point. It should be noted that the excitation source can be a loop source or an electrical source; however, in this embodiment, in the semi-airborne transient electromagnetic scenario, the excitation source is an electrical source, and the wire source node is the node within the excitation source.

[0084] Step 3.2.2: Perform line source segmentation on the calculated intersection points.

[0085] Based on the intersection points sorted in step 3.2.1, each line source is divided into the Yee grid cells it passes through, ensuring that each line source is within a Yee grid cell.

[0086] Specifically, the calculation of intersection points is as follows: First, determine whether the line source crosses a grid cell. If it does, calculate its intersection point. Then, determine the number and coordinates of the intersection points according to the direction (X, Y, Z) of the line source, and calculate the distance from the intersection point to the starting point in turn. This completes the sorting of the intersection points. Since the intersection point is the intersection of the line source and the Yee grid surface, each adjacent intersection point forms a sub-segment. Each line source corresponds precisely to a Yee grid cell, thus achieving segmentation.

[0087] Step 3.2.3: Based on the idea of ​​interpolation basis functions, the midpoint of the line source segment is mapped by combining the spatial distribution of the electric field in the Yee grid.

[0088] Since the electric field components of the Yee mesh are defined at the midpoints of the element edges, the midpoints of sub-segments can be used to represent the equivalent excitation effect of the sub-segment within the element during discretization, and mapped to the corresponding edge positions, thus realizing the mapping between the source term and the mesh field quantity. Line sources of arbitrary shapes, after being segmented, can be mapped segment by segment from the midpoints of these sub-segments, thus effectively reflecting the arbitrariness of the excitation source.

[0089] Specifically, the coordinates of the midpoint of the source segment within each Yee grid cell are calculated. Based on the interpolation basis function concept in vector finite element method, as shown in formulas (5) to (16), and combined with the spatial distribution of the electric field in the Yee grid, the coordinates of the midpoint of each source segment are mapped to the midpoint of the 12 edges of the cell. This completes the effective mapping of the excitation source of any shape to the Yee grid. The calculation results are then fed into the electromagnetic field iterative calculation process of the BEDS-FDTD forward modeling program to complete the transient electromagnetic three-dimensional forward modeling of any emission source.

[0090] (5),

[0091] (6),

[0092] (7),

[0093] (8),

[0094] (9),

[0095] (10),

[0096] (11),

[0097] (12),

[0098] (13),

[0099] (14),

[0100] (15),

[0101] (16).

[0102] In the formula, Representing units respectively The length of the edge in the direction, Represents the coordinates of the cell center point. Let be the coordinates of any point within this unit, where the subscript is . The preceding number indicates the serial number, for example... They represent the points along number 1 respectively. The interpolation basis functions for the directions are similar, and so on.

[0103] any point in the unit electric field vector It can be expanded using edge basis functions as follows:

[0104] (17).

[0105] In the formula, Indicates a time step.

[0106] Here, the electric field at the midpoint of the non-mesh edge is calculated using the vector finite element edge basis function. This interpolation basis function is mainly used for spatial interpolation; it should be noted that other interpolation methods are also feasible. Considering the transmitting wire as being composed of a large number of electric dipoles, and dividing the wire into multiple line elements, the current in each line element can be written as:

[0107] (18).

[0108] In the formula, It is the number of line units. It is a unit Current intensity on It is a one-dimensional basis function, when Time equals 1, When the current is equal to 0, the current density on the line element can be written as:

[0109] (19).

[0110] In the formula, It refers to the spatial position of a line segment, that is, its distance from the line unit. The distance can be represented by the location of its midpoint. This represents the line element number. The electric field on the edges of a Yee cell is generated by the combined action of each line element, and the distributed current density on the edges is also caused by the combined action of all line elements. Therefore, the distributed current density on the edges can be written as:

[0111] (20).

[0112] In the formula, Representing the element along The length in three directions.

[0113] Step 4: Obtain the three-dimensional forward modeling results through iterative calculation of the forward electromagnetic field.

[0114] The BEDS-FDTD governing equations are designed as follows:

[0115] In nonmagnetic, active media, Maxwell's equations are:

[0116] (twenty one),

[0117] (twenty two).

[0118] In the formula, They represent the magnetic field and the electric field, respectively. For current density, For source current density, and These are the vacuum permittivity and vacuum permeability, respectively.

[0119] The spatial discretization of the above equations is performed using the central difference method, and the time discretization is performed using the first-order back-eule Euler (BE) method. A direct decomposition (DS) strategy is also introduced to obtain the fully discrete equations for the BEDS-FDTD forward modeling algorithm:

[0120] (twenty three),

[0121] (twenty four),

[0122] (25).

[0123] In the formula, ( ) represents a second-order difference operator along the Cartesian coordinate direction, such as ,but and . , , , , The conductivity of the medium, For virtual electric field, and Indicates the time.

[0124] The BEDS-FDTD forward modeling algorithm in this embodiment first introduces the unconditionally stable back Euler method, which makes the solution not strictly limited by the Kronen condition and greatly reduces the number of time iterations. Secondly, it introduces a direct decomposition strategy to reconstruct the large sparse matrix into a low-order tridiagonal matrix with the main diagonal dominant, which is convenient for solving. Moreover, the electromagnetic field components are decoupled and can be computed in parallel, which greatly speeds up the solution efficiency.

[0125] To better illustrate the method in this embodiment, the following actual experiment is conducted:

[0126] Establish such as Figure 5 The uniform half-space model shown in (a) (only the core region is shown here) is illustrated in the triangular facet partition diagram. Figure 5 As shown in (b) above, the schematic diagram of the excitation source and receiving measurement point on the XOY plane is as follows. Figure 6 As shown. The model parameters are as follows: The red solid line represents an irregularly arranged electrical source on the ground. The XY coordinates of the electrical source are (-200, -200), (-150, 100), (0, -300), (50, 100), (200, 200), and (300, 120), respectively. The emission current is 1A, and the model uses a rising edge of 10. -6 s, duration is 30ms, falling edge is 10 -7 The trapezoidal wave of s is used as the transmitted waveform, and the observation time is 10 seconds after the current is turned off. -5 s~0.02s. Four receiving points were selected (as shown by the blue pentagram), with XY coordinates of (-150,0), (0,0), (100,-100), and (200,130), at a receiving altitude of 50m in the air. The air resistivity is 10. 6 The formation resistivity is 100 The model dimensions are 219092.826m × 219112.826m × 218692.826m, with a core region of 1200m × 1200m × 800m and the remaining area being the external computational region. First, the entire model was meshed using a Yee mesh. The core computational region was meshed with a uniform 20m × 20m × 20m mesh, while the three directions outside the core computational region used non-uniform meshes. The ratio of adjacent mesh sizes was set to 1.2, resulting in a total mesh count of 138 × 139 × 118 = 2263476. Then, the same model was constructed using software, meshing the entire surface with triangular facets. After construction, the model's coordinates and node information were output, and calculations were performed. The computation time was 285 seconds. The numerical solution of the BEDS-FDTD method was compared with the analytical solution of the uniform half-space method. Figure 7 The measurement point (a) in the diagram is (-150, 0, -50). Figure 7 The measurement point (b) in the diagram is (0,0,-50). Figure 7 The measurement point (c) in the diagram is (100, -100, -50). Figure 7 The measurement point (d) is (200, 130, -50). As shown in the figure, the calculated results at the measurement point within the observation time range are in good agreement with the analytical solution, indicating that the method can realize semi-airborne transient electromagnetic numerical simulation of arbitrary electrical sources and the calculation accuracy meets the requirements.

[0127] Therefore, the method proposed in this embodiment can realize numerical simulation of complex geological conditions of semi-airborne transient electromagnetic sources with arbitrary electrical sources, and has high calculation accuracy, which can provide guidance for engineering practice.

[0128] Example 2:

[0129] Embodiment 2 of the present invention provides a three-dimensional forward modeling method system for FDTD (Fluid Dynamics Topometry) of complex terrain with electrical source semi-airborne transient electromagnetic characteristics, comprising:

[0130] The forward model module is configured to construct a forward model based on the terrain information of the target area and to perform mesh subdivision on the forward model;

[0131] The surface model module is configured to construct the surface model of the forward model based on the meshed model size, and to mesh the surface model.

[0132] The Finite-Difference Time-Domain (FDTD) method module is configured to process the information after meshing the forward model and the surface model using the BEDS-FDTD method. Specifically, it uses conformal mesh technology to determine the spatial location attributes of the model based on the information after meshing, and further calculates the equivalent conductivity. Based on the idea of ​​interpolation basis functions, it applies excitation sources of arbitrary complex shapes to the forward model.

[0133] The iterative calculation module is configured to obtain three-dimensional forward modeling results through iterative calculation of the forward electromagnetic field.

[0134] Example 3:

[0135] Embodiment 3 of the present invention provides a computer-readable storage medium storing a computer program adapted for loading by a processor and executing the steps in the FDTD three-dimensional forward modeling method for electrically sourced semi-airborne transient electromagnetic complex terrain as described in Embodiment 1 of the present invention.

[0136] Example 4:

[0137] Embodiment 4 of the present invention provides a computer device, the device comprising:

[0138] A processor, adapted to execute computer programs;

[0139] A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the steps in the FDTD three-dimensional forward modeling method for electrical source semi-airborne transient electromagnetic complex terrain as described in Embodiment 1 of the present invention.

[0140] The steps and methods involved in Examples 2, 3 and 4 above correspond to those in Example 1. For specific implementation details, please refer to the relevant description section of Example 1.

[0141] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0142] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can access or a data processing device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0143] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A three-dimensional forward modeling method for complex terrain using electrical source semi-airborne transient electromagnetic FDTD, characterized in that, Includes the following steps: A forward model is constructed based on the terrain information of the target area, and the forward model is meshed. The target area includes the core area of ​​the transmitter and receiver measurement points, as well as the extended area to prevent boundary influence. Construct the surface model of the forward model based on the model size of the meshed model, and then mesh the surface model. The BEDS-FDTD method is used to process the information after meshing the forward model and the surface model. Specifically, conformal meshing technology is used to determine the spatial location attributes of the model based on the meshed information, and the equivalent conductivity is further calculated. Based on the interpolation basis function concept, excitation sources of arbitrary complex shapes are applied to the forward model. The specific steps for determining the spatial location attributes of the model based on the meshed information and further calculating the equivalent conductivity are as follows: Ray tracing technology is used to calculate the nesting relationship between the forward model mesh and the surface model mesh to determine the model's spatial location attributes; based on the model's spatial location attributes, the equivalent conductivity of the complex interface is calculated using a linear weighted average method. The three-dimensional forward modeling results are obtained through iterative calculations of the forward electromagnetic field.

2. The FDTD three-dimensional forward modeling method for complex terrain with electrical source semi-airborne transient electromagnetic interference as described in claim 1, characterized in that, The forward model is meshed using Yee meshes. The core region is meshed using a uniform mesh, while the extended regions outside the core region are meshed using a non-uniform mesh that is expanded according to a set scaling factor.

3. The FDTD three-dimensional forward modeling method for complex terrain with electrical source semi-airborne transient electromagnetic interference as described in claim 1, characterized in that, The surface model includes an air layer, a formation, and an anomaly. The surface model is divided using a triangular mesh. By modifying the surface normal direction, the normal directions of the air layer, formation, and anomaly are made to point inward. When an anomaly is contained in the formation, the formation normal points inward, and the anomaly surface normal points outward.

4. The FDTD three-dimensional forward modeling method for complex terrain with electrical source semi-airborne transient electromagnetic interference as described in claim 1, characterized in that, Based on the spatial location attributes of the model, the specific steps for calculating the equivalent conductivity of complex interfaces using the linear weighted average method are as follows: Assume that the surface model mesh is divided into two spaces, each filled with a medium with different electrical parameters; The equivalent conductivity is calculated by weighted average of the lengths of the edges containing different media.

5. The FDTD three-dimensional forward modeling method for complex terrain with electrical source semi-airborne transient electromagnetic interference as described in claim 2, characterized in that, The specific steps for applying arbitrarily complex shape excitation sources to the forward model based on the interpolation basis function idea are as follows: Calculate and sort the intersection points of the line source segment with the Yee mesh surface; Line source segments are divided based on the calculated intersection points; Based on the idea of ​​interpolation basis functions, the midpoint of the line source segment is mapped by combining the spatial distribution of the electric field in the Yee grid.

6. A three-dimensional forward modeling method system for complex terrain using electrical source semi-airborne transient electromagnetic FDTD, characterized in that, include: The forward model module is configured to construct a forward model based on the terrain information of the target area and to perform mesh partitioning on the forward model. The target area includes the core area of ​​the transmitter and receiver measurement points as well as the extended area to prevent boundary influence. The surface model module is configured to construct the surface model of the forward model based on the meshed model size, and to mesh the surface model. The Finite-Difference Time-Domain (FDTD) method module is configured to process the information after meshing the forward model and the surface model using the BEDS-FDTD method. Specifically, it uses conformal meshing technology to determine the spatial location attributes of the model based on the meshed information and further calculates the equivalent conductivity. Based on the interpolation basis function concept, it applies excitation sources of arbitrary complex shapes to the forward model. The specific steps for determining the spatial location attributes of the model using conformal meshing technology and further calculating the equivalent conductivity are as follows: Ray tracing technology is used to calculate the nesting relationship between the forward model mesh and the surface model mesh to determine the model's spatial location attributes; based on the model's spatial location attributes, the equivalent conductivity of the complex interface is calculated using a linear weighted average method. The iterative calculation module is configured to obtain three-dimensional forward modeling results through iterative calculation of the forward electromagnetic field.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1-5, the electrical source semi-airborne transient electromagnetic complex terrain FDTD three-dimensional forward modeling method.

8. A computer device, characterized in that, include: A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the electrical source semi-airborne transient electromagnetic complex terrain FDTD three-dimensional forward modeling method as described in any one of claims 1-5.

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