Ultra-wideband electromagnetic method anisotropic medium three-dimensional forward simulation method and system

Abstract

The application belongs to the technical field of electromagnetic prospecting and numerical simulation, and provides a three-dimensional forward simulation method and system for anisotropic medium of electromagnetic method with ultra-wide frequency band, which is based on the vector finite element method, discretizes the electric field equation of unified traditional current and displacement current, fully considers the influence of arbitrary anisotropic conductivity, arbitrary anisotropic dielectric constant and magnetic conductivity, and provides a basis for the theoretical research, field survey and data inversion of the electromagnetic method with ultra-wide frequency band.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic exploration and numerical simulation technology, specifically to a three-dimensional forward modeling method and system for anisotropic media using electromagnetic methods with an ultra-wideband bandwidth. 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] Frequency-domain electromagnetic methods are geophysical techniques that utilize frequency-domain electromagnetic waves from natural or artificially controlled sources to probe subsurface electrical structures. Traditional frequency-domain electromagnetic methods include magnetotellurics (MT), audio-frequency magnetotellurics (AMT), controlled-source audio-frequency magnetotellurics (CSAMT), and controlled-source electromagnetic methods (CSAMT), with observation frequencies typically below 100 kHz. In recent years, significant advancements in instrumentation technology have spurred the development of radio-frequency electromagnetic wave detection technologies and equipment, including radio-frequency magnetotellurics (RMT) and controlled-source radio-frequency magnetotellurics (CSRMT), which can achieve observation frequencies up to 1 MHz and are widely used in near-surface environment exploration. Currently, frequency domain electromagnetic methods have covered observation frequency bands (0-1MHz) spanning ten orders of magnitude, and can be called ultra-wideband electromagnetic methods. These include low-frequency MT (0-1KHz), mid-frequency AMT, CSAMT, and CSEM (10Hz-100KHz), and high-frequency RMT and CSRMT (10KHz-1MHz). The detection depth can cover depths from a few meters to hundreds of kilometers underground, and it is widely used in fields such as deep underground structure detection, engineering exploration, mineral exploration, and environmental engineering detection.

[0004] Traditional frequency-domain electromagnetic numerical simulation methods typically calculate frequencies below 10 kHz, where induced diffusion is the dominant phenomenon. These simulations often employ quasi-static assumptions, neglecting the influence of displacement current. However, current research indicates that displacement current and dielectric constant significantly impact observational data in the RMT band. Ignoring displacement current can lead to inversion errors, especially in high-resistivity regions such as glaciers and granite fields, potentially causing misinterpretations. Therefore, considering the effects of dielectric constant and displacement current in high-frequency domain electromagnetic simulations is crucial.

[0005] Currently, research on radio frequency electromagnetic forward modeling mainly focuses on one-dimensional and two-dimensional models. However, due to the influence of geological activity, the actual geological structure is very complex, requiring the establishment of accurate three-dimensional geological models to obtain precise electromagnetic responses. Furthermore, the Earth's medium exhibits widespread anisotropy, which has a non-negligible impact on the propagation of frequency-domain electromagnetic fields. However, a three-dimensional numerical simulation method for frequency-domain electromagnetics that simultaneously considers conduction current, displacement current, arbitrary anisotropic resistivity, and dielectric constant is currently lacking. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a three-dimensional forward modeling method and system for anisotropic media using ultra-wideband electromagnetic methods. Based on the vector finite element method, the electric field equations for unified traditional current and displacement current are discretized, fully considering the influence of arbitrary anisotropic conductivity, arbitrary anisotropic permittivity, and magnetic permeability. This provides a foundation for theoretical research, field exploration, and data inversion using ultra-wideband electromagnetic methods.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a three-dimensional forward modeling simulation method for anisotropic media using an ultra-wideband electromagnetic method.

[0009] A three-dimensional forward modeling method for anisotropic media using an ultra-wideband electromagnetic method includes the following steps:

[0010] An unstructured tetrahedral mesh 3D model is constructed, and anisotropic conductivity, dielectric constant, and magnetic permeability are assigned to different regions or different materials in the unstructured tetrahedral mesh 3D model.

[0011] A unified electric field double curl control equation for conduction current and displacement current is constructed. The electric field double curl control equation is discretized by vector finite element method and boundary conditions are applied to obtain the global finite element linear system equation.

[0012] Solve the global finite element linear system equations to obtain solutions for two polarization modes. Based on the solutions for the two polarization modes, perform three-dimensional forward modeling to obtain electric field components, magnetic field components, impedance, phase, apparent resistivity, and tilter response data.

[0013] Secondly, the invention provides an ultra-wideband electromagnetic method three-dimensional forward modeling simulation system for anisotropic media.

[0014] A three-dimensional forward modeling system for anisotropic media using an ultra-wideband electromagnetic method, comprising:

[0015] The mesh 3D model building unit is configured to: construct an unstructured tetrahedral mesh 3D model, and in the unstructured tetrahedral mesh 3D model, assign anisotropic conductivity, dielectric constant and magnetic permeability to different regions or different materials;

[0016] The global finite element linear system equation generation unit is configured to: construct the electric field double curl control equations for unified conduction current and displacement current, perform vector finite element discretization on the electric field double curl control equations, and apply boundary conditions to obtain the global finite element linear system equations;

[0017] The three-dimensional forward modeling unit is configured to: solve the global finite element linear system equations to obtain solutions for two polarization modes; and perform three-dimensional forward modeling based on the solutions for the two polarization modes to obtain electric field components, magnetic field components, impedance, phase, apparent resistivity, and tilter response data.

[0018] Compared with the prior art, the beneficial effects of the present invention are:

[0019] 1. This invention proposes a three-dimensional forward modeling method for anisotropic media using electromagnetic methods in an ultra-wideband environment. It employs a complete and unified double curl equation for the electric field and considers the effects of conventional current and displacement current, which can simulate the electromagnetic response in an ultra-wideband range.

[0020] 2. This invention utilizes unstructured tetrahedral meshes, which can flexibly simulate complex geological structures, accurately capture terrain features and geological layer changes, and enhance the realism and reliability of the simulation.

[0021] 3. This invention takes into account the effects of anisotropic conductivity, anisotropic permittivity and magnetic permeability, which can more accurately simulate the electromagnetic response under complex geological structures and improve the reliability and accuracy of the simulation results.

[0022] 4. This invention employs a direct solver and a parallel scheme, which can efficiently solve linear systems, ensuring the accuracy and efficiency of the simulation, and improving the practicality and application value of the algorithm.

[0023] 5. This invention overcomes the limitations of existing technologies that cannot simultaneously consider displacement current, conduction current, and arbitrary anisotropic media, providing a foundation for theoretical research and inversion interpretation of actual observation data in ultra-wideband electromagnetic methods, thus enabling better application in fields such as deep earth scientific exploration, engineering exploration, mineral resource exploration, and environmental engineering exploration.

[0024] 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

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 This is a flowchart of the three-dimensional forward modeling method for anisotropic media using ultrawideband electromagnetic methods provided in Embodiment 1 of the present invention;

[0027] Figure 2 This is an arbitrary anisotropic conductivity blocky anomaly model provided in Case 1 of Embodiment 1 of the present invention;

[0028] Figure 3 This is a schematic diagram comparing the results of this invention with those of Bai et al. in the arbitrary anisotropic conductivity block anomaly model provided in Case 1 of Embodiment 1 of this invention. At x = 0 m on the ground surface, the first to fourth columns represent the apparent resistivity of the xy mode, the apparent resistivity of the yx mode, the phase of the xy mode, and the phase of the yx mode, respectively.

[0029] Figure 4 A schematic diagram of a one-dimensional layered model and its electrical parameters provided in Case 2 of Embodiment 1 of the present invention;

[0030] Figure 5 The response comparison diagram of the present invention and the 1D analytical solution in the two-layer model provided in Case 2 of Embodiment 1 of the present invention is shown. The first to fourth columns represent the apparent resistivity of the xy mode, the apparent resistivity of the yx mode, the phase of the xy mode, and the phase of the yx mode, respectively.

[0031] Figure 6 This is a schematic diagram of a three-dimensional forward modeling system for anisotropic media using the ultrawideband electromagnetic method provided in Embodiment 2 of the present invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] 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.

[0034] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0035] Example 1:

[0036] This implementation proposes a three-dimensional forward modeling method for anisotropic media using the ultra-wideband electromagnetic method. It overcomes the limitations of existing radio frequency magnetotelluric three-dimensional forward modeling methods, which neglect the influence of displacement current and are unable to calculate dielectric constant and its anisotropy. Based on the vector finite element method, it discretizes and unifies the electric field equations for both traditional current and displacement current. Its innovations and advantages include: the ability to simulate electromagnetic responses over an ultra-wideband range; consideration of the influence of anisotropic conductivity, anisotropic dielectric constant, and magnetic permeability, resulting in more accurate electromagnetic responses; the ability to flexibly simulate complex geological structures using unstructured tetrahedral meshes; and the use of direct solvers and parallel schemes to solve linear systems, ensuring both accuracy and efficiency in the simulation.

[0037] Specifically, such as Figure 1 As shown, the process includes the following:

[0038] S1: Construct an unstructured tetrahedral mesh 3D model.

[0039] Based on actual geological conditions and research needs, a detailed three-dimensional geological structure geometric model is constructed using software such as Comsol or GID, employing an unstructured tetrahedral mesh to discretize the geometric model. This invention combines three-dimensional geological modeling technology with unstructured tetrahedral mesh technology, thus possessing the advantage of accurately capturing complex terrain features and complex geological structures.

[0040] S2: Assigned values ​​to the material properties of anisotropic conductivity, anisotropic permittivity, and magnetic permeability.

[0041] In the unstructured tetrahedral mesh 3D model, anisotropic physical properties such as electrical conductivity, dielectric constant, and magnetic permeability are assigned to different regions or materials to reflect the electromagnetic properties in real geological environments. The Dirichlet boundary conditions applied to the outer boundary of the model are calculated by a one-dimensional forward modeling algorithm for plane waves in layered media. This algorithm considers the anisotropy of electrical conductivity and dielectric constant, as well as the influence of magnetic permeability, thereby improving the accuracy of the boundary conditions.

[0042] In nature, electrical conductivity and permittivity vary considerably, while magnetic permeability varies relatively little; therefore, we only consider isotropic magnetic permeability. In the anisotropic Earth medium, electrical conductivity and relative permittivity are tensors, which can be represented using the Euler transformation of the principal axis parameters:

[0043]

[0044] In equations (1) and (2), σ x σ y and σ z These are the three principal axis conductivities, ε x ε y and ε z The dielectric constants of the three principal axes, α S α D and α L These are three Euler rotation angles, with superscripts "σ" and "ε" used to distinguish between conductivity and dielectric constant. R x and R z It is defined as an Euler rotation matrix, expressed as:

[0045]

[0046]

[0047] In this implementation, after applying the Dirichlet boundary condition, the finite element coefficient matrix A for the two polarization modes at each frequency is the same, only the right-hand side is different.

[0048] S3: Construct the electric field double curl control equations for unified conduction current and displacement current.

[0049] Ultra-wideband electromagnetic forward modeling encompasses both low-frequency electromagnetic diffusion and high-frequency electromagnetic wave phenomena, governed by the complete Maxwell's equations, including its conduction current density and displacement current density terms. This is achieved by introducing the time harmonic factor e. iωt After performing a Fourier transform, the expressions for Faraday's law and the Ampère-Maxwell equations are:

[0050]

[0051] Where E and H represent the electric field and magnetic field, respectively. ω is the angular frequency, where ω = 2πf, f is the frequency, and μ is the permeability, μ = μ r μ0, μ r Where μ is the relative permeability, μ0 is the free permeability, and J and D represent the conduction current and displacement current, respectively. Their constitutive relations are shown below:

[0052] J = σE (7);

[0053] D = εE (8);

[0054] Taking the curl of both sides of equation (5), and substituting equations (6), (7), and (8) into equation (5) to eliminate the magnetic field term, we can obtain the frequency domain electric field double curl control equation:

[0055]

[0056] S4: The electric field double curl control equation is discretized by vector finite element method and boundary conditions are applied. The frequency domain electromagnetic control equation (9) is processed by Galerkin finite element analysis, and the weak integral equation of the control equation is derived as follows:

[0057]

[0058] Where Ω represents the model domain under study, and N represents the vector linear interpolation basis function of the tetrahedral element, defined as:

[0059]

[0060] In the formula, L is the node basis function, l is the length of the edge, the superscript "e" represents the tetrahedral element number, and the subscripts "i", "i1", and "i2" represent the edge number, the starting node of the i-th edge, and the terminal node of the i-th edge in the tetrahedral element e, respectively.

[0061] Using Green's theorem for the first vector, the discrete form of equation (12) is obtained within each tetrahedral element:

[0062]

[0063] Among them, stiffness matrices K and M σ and M ε Defined as:

[0064]

[0065] Where Ωe represents the tetrahedral element domain, and the subscripts “i” and “j” represent the edge numbers. The above integral is calculated using analytical methods. The local matrix of formula (12) is globally assembled and Dirichlet boundary is applied to obtain the global finite element linear system equation:

[0066] AE = b (16);

[0067] Where A = K + (ω 2 M ε +iωM σ ), is a complex sparse symmetric matrix of size Ne×Ne. The electric field vector to be solved on the edge of E and b represent the right-hand side terms containing boundary condition information. Both of them are of size Ne×1, where Ne is the number of edges of the model mesh.

[0068] S5: Parallel solution of finite element sparse linear equations.

[0069] The direct solver PARDIASO is used to solve the finite element sparse linear equation system. Since the finite element coefficient matrix A is the same in both polarization modes, only one matrix decomposition and two back substitutions are needed to obtain the solutions for both polarization modes, which improves the solution efficiency.

[0070] In this implementation, parallel computing is adopted, which includes frequency point process parallelism and PARDIASOOpenMP thread parallelism. The two-layer parallelism further improves the computing efficiency.

[0071] S6: Solve for electric field components, magnetic field components, impedance, phase, apparent resistivity, and tilter response data.

[0072] When the measuring point is in the e-th tetrahedral element, the three components of the electric field at the measuring point It can be represented by vector shape functions as:

[0073]

[0074] in, These are the three components of the vector basis functions. It is a solution on the edge. According to Faraday's law, the three components of the magnetic field at the measuring point... Represented as:

[0075]

[0076] in, These are the three components of the vector basis functions. It is a solution on the edge.

[0077] Each component Z of the impedance tensor xx Z xy Z yx Z yy The calculation expression is:

[0078]

[0079] Among them, E x1 E x2 E y1 E y2 H x1 H x2 H y1 H y2 The horizontal components of the electric field and magnetic field are calculated at the measuring point. The subscripts "x" and "y" represent the two horizontal directions, and the subscripts "1" and "2" represent the two polarization modes.

[0080] After calculating the impedance tensor, the apparent resistivity and phase can be obtained, i.e.:

[0081]

[0082] Among them, Z ij The components of the impedance tensor are represented by "i" and "j", which represent the "x" and "y" directions, respectively.

[0083] The expression for calculating the tilt vector is:

[0084]

[0085] Among them, H x1 H x2 H y1 H y2 H z1 H z2 The three components of the magnetic field at the measuring point are represented by the subscripts "x", "y" and "z" which represent the directions of the three components, and the subscripts "1" and "2" which represent the two polarization modes.

[0086] To better illustrate the advantages and objectives of this invention, and to verify the correctness and accuracy of the vector finite element-based three-dimensional ultra-wideband forward modeling algorithm, two case studies are employed. In the first case study, the algorithm of this invention is compared with the open-source algorithm of Bai et al. (2022), verifying the accuracy of magnetotelluric forward modeling and anisotropic algorithms under low-frequency conditions. In the second case study, the algorithm of this invention is compared with a one-dimensional radio frequency magnetotelluric analytical solution, verifying the accuracy of high-frequency calculations considering displacement current in the 10kHz to 1MHz frequency range.

[0087] Case 1 discloses a preferred model of an arbitrary anisotropic conductivity block anomaly body open-sourced by Bai et al. (2022). The algorithm of this invention is compared with the hybrid finite element method algorithm based on the Aψ potential control equation proposed by Bai et al. (2022) to verify the accuracy of the algorithm in low-frequency cases.

[0088] Arbitrary anisotropic conductivity blocky anomaly model, such as Figure 2 As shown, a block measuring 20km × 40km × 10km is embedded in an isotropic, homogeneous half-space, located at the center of coordinates (0km, 0km, 5km). The resistivity of the homogeneous Earth is 1000 Ω·m, while the principal resistivity of the block is ρ. x / ρ y / ρ z =100 / 10 / 100Ω·m, the angle of anisotropy is The model has a relative permeability of 1 and a dielectric constant of 0. The computation frequency is 1 Hz. The model consists of 528,081 tetrahedra and 621,174 edges. The computation using two OpenMP threads took 127 seconds.

[0089] Figure 3 A comparison of apparent resistivity and phase results for the xy- and yx- modes at x = 0 m on the Earth's surface is presented, and the results calculated by the algorithm of this invention are consistent with those of Bai et al. (2022). This demonstrates that the algorithm of this invention can accurately calculate the low-frequency MT response with anisotropy of arbitrary conductivity.

[0090] Case 2 discloses a preferred layered model, such as Figure 4 As shown, the two-layer model consists of a first layer of limestone with a thickness of 10 meters, an isotropic resistivity of 2000 Ω·m, and an isotropic dielectric constant of 8ε₀. The second layer is a gneiss basement with an isotropic resistivity of 20000 Ω·m and an anisotropic dielectric constant of ε₀. x / ε y / ε z =8ε0 / 5ε0 / 6ε0, anisotropic angle and It is 0, and The angle is 45°. The calculation frequency range is from 10kHz to 1MHz, with a total of 11 logarithmically spaced points. The model consists of 922,150 tetrahedrons and 1,090,145 edges, and the parallel computation on the 11 frequencies took a total of approximately 544 seconds.

[0091] Figure 5 The consistency between the proposed method and the apparent resistivity and phase results obtained from one-dimensional analytical calculations is demonstrated, proving that the algorithm of the proposed method can accurately calculate high-frequency RMT response data with dielectric anisotropy constants. In the model of Case 2, using two OpenMP threads to solve a single frequency equation, the time required for serial calculation of 11 frequencies was 5363.8 seconds. Using 11 parallel processes to calculate all frequencies took 552.1 seconds, with the parallel calculation speed being 9.7 times that of the serial method and a parallel efficiency of 88.3%, indicating that the proposed method has high parallel calculation efficiency.

[0092] Example 2:

[0093] like Figure 6 As shown, this implementation provides a three-dimensional forward modeling system for anisotropic media using the electromagnetic method with an ultra-wideband bandwidth, comprising:

[0094] The mesh 3D model building unit is configured to: construct an unstructured tetrahedral mesh 3D model, and in the unstructured tetrahedral mesh 3D model, assign anisotropic conductivity, dielectric constant and magnetic permeability to different regions or different materials;

[0095] The global finite element linear system equation generation unit is configured to: construct the electric field double curl control equations for unified conduction current and displacement current, perform vector finite element discretization on the electric field double curl control equations, and apply boundary conditions to obtain the global finite element linear system equations;

[0096] The three-dimensional forward modeling unit is configured to: solve the global finite element linear system equations to obtain solutions for two polarization modes; and perform three-dimensional forward modeling based on the solutions for the two polarization modes to obtain electric field components, magnetic field components, impedance, phase, apparent resistivity, and tilter response data.

[0097] It is understood that the aforementioned units can be individually or entirely merged into one or more other units, or some of the units can be further divided into multiple functionally smaller units. This achieves the same operation without affecting the technical effects of the embodiments of this application. The aforementioned units are based on logical functional division. In practical applications, the function of one unit can be implemented by multiple units, or the function of multiple units can be implemented by one unit. In other embodiments of this application, the system may also include other units. In practical applications, these functions can also be implemented with the assistance of other units, and can be implemented collaboratively by multiple units.

[0098] According to another embodiment of this application, the system described in this embodiment, and the method of embodiment 1 of this application, can be constructed and the method of embodiment 1 of this application implemented by running a computer program (including program code) capable of performing the steps involved in the corresponding method described in embodiment 1 on a general-purpose computing device including processing elements and storage elements such as a central processing unit (CPU), random access memory (RAM), and read-only memory (ROM). The computer program can be recorded on, for example, a computer-readable recording medium, loaded into the aforementioned computing device through the computer-readable recording medium, and run therein.

[0099] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-dimensional forward modeling method for anisotropic media using an ultra-wideband electromagnetic method, characterized in that, Includes the following processes: An unstructured tetrahedral mesh 3D model is constructed, and anisotropic conductivity, dielectric constant, and magnetic permeability are assigned to different regions or different materials in the unstructured tetrahedral mesh 3D model. A unified electric field double curl control equation for conduction current and displacement current is constructed. The electric field double curl control equation is discretized by vector finite element method and boundary conditions are applied to obtain the global finite element linear system equation. Solve the global finite element linear system equations to obtain solutions for two polarization modes. Based on the solutions for the two polarization modes, perform three-dimensional forward modeling to obtain electric field components, magnetic field components, impedance, phase, apparent resistivity, and tilter response data. The electric field double curl governing equations for unified conduction current and displacement current are constructed, including: ； in, , It is the relative permeability. It is the vacuum permeability. It is angular frequency. Represents electric field, Where is the dielectric constant. For electrical conductivity, ; The electric field double curl governing equations are discretized using vector finite element method, and boundary conditions are applied to obtain the global finite element linear system equations, including: By using finite element analysis to process the double curl governing equations of the electric field, a weak integral form of the governing equations is derived: ； in, This represents the model domain of the study. Describes the vector linear interpolation basis functions for tetrahedral elements. In the formula, For node basis functions, Let be the length of the side. Represents the tetrahedral element number. In , , Representing tetrahedral units The inner edge number, the first The starting node and the first edge Terminal nodes of the edge; Using Green's theorem for the first vector, the discrete form is obtained within each tetrahedral element: ； in, , and These are the stiffness matrices. , and Elements in; By globally assembling the discrete local matrices and applying Dirichlet boundaries, the global finite element linear system equations are obtained: ,in, , is the size of × Complex sparse symmetric matrices, Let be the electric field vector to be solved on the edge. This represents the right-hand side term containing boundary condition information; both have a size of [missing value]. ×1, It is the number of edges of the model mesh.

2. The ultra-wideband electromagnetic method for three-dimensional forward modeling of anisotropic media as described in claim 1, characterized in that, in, Represents a tetrahedral element field. and Indicates the edge number.

3. The ultra-wideband electromagnetic method for three-dimensional forward modeling of anisotropic media as described in claim 1, characterized in that, The global finite element linear system equations are solved using the direct solver PARDIASO.

4. The ultra-wideband electromagnetic method for three-dimensional forward modeling of anisotropic media as described in claim 1, characterized in that, The measuring point is at the 1st e When the electric field is in a tetrahedral element, the three components of the electric field at the measuring point are... Represented by vector shape functions: in, These are the three components of the vector basis functions. The solution is on the edge; Three components of the magnetic field at the measuring point Represented as: ； in, These are the three components of the vector basis functions. The solution is on the edge, and i=1,…,6 is the local number of the edge of the tetrahedron.

5. The ultra-wideband electromagnetic method for three-dimensional forward modeling of anisotropic media as described in claim 1, characterized in that, Each component of the impedance tensor , , , The calculation expression is: ； ； ； ； in, , , , , , , , The horizontal components of the electric field and magnetic field are calculated at the measuring point. The subscripts x and y represent two horizontal directions, and the subscripts 1 and 2 represent two polarization modes.

6. The ultra-wideband electromagnetic method for three-dimensional forward modeling of anisotropic media as described in claim 5, characterized in that, Calculate apparent resistivity and phase ,include: ； ； in, Represents the components of the impedance tensor. , They represent , direction, It is the vacuum permeability. It is angular frequency.

7. The ultra-wideband electromagnetic method for three-dimensional forward modeling of anisotropic media as described in claim 1, characterized in that, The tilter response data is the tilter vector, and the tilter vector... and The calculation expression is: ； ； in, , , , , , The three components of the magnetic field at the measuring point are represented by the subscripts x, y, and z, which represent the directions of the three components. Subscripts 1 and 2 represent the two polarization modes.

8. A three-dimensional forward modeling system for anisotropic media using an ultra-wideband electromagnetic method, characterized in that, include: The mesh 3D model building unit is configured to: construct an unstructured tetrahedral mesh 3D model, and in the unstructured tetrahedral mesh 3D model, assign anisotropic conductivity, dielectric constant and magnetic permeability to different regions or different materials; The global finite element linear system equation generation unit is configured to: construct the electric field double curl control equations for unified conduction current and displacement current, perform vector finite element discretization on the electric field double curl control equations, and apply boundary conditions to obtain the global finite element linear system equations; The three-dimensional forward modeling unit is configured to: solve the global finite element linear system equations to obtain the solutions of the two polarization modes; and perform three-dimensional forward modeling based on the solutions of the two polarization modes to obtain electric field components, magnetic field components, impedance, phase, apparent resistivity and tilter response data. The electric field double curl governing equations for unified conduction current and displacement current are constructed, including: ； in, , It is the relative permeability. It is the vacuum permeability. It is angular frequency. Represents electric field, Where is the dielectric constant. For electrical conductivity, ; The electric field double curl governing equations are discretized using vector finite element method, and boundary conditions are applied to obtain the global finite element linear system equations, including: By using finite element analysis to process the double curl governing equations of the electric field, a weak integral form of the governing equations is derived: ； in, This represents the model domain of the study. Describes the vector linear interpolation basis functions for tetrahedral elements. In the formula, For node basis functions, Let be the length of the side. Represents the tetrahedral element number. , , Representing tetrahedral units The inner edge number, the first The starting node and the first edge Terminal nodes of the edge; Using Green's theorem for the first vector, the discrete form is obtained within each tetrahedral element: ； in, , and These are the stiffness matrices. , and Elements in; By globally assembling the discrete local matrices and applying Dirichlet boundaries, the global finite element linear system equations are obtained: ,in, , is the size of × Complex sparse symmetric matrices, Let be the electric field vector to be solved on the edge. This represents the right-hand side term containing boundary condition information; both have a size of [missing value]. ×1, It is the number of edges of the model mesh.

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