Dimension reduction rapid calculation method for electromagnetic wave complex model while drilling

Abstract

The invention provides a dimension reduction rapid calculation method for an electromagnetic wave complex model while drilling, and relates to the technical field of oil-gas exploration and development, and the method comprises the steps: constructing a series of two-dimensional stratum models for a complex three-dimensional stratum model according to instrument parameters and stratum distribution characteristics; in the complex three-dimensional stratum model, performing three-dimensional gridding processing on the background stratum to obtain a three-dimensional gridding model; based on the three-dimensional grid model, calculating a series of spectral domain background electric fields corresponding to different wave numbers under a two-dimensional plane; a spectral domain two-dimensional electric field wave equation is obtained according to the spatial domain three-dimensional electric field wave equation, and a spectral domain finite difference format electric field is obtained through derivation; combining the spectral domain background electric field and the spectral domain finite difference format electric field to construct a spectral domain sparse matrix linear equation set; and solving the spectral domain sparse matrix linear equation set to obtain a two-dimensional spectral domain electric field. According to the method, the accuracy and precision of the stratum model are ensured, the complexity of the calculation process is reduced, the calculation efficiency can be improved, and the economic cost is saved.

Description

Technical Field

[0001] This invention relates to the field of oil and gas exploration and development technology, and more specifically, to a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling. Background Technology

[0002] Electromagnetic logging while drilling (EMWL) is widely used in geological steering and formation resistivity measurement in highly deviated / horizontal wells, serving as a crucial means to ensure wellbore penetration into oil and gas reservoirs and enhance oil and gas recovery. However, under highly deviated / horizontal well conditions, EMWL is severely affected by well deviation, surrounding rock, and formation heterogeneity, resulting in highly complex logging responses. Therefore, it is necessary to combine electromagnetic field calculation methods in heterogeneous media to simulate logging response characteristics under different environments and systematically analyze the influence of various factors on the response. Traditional methods typically consider only the vertical variations of formation properties, simplifying the formation into a one-dimensional model and then using analytical methods to solve for the logging response, which has the advantage of speed. However, simplifying the formation model to one dimension ignores the lateral heterogeneity of formation properties, failing to simulate complex geological structures such as faults. For such complex models, further three-dimensional (3D) algorithms are needed to achieve precise simulation of the logging response.

[0003] Finite difference algorithms play a crucial role in forward modeling of electromagnetic logging while drilling (EMWD). Among them, three-dimensional (3D) finite difference algorithms have become an important tool for the development of EMWD instruments and the analysis of factors affecting logging response. They are particularly important in the forward and inverse simulation calculations of EMWD long-range and advanced detection technologies. However, 3D algorithms suffer from problems such as cumbersome computation, slow computation speed, and high memory consumption, often requiring several days or even months to complete a single simulation calculation using clusters or large parallel computing centers.

[0004] To address the problems of existing technologies, this invention provides a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling. Summary of the Invention

[0005] In view of the problems of existing technologies, the purpose of this invention is to overcome the problems of slow calculation speed and poor accuracy of traditional simulation calculation methods, as well as the problems of large memory consumption and slow calculation speed of 3D algorithms.

[0006] This invention provides a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, the method comprising:

[0007] For complex three-dimensional stratigraphic models, a series of two-dimensional stratigraphic models are constructed based on instrument parameters and stratigraphic distribution characteristics;

[0008] In the complex three-dimensional stratigraphic model, the background stratigraphic layers are subjected to three-dimensional meshing to obtain a three-dimensional meshed model;

[0009] Based on the three-dimensional meshed model, a series of spectral background electric fields corresponding to different wave numbers in the two-dimensional plane are calculated.

[0010] Based on the three-dimensional electric field wave equation in the spatial domain, the two-dimensional electric field wave equation in the spectral domain is obtained, and the electric field in the finite difference scheme in the spectral domain is derived.

[0011] By combining the background electric field in the spectral domain and the electric field of the finite difference scheme in the spectral domain, a system of linear equations with sparse matrices in the spectral domain is constructed.

[0012] Solve the linear equations of the sparse matrix in the spectral domain to obtain the two-dimensional electric field in the spectral domain.

[0013] According to an embodiment of the present invention, the complex three-dimensional stratigraphic model includes: a heterogeneous, faulted, folded, and multi-layered three-dimensional stratigraphic model, and the two-dimensional stratigraphic model is obtained through the following steps:

[0014] The frequency and source distance of the drilling electromagnetic wave instrument are obtained as the instrument parameters;

[0015] The spatial distribution characteristics of formation resistivity are obtained as the formation distribution characteristics;

[0016] Based on the instrument parameters and the stratigraphic distribution characteristics, a series of two-dimensional stratigraphic models are constructed, in which the stratigraphic properties remain constant along the Y direction and vary along the XOZ plane.

[0017] According to an embodiment of the present invention, the three-dimensional meshed model is obtained through the following steps:

[0018] In the complex three-dimensional formation model, the formation where the current logging point is located is used as the background formation;

[0019] The skin depth of the background formation is calculated based on the resistivity of the background formation and the frequency of the drilling electromagnetic wave instrument.

[0020] A cubic region is established with the instrument's launch point as the center, wherein the size of the cubic region is determined based on the skin depth of the background strata;

[0021] The cube region is divided into uniform meshes in the Y direction and into finer non-uniform meshes in the X and Z directions to obtain the three-dimensional meshed model.

[0022] According to an embodiment of the present invention, the spectral background electric field is obtained through the following steps:

[0023] Based on Maxwell's theory, the spatial domain background electric field is calculated according to the spatial coordinates of the grid nodes in the three-dimensional gridded model.

[0024] For the spatial domain background electric field, a Fourier transform is applied in the Y direction to obtain a series of spectral domain background electric fields corresponding to different wavenumbers in the XOZ two-dimensional plane.

[0025] According to an embodiment of the present invention, the two-dimensional electric field wave equation in the spectral domain is obtained through the following steps:

[0026] Based on Maxwell's equations in the spatial domain, the three-dimensional electric field wave equation in the spatial domain is obtained.

[0027] By applying a Fourier transform in the Y direction to the three-dimensional electric field wave equation in the spatial domain, the two-dimensional electric field wave equation in the spectral domain is obtained.

[0028] According to an embodiment of the present invention, the electric field of the finite difference scheme in the spectral domain is obtained through the following steps:

[0029] The two-dimensional electric field wave equation in the spectral domain is discretized using an interleaved grid in the X and Z directions respectively to obtain the electric field in the finite difference scheme of the spectral domain.

[0030] According to one embodiment of the present invention, the system of linear equations for the spectral domain sparse matrix is ​​as follows:

[0031] Ax = b

[0032] Where: A represents the sparse matrix, obtained according to the electric field of the finite difference scheme in the spectral domain; x represents the electric field value to be solved; b represents the source term, obtained according to the background electric field in the spectral domain.

[0033] According to an embodiment of the present invention, the two-dimensional spectral domain electric field is obtained through the following steps:

[0034] Set the initial wavenumber and maximum wavenumber corresponding to the solution range, and set a series of sampling points within the solution range;

[0035] Input the wavenumber corresponding to the current sampling point into the linear equation system of the sparse matrix in the spectral domain, and solve to obtain the corresponding two-dimensional electric field in the spectral domain.

[0036] Determine whether the wavenumber of the current sampling point has reached the maximum wavenumber. If the determination result is yes, the solution ends; if the determination result is no, input the wavenumber corresponding to the next sampling point.

[0037] According to another aspect of the invention, a storage medium is also provided, which includes instructions for performing the methods described in any of the preceding claims.

[0038] According to another aspect of the present invention, a system for rapid dimensionality reduction calculation of complex models of electromagnetic waves during drilling is also provided, which performs the method as described in any of the preceding claims, the system comprising:

[0039] The two-dimensional stratigraphic module is designed for complex three-dimensional stratigraphic models. Based on instrument parameters and stratigraphic distribution characteristics, it constructs a series of two-dimensional stratigraphic models.

[0040] The three-dimensional meshing module performs three-dimensional meshing processing on the background strata in the complex three-dimensional stratigraphic model to obtain a three-dimensional meshed model;

[0041] The spectral background module, based on the three-dimensional meshed model, calculates a series of spectral background electric fields corresponding to different wavenumbers in a two-dimensional plane.

[0042] The finite difference module derives the two-dimensional electric field wave equation in the spectral domain from the three-dimensional electric field wave equation in the spatial domain, thereby deriving the electric field in the finite difference scheme in the spectral domain.

[0043] The equation module combines the background electric field in the spectral domain with the finite difference scheme in the spectral domain to construct a sparse matrix linear equation system in the spectral domain.

[0044] The solver module solves the linear equations of the sparse matrix in the spectral domain to obtain the two-dimensional electric field in the spectral domain.

[0045] This invention provides a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, which has the following advantages compared with existing technologies:

[0046] (1) This invention proposes a method for rapid calculation of dimensionality reduction of complex electromagnetic wave models while drilling. Under certain conditions, the logging response of electromagnetic resistivity of complex 3D formation models while drilling is transformed into the problem of solving the 3D electromagnetic field response in 2D formation models, which can effectively improve the efficiency of electromagnetic wave logging simulation calculation while drilling.

[0047] (2) The dimensionality reduction method not only ensures the accuracy and calculation precision of the stratigraphic model, but also reduces the complexity of the calculation process, improves the calculation efficiency, and can save a lot of economic costs.

[0048] (3) The present invention has a wide coverage and can be used in different types of logging-while-drilling electromagnetic wave instruments, including but not limited to logging-while-drilling electromagnetic wave resistivity logging and logging-while-drilling azimuth electromagnetic wave logging.

[0049] (4) This invention has strong applicability and is applicable to any complex formation model, including but not limited to fault, fold, unconformity and other models. It can be used to analyze the logging response and influencing factors in different complex formations.

[0050] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims and drawings. Attached Figure Description

[0051] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0052] Figure 1 The flowchart shows the steps of a method for rapid dimensionality reduction calculation of a complex electromagnetic wave model during drilling according to an embodiment of the present invention.

[0053] Figure 2 A diagram of a two-dimensional formation model logging response calculation model according to an embodiment of the present invention is shown.

[0054] Figure 3 A schematic diagram of the background electric field Exz components on the XOZ plane according to an embodiment of the present invention is shown;

[0055] Figure 4 A flowchart illustrating the steps of a drilling electromagnetic resistivity semi-spectral domain simulation method according to an embodiment of the present invention is shown.

[0056] Figure 5 The diagram shows the real component of the half-spectral magnetic field at different wavenumbers at the measurement point according to an embodiment of the present invention.

[0057] Figure 6 This shows a real component plot of the full-spectrum magnetic field at different wavenumbers at a measurement point according to an embodiment of the present invention;

[0058] Figure 7 The diagram shows the magnetic field response at a measurement point of an electromagnetic logging-while-drilling (EMD) well in a horizontal well according to an embodiment of the present invention.

[0059] In the accompanying drawings, the same parts use the same reference numerals. Also, the drawings are not drawn to scale. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0061] For complex three-dimensional formation models, 3D simulation of electromagnetic logging while drilling has become an important means of understanding the logging response and obtaining formation structure characteristics in complex formation models. However, 3D algorithms suffer from problems such as cumbersome calculation process, slow calculation speed, and high memory consumption.

[0062] Based on this, the present invention provides a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling. It can realize the logging response of electromagnetic wave resistivity of complex 3D formation models during drilling, and under certain conditions, convert it into solving the problem of 3D electromagnetic field response in 2D formation models. It can realize rapid simulation calculation of electromagnetic wave resistivity of complex 3D formations during drilling, which helps to understand the logging response in complex three-dimensional formation models and obtain formation structure characteristics.

[0063] The method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling provided by this invention (hereinafter referred to as "dimensionality reduction method") not only ensures the accuracy of the formation model and the calculation precision, but also reduces the complexity of the calculation process, improves the calculation efficiency, and can save a lot of economic costs.

[0064] Figure 1 A flowchart illustrating the steps of a method for rapid dimensionality reduction calculation of a complex electromagnetic wave model during drilling, according to an embodiment of the present invention, is shown.

[0065] like Figure 1 As shown, in step S101, for complex three-dimensional stratigraphic models, a series of two-dimensional stratigraphic models are constructed based on instrument parameters and stratigraphic distribution characteristics.

[0066] In one embodiment, a complex three-dimensional stratigraphic model includes, but is not limited to, heterogeneous, faulted, folded, and multi-interface three-dimensional stratigraphic models.

[0067] In step S101, a two-dimensional formation model is obtained through the following steps: the frequency and source distance of the drilling electromagnetic wave instrument are obtained as instrument parameters; the spatial distribution characteristics of formation resistivity are obtained as formation distribution characteristics; and a series of two-dimensional formation models are constructed by combining the instrument parameters and formation distribution characteristics, in which the formation properties remain unchanged along the Y direction and vary along the XOZ plane.

[0068] It should be noted that the instrument parameters include, but are not limited to, the frequency and source distance of the drilling electromagnetic wave instrument, and the formation distribution characteristics include, but are not limited to, the spatial distribution characteristics of formation resistivity. This invention does not limit the instrument parameters or the parameter / characteristic types of formation distribution characteristics.

[0069] Figure 2 The left-hand image shows a schematic diagram of a two-dimensional (fault) formation model. In one embodiment, the formation resistivity from top to bottom is 1 Ω·m, 10 Ω·m, and 2 Ω·m, the thickness of the middle layer is 2 m, and both the upper and lower layers are semi-infinite; the fault dip angle is 45 degrees, and the fault displacement is 3 m; the source and measurement points of the drilling electromagnetic wave logging instrument are located on both sides of the fault plane, the magnetic dipole source frequency is 100 kHz, and the distance between the source and measurement points is 2.44 m. Figure 2The right-hand side of the figure shows the results of two-dimensional finite difference mesh generation and conductivity assignment in the XOZ plane. To improve the accuracy of finite difference simulation, this invention uses a non-uniform mesh, that is, the mesh is densified at the source point and measurement point to obtain denser electric and magnetic field calculation point data.

[0070] like Figure 1 As shown, in step S102, the background strata are subjected to three-dimensional meshing in the complex three-dimensional strata model to obtain a three-dimensional meshed model.

[0071] In step S102, a three-dimensional meshed model is obtained through the following steps: In the complex three-dimensional formation model, the formation where the current logging point is located is taken as the background formation; the skin depth of the background formation is calculated based on the resistivity of the background formation and the frequency of the drilling electromagnetic wave instrument; a cubic region is established with the instrument emission point as the center, wherein the size of the cubic region is determined according to the skin depth of the background formation; the cubic region is uniformly meshed in the Y direction, and finely non-uniformly meshed in the X and Z directions to obtain a three-dimensional meshed model.

[0072] In one embodiment, the size L (length-width-height) of the cubic region is determined based on the skin depth δ of the background strata, for example, L = A1 × δ; the size l of the uniform grid in the Y direction of the cubic region is determined based on the skin depth δ of the background strata, for example, l = δ ÷ A2; where A1 and A2 are both coefficients.

[0073] In one embodiment, if the source point is located in a lower formation with a resistivity of 2 Ω·m, the background formation is set as a uniform formation with a resistivity of 2 Ω·m. When meshing it, a grid is applied in the X and Z directions. Figure 2 The non-uniform mesh shown in the right-hand figure is obtained by densifying the mesh at the source and measurement points to obtain denser data for electric and magnetic field calculations. Since variations along the Y-direction are negligible, a uniform mesh is used in the Y-direction. This improves both the accuracy of the mesh and computational efficiency.

[0074] like Figure 1 As shown, in step S103, based on the three-dimensional mesh model, a series of spectral background electric fields corresponding to different wave numbers in the two-dimensional plane are calculated.

[0075] In step S103, the spectral background electric field is obtained through the following steps: based on Maxwell's theory, the spatial background electric field is calculated according to the spatial coordinates of the grid nodes in the three-dimensional gridded model; for the spatial background electric field, a Fourier transform is applied in the Y direction to obtain a series of spectral background electric fields corresponding to different wavenumbers in the XOZ two-dimensional plane.

[0076] In one embodiment, Figure 3 For different wavenumbers k in the XOZ two-dimensional planey (where k) y The schematic diagram of the background electric field Exz components corresponding to (e.g., 1.0, 2.0, 4.0, 8.0, 16.0, 32.0) shows that the electric field shape is consistent at different wavenumbers in the spectral domain, but the electric field modulus decreases continuously as the wavenumber increases. Furthermore, the electric field modulus decays continuously as the field point moves further away from the source point in the spectral domain.

[0077] like Figure 1 As shown, in step S104, the two-dimensional electric field wave equation in the spectral domain is obtained based on the three-dimensional electric field wave equation in the spatial domain, so as to derive the electric field in the finite difference scheme in the spectral domain.

[0078] In step S104, the two-dimensional electric field wave equation in the spectral domain is obtained through the following steps: based on Maxwell's equations in the spatial domain, the three-dimensional electric field wave equation in the spatial domain is obtained; for the three-dimensional electric field wave equation in the spatial domain, a Fourier transform is applied in the Y direction to obtain the two-dimensional electric field wave equation in the spectral domain.

[0079] In step S104, the finite difference electric field in the spectral domain is obtained through the following steps: the two-dimensional electric field wave equation in the spectral domain is discretized using an interleaved grid in the X and Z directions, respectively, to obtain the finite difference electric field in the spectral domain.

[0080] like Figure 1 As shown, in step S105, a system of linear equations of a sparse matrix in the spectral domain is constructed by combining the background electric field in the spectral domain and the electric field of the finite difference scheme in the spectral domain.

[0081] In one embodiment, the system of linear equations for a sparse matrix in the spectral domain is as follows:

[0082] Ax = b

[0083] Where: A represents the sparse matrix, obtained from the electric field using the finite difference scheme in the spectral domain; x represents the electric field value to be solved; b represents the source term, obtained from the background electric field in the spectral domain.

[0084] like Figure 1 As shown, in step S106, the linear equations of the sparse matrix in the spectral domain are solved to obtain the two-dimensional electric field in the spectral domain.

[0085] In step S106, the two-dimensional spectral electric field corresponding to the two-dimensional stratigraphic model is obtained through the following steps: setting the initial wavenumber and maximum wavenumber corresponding to the solution range, and setting a series of sampling points within the solution range; inputting the wavenumber corresponding to the current sampling point into the linear equation system of the sparse matrix in the spectral domain, and solving to obtain the corresponding two-dimensional spectral electric field; determining whether the wavenumber of the current sampling point has reached the maximum wavenumber. If the determination result is yes, the solution ends; if the determination result is no, the wavenumber corresponding to the next sampling point is input.

[0086] In one embodiment, the solution range can be set to the full spectrum range (-k). ym， k ym For any interval within ), a series of sampling points k yi The number of sampling points, i, is determined by the Gaussian points and lies within the solution range. Furthermore, to maximize computational efficiency, the solution range can be set to the semi-spectral domain (k...). y0， k ym For example, k y0 Set to 0, i.e., k y0 =0,k ym Set to 2.54. Additionally, the maximum wavenumber k... ym The parameters can be determined based on formation resistivity and the frequency of the drilling electromagnetic wave instrument, and can also be set based on experience in actual selection. This invention does not impose any restrictions on this.

[0087] The present invention provides a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, which not only ensures the accuracy of the formation model and the calculation precision, but also reduces the complexity of the calculation process, improves the calculation efficiency, and can save a lot of economic costs.

[0088] The dimension reduction method provided by this invention combines the characteristics of formation structure and the features of drilling electromagnetic wave instruments to construct a series of two-dimensional formation models and perform spatial grid division. It can transform the logging response of the resistivity of the drilling electromagnetic wave in the complex 3D formation model into the problem of solving the 3D electromagnetic field response in the 2D formation model under certain conditions. Compared with the existing 3D algorithms, it can significantly reduce the calculation time.

[0089] Furthermore, this invention constructs a series of two-dimensional stratigraphic models in which stratigraphic properties vary only in the XOZ plane, with negligible variations along the Y direction. Wavenumbers are used in the Y direction to simulate the propagation characteristics of electromagnetic waves in the stratigraphy. In this case, the series of two-dimensional stratigraphic models are symmetric about the XOZ plane, and the electromagnetic field in space is also symmetric (or antisymmetric) about the XOZ plane. Based on this symmetric / antisymmetric characteristic, this invention determines the solution range (which can be any set range within the full spectrum, such as the half-spectrum) by using the initial and maximum wavenumbers, and determines the number of solutions by using the number of sampling points (each sampling point corresponds to a two-dimensional problem to be solved). This allows for further reduction of the solution time for the linear equation system of sparse matrices in the spectral domain without compromising the accuracy of the stratigraphic models, thus improving computational efficiency.

[0090] According to another embodiment of the present invention, the present invention provides a fast calculation system for dimensionality reduction of complex electromagnetic wave models during drilling, and executes a fast calculation method for dimensionality reduction of complex electromagnetic wave models during drilling. The system includes: a two-dimensional formation module, a three-dimensional meshing module, a spectral background module, a finite difference module, an equation system module, and a solution module.

[0091] The 2D stratigraphy module is used to construct a series of 2D stratigraphic models for complex 3D stratigraphic models based on instrument parameters and stratigraphic distribution characteristics. The 3D meshing module is used to perform 3D meshing processing on the background stratigraphy in complex 3D stratigraphic models to obtain 3D meshed models. The spectral background module is used to calculate a series of spectral background electric fields corresponding to different wavenumbers in the 2D plane based on the 3D meshed models. The finite difference module is used to derive the spectral two-dimensional electric field wave equation based on the spatial domain 3D electric field wave equation to obtain the spectral finite difference scheme electric field. The equation system module is used to construct a spectral sparse matrix linear equation system by combining the spectral background electric field and the spectral finite difference scheme. The solution module is used to solve the spectral sparse matrix linear equation system to obtain the 2D spectral electric field.

[0092] This invention provides a method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, which has the following advantages compared with existing technologies:

[0093] (1) This invention proposes a method for rapid calculation of dimensionality reduction of complex electromagnetic wave models while drilling. Under certain conditions, the logging response of electromagnetic resistivity of complex 3D formation models while drilling is transformed into the problem of solving the 3D electromagnetic field response in 2D formation models, which can effectively improve the efficiency of electromagnetic wave logging simulation calculation while drilling.

[0094] (2) The dimensionality reduction method not only ensures the accuracy and calculation precision of the stratigraphic model, but also reduces the complexity of the calculation process, improves the calculation efficiency, and can save a lot of economic costs.

[0095] (3) The present invention has a wide coverage and can be used in different types of logging-while-drilling electromagnetic wave instruments, including but not limited to logging-while-drilling electromagnetic wave resistivity logging and logging-while-drilling azimuth electromagnetic wave logging.

[0096] (4) This invention has strong applicability and is applicable to any complex formation model, including but not limited to fault, fold, unconformity and other models. It can be used to analyze the logging response and influencing factors in different complex formations.

[0097] Figure 4 A flowchart illustrating the steps of a symmetric field drilling electromagnetic resistivity semi-spectral domain simulation method according to an embodiment of the present invention is shown.

[0098] In one embodiment, the present invention provides a symmetrical field drilling electromagnetic resistivity semi-spectral domain simulation method: First, the two-dimensional spectral domain electric field corresponding to the two-dimensional formation model is calculated in the semi-spectral domain using the "dimensionality reduction processing method" provided by the present invention to obtain the semi-spectral domain electric field; then, the semi-spectral domain electric field is converted into a semi-spectral domain magnetic field, and the semi-spectral domain magnetic field is symmetrically processed to obtain the full-spectral domain magnetic field; finally, the full-spectral domain magnetic field is subjected to a fast inverse Fourier transform to obtain the spatial domain three-dimensional magnetic field distribution result corresponding to the complex three-dimensional formation model.

[0099] like Figure 4 As shown, in step S401, the complex three-dimensional formation is reduced in size by constructing a series of two-dimensional formation models based on parameters such as the frequency and source distance of the drilling electromagnetic wave instrument, combined with the spatial distribution characteristics of formation resistivity.

[0100] In complex three-dimensional formation models, a series of complex two-dimensional formation models are constructed first, based on parameters such as the frequency and source distance of the drilling electromagnetic wave instrument, and then combined with the spatial distribution characteristics of formation resistivity (e.g., the resistivity distribution characteristics of horizontally layered formations). In these models, the formation properties only vary in the XOZ plane, with negligible variations along the Y direction. Wavenumbers are used in the Y direction to simulate the propagation characteristics of electromagnetic waves in the formation. At this point, the formation model is symmetric about the XOZ plane, and the electromagnetic field in space is also symmetric (or antisymmetric) about the XOZ plane.

[0101] Figure 2 The left-hand image shows a schematic diagram of a two-dimensional (fault) formation model. In one embodiment, the formation resistivity from top to bottom is 5 Ω·m, 50 Ω·m, and 10 Ω·m, with a middle layer thickness of 2 m and both upper and lower layers being semi-infinite thickness; the fault dip angle is 45 degrees, and the fault displacement is 3 m; the source and measurement points of the drilling electromagnetic wave logging instrument are located on opposite sides of the fault plane, with a magnetic dipole source frequency of 200 kHz and a distance of 2.44 m between the source and measurement points. Figure 2 The right-hand side of the figure shows the results of two-dimensional finite difference mesh generation and conductivity assignment in the XOZ plane. To improve the accuracy of finite difference simulation, this invention uses a non-uniform mesh, that is, the mesh is densified at the source point and measurement point to obtain denser electric and magnetic field calculation point data.

[0102] like Figure 4 As shown, in step S402, the resistivity of the background formation is determined based on the location of the current logging point, and the background formation is processed into a three-dimensional grid with the instrument launch point as the center.

[0103] The resistivity of the background formation is determined based on the location of the current logging point, and the background formation is then processed into a three-dimensional grid. In the three-dimensional grid, the electric field components and magnetic field components surround each other, satisfying the requirements of the electromagnetic wave equation.

[0104] In step S402, a three-dimensional meshed model is obtained through steps S21 to S23.

[0105] Step S21: Set the stratum at the instrument location as the background stratum, and set its resistivity as the background stratum resistivity.

[0106] Step S22: Calculate the skin depth of the background formation based on the background formation resistivity and the frequency of the drilling electromagnetic wave instrument, denoted as δ.

[0107] Step S23: Centered on the instrument launch point, establish a cubic region with length-width-height L of A1×δ (e.g., L=4·δ), and perform uniform meshing along the Y-axis, with mesh size l of δ÷A2 (e.g., l=0.05·δ). This achieves three-dimensional meshing of the background strata, resulting in a three-dimensional meshed model.

[0108] In one embodiment, if the source point is located in a lower formation with a resistivity of 10 Ω·m, the background formation is set as a uniform formation with a resistivity of 10 Ω·m. When meshing it, a grid is applied in the X and Z directions. Figure 2 The non-uniform mesh shown in the right-hand figure is obtained by densifying the mesh at the source and measurement points to obtain denser data for electric and magnetic field calculations. Since variations along the Y-direction are negligible, a uniform mesh is used in the Y-direction. This improves both the accuracy of the mesh and computational efficiency.

[0109] like Figure 4 As shown, in step S403, the electric field value of the spatial domain node is calculated based on the spatial coordinates of the grid node, and then a series of spectral domain background electric fields corresponding to different wave numbers in two-dimensional space are obtained by using Fourier transform.

[0110] Based on Maxwell's theory, the transmitting coil of a logging-while-drilling (LWD) electromagnetic wave instrument can be equivalent to a magnetic dipole source. By combining the analytical solution of the electromagnetic wave field generated by the spatial domain magnetic dipole source, the electric field values ​​at the grid nodes (spatial domain node electric field values) can be obtained. Then, a Fourier transform is used to obtain the spectral domain background electric field E. fi .

[0111] In step S403, the spectral background electric field E is obtained through steps S31 to S32. fi .

[0112] Step S31, based on the spatial coordinates (X, X) of the mesh nodes in the 3D meshed model i ,Y j Z k The spatial domain background electric field is obtained by calculating the nodal electric field values ​​in the spatial domain. The electric field values ​​are calculated using the following formula:

[0113]

[0114] Where: E X E Y E Z All are electric field vectors, with subscripts X, Y, and Z representing the direction of the source, M E ω is the magnetic dipole moment, k is the wave number, ω is the angular frequency, and x is the magnetic dipole moment. s y s z s Let x, y, and z be the coordinates of the magnetic dipole source, and let x, y, and z be the spatial coordinates of the field point, i.e., (X...i ,Y j Z k ); r is the Euclidean distance from the field point to the source point.

[0115] Step S32: Apply a Fourier transform in the Y direction to the background electric field in the spatial domain to obtain different wavenumbers k in the XOZ two-dimensional space. y The corresponding series of spectral background electric fields.

[0116] like Figure 4 As shown, in step S404, a Fourier transform is applied to the three-dimensional electric field wave equation in the spatial domain to obtain the two-dimensional electric field wave equation in the spectral domain. The electric field in the spectral domain finite difference scheme is discretized using an interlaced grid, and parameters such as the distance between interlaced grid nodes and the node center are determined.

[0117] Applying a Fourier transform to the three-dimensional electric field wave equation in the spatial domain yields the two-dimensional electric field wave equation f in the spectral domain. E2D And derive the electric field of the finite difference scheme in the spectral domain. The transformation from a 3D mesh space to a 2D stratigraphic interlaced mesh is performed, followed by subdivision of the 2D stratigraphic interlaced mesh. Wherein, Δx i =x i+1 -x i Δz k =z k+1 -z k Δx represents the distance between staggered grid nodes. i-1 / 2 =x i+1 / 2 -x i-1 / 2 Δz k-1 / 2 =z k+1 / 2 -z k-1 / 2 The key parameters for mesh generation were determined by the center distance between staggered mesh nodes.

[0118] In step S404, the finite difference electric field in the spectral domain is obtained through steps S41 to S43.

[0119] Step S41: Obtain the three-dimensional electric field wave equation in the spatial domain.

[0120] The system of Maxwell's equations in the spatial domain can be expressed as:

[0121]

[0122] Where E and H are the electric field and magnetic field, respectively; M and J are the magnetic source and electric source, respectively; and σ, ε, and μ are the conductivity, dielectric constant, and magnetic permeability, respectively.

[0123] Eliminating the magnetic field in equation (2) yields the three-dimensional electric field wave equation in the spatial domain:

[0124]

[0125] Step S42: Apply a Fourier transform to equation (3) along the Y direction to obtain the Maxwell equations in the spectral domain, which is the two-dimensional electric field wave equation f in the spectral domain. E2D :

[0126]

[0127] In step S43, the electric field in the finite difference scheme of the spectral domain is obtained by discretizing the fields in the X and Z directions using the staggered grid formula (4).

[0128] In one embodiment, equation (5) takes the X direction as an example (the solution method for the Z direction is similar to that for the X direction, and will not be repeated here):

[0129]

[0130] Where, Δx i =x i+1 -x i Δz k =z k+1 -z k Indicates the distance between staggered grid nodes; E represents the center distance between staggered grid nodes. i E s These represent the incident field and the scattered field, respectively.

[0131] It should be noted that the X and Z directions are adopted Figure 2 The non-uniform mesh shown in the right-hand figure (two-dimensional meshing uses a non-uniform mesh) is a finer mesh at the source and measurement points to obtain denser electric and magnetic field calculation data. Therefore, Δx in equation (5) i Δz k , These are not fixed values, but rather a series of parameters selected according to certain rules.

[0132] like Figure 4 As shown, in step S405, the spectral domain background electric field and the spectral domain finite difference scheme electric field are combined to construct a spectral domain sparse matrix linear equation system. The sparse matrix is ​​obtained by assembling the coefficients in front of the spectral domain finite difference scheme electric field.

[0133] Combined with the background electric field E in the spectral domain fi Electric field in finite difference scheme of the spectral domain Constructing a system of linear equations Ax = b for a sparse matrix in the spectral domain is a crucial step in determining the system of linear equations for a sparse matrix in the spectral domain, as the coefficients of the sparse matrix A are key to determining the accuracy and computational precision of the solution model.

[0134] In one embodiment, the system of linear equations for a sparse matrix in the spectral domain is as follows:

[0135] Ax=b (6)

[0136] Where: x is the nodal electric field value to be solved; b is the source term, obtained from the background electric field in the spectral domain; A is the sparse matrix, obtained from the electric field in the finite difference scheme of the spectral domain in formula (5). The coefficients in the equation are assembled.

[0137] like Figure 4 As shown, in step S406, the wavenumber of the current sampling point is input, and the corresponding two-dimensional spectral electric field is solved until the wavenumber reaches its maximum value.

[0138] In step S406, the linear equations of the sparse matrix in the spectral domain are solved through steps S61 to S63.

[0139] Step S61: Set the initial wavenumber and maximum wavenumber corresponding to the solution range, and set a series of sampling points within the solution range.

[0140] In one embodiment, the solution range can be set to the full spectrum range (-k). ym， k ym For any interval within ), a series of sampling points k yi The number of sampling points, i, is determined by the Gaussian points and lies within the solution range. Furthermore, to maximize computational efficiency, the solution range is set to the semi-spectral domain (k...). y0， k ym For example, k y0 Set to 0, i.e., k y0 =0,k ym Set to 2.84. Additionally, the maximum wavenumber k... ym The parameters can be determined based on formation resistivity and the frequency of the drilling electromagnetic wave instrument, and can also be set based on experience in actual selection. This invention does not impose any restrictions on this.

[0141] Step S62: Input the wavenumber corresponding to the current sampling point into the linear equation system of the sparse matrix in the spectral domain, and solve to obtain the corresponding two-dimensional electric field in the spectral domain.

[0142] Step S63: Determine whether the wavenumber of the current sampling point has reached the maximum wavenumber. If the determination result is yes, the solution ends. If the determination result is no, input the wavenumber corresponding to the next sampling point and continue the calculation until the maximum wavenumber is reached.

[0143] like Figure 4 As shown, in step S407, the half-spectral electric field is converted into a half-spectral magnetic field.

[0144] Within the semi-spectral domain, different wavenumbers (k) will be used. y0 and kym To convert the two-dimensional electric field to a two-dimensional magnetic field, we can use the following formula to convert the semi-spectral electric field to a semi-spectral magnetic field:

[0145]

[0146] Where: H represents the magnetic field; ω and μ0 represent the angular frequency and permeability, respectively; k y Indicates wave number; E X E Y E Z All are electric field vectors, with subscripts X, Y, and Z representing the direction of the source; x, y, and z represent spatial coordinates; All are unit vectors.

[0147] like Figure 5 Let H be the real part of the half-spectral magnetic field component at the measurement point, where the vertical axis H ij This represents the magnetic field component in the j-direction generated by the i-direction magnetic dipole source. The horizontal axis represents the wavenumber k. y In (k) y0， k ym )between.

[0148] like Figure 4 As shown, in step S408, a two-dimensional full-spectrum magnetic field is generated through symmetry processing.

[0149] In step S408, the (two-dimensional) full-spectrum magnetic field is obtained through the following steps: at wavenumber k y0 and k ym Within the semi-spectral magnetic field between the two wavenumbers, the two-dimensional spectral magnetic fields corresponding to different wavenumbers are symmetrically processed, i.e., the wavenumber threshold (k) is used. y0， k ym ) transform into (-k ym k y0 This generates a (two-dimensional) full-spectrum magnetic field, thus improving the efficiency of this calculation step by 50%.

[0150] like Figure 6 for Figure 5 The half-spectral magnetic field shown is obtained by symmetry processing to obtain the full-spectral magnetic field, where the vertical axis H ij This represents the magnetic field component in the j-direction generated by the i-direction magnetic dipole source. The horizontal axis represents the wavenumber k. y In (-k) ym， k ym The range between ) represents the full-spectrum magnetic field.

[0151] like Figure 4 As shown, in step S409, a fast inverse Fourier transform is performed on the full-spectrum magnetic field to obtain the spatial domain three-dimensional magnetic field distribution results corresponding to the complex three-dimensional stratigraphic model.

[0152] By applying the inverse fast Fourier transform to the spectral magnetic fields corresponding to different wavenumbers obtained from the calculation, the distribution results of the three-dimensional magnetic field in the spatial domain can be obtained, realizing the rapid simulation calculation of the drilling electromagnetic wave logging response of complex formation models. To further improve computational efficiency, the Gaussler-Gande product, which offers high accuracy and flexibility, is used to approximate the Fourier transform.

[0153] like Figure 7 for Figure 2 The rapid calculation results corresponding to the two-dimensional formation model shown demonstrate the magnetic field response map of the measurement point of the electromagnetic wave logging while drilling in the horizontal well. Figure 7 The left side of the diagram represents the imaginary part of the magnetic field, while the right side represents the real part.

[0154] In this example, when the instrument is located on the hanging wall of the fault, the distance between the instrument and the lower interface of the intermediate strata is 0.5m; when the instrument is located on the footwall of the fault, the distance between the instrument and the upper interface of the intermediate strata is 0.5m. The magnetic field response curves also show that the magnetic field value changes significantly when the instrument approaches the fault plane. This is because the measurement signal near the fault plane is affected by the complex fault structure.

[0155] For complex formation models such as heterogeneous, faulted, folded, and multi-layered interfaces, 3D simulation of electromagnetic wave logging while drilling (EMWL) has become an important means of understanding the logging response and obtaining formation structural characteristics in complex formation models. However, 3D algorithms suffer from problems such as cumbersome calculation processes, slow calculation speed, and high memory consumption. This invention transforms the logging response of EWL resistivity in complex formation 3D models into solving the 3D electromagnetic field response problem in 2D formation models under certain conditions, enabling rapid simulation calculation of EWL resistivity in complex formations.

[0156] For the 2D stratigraphic model provided by this invention, the variation of its properties along the Y direction is negligible, and the wavenumber is used to simulate the propagation characteristics of electromagnetic waves in the stratigraphic region along the Y direction. In this case, the stratigraphic model is symmetric about the XOZ plane, and the electromagnetic field in space is also symmetric (or antisymmetric) about the XOZ plane; correspondingly, the two-dimensional electromagnetic field in the spectral domain is related to k... y =0 is symmetric (or antisymmetric). Therefore, by solving k y Obtaining the electromagnetic field in the ≥0 region and then using symmetry to obtain the field in the full spectrum becomes an effective way to improve computational efficiency.

[0157] Based on the symmetry characteristics of electromagnetic fields, this invention can reduce the number of two-dimensional problems to be calculated, thereby significantly improving the efficiency of electromagnetic logging-while-drilling simulation calculations.

[0158] According to another aspect of the present invention, a symmetric field drilling electromagnetic resistivity semi-spectral domain simulation system is also provided, which performs a symmetric field drilling electromagnetic resistivity semi-spectral domain simulation method. The system includes: a model building module, a semi-spectral domain module, a full-spectral domain module, and a three-dimensional magnetic field module.

[0159] The model building module is used to construct a series of two-dimensional stratigraphic models for complex three-dimensional stratigraphic models based on instrument parameters and stratigraphic distribution characteristics; the semi-spectral domain module is used to calculate the two-dimensional spectral domain electric field corresponding to the two-dimensional stratigraphic model within the semi-spectral domain to obtain the semi-spectral domain electric field; the full-spectral domain module is used to convert the semi-spectral domain electric field into a semi-spectral domain magnetic field and perform symmetric processing on the semi-spectral domain magnetic field to obtain the full-spectral domain magnetic field; the three-dimensional magnetic field module is used to perform a fast Fourier inverse transform on the full-spectral domain magnetic field to obtain the spatial domain three-dimensional magnetic field distribution results corresponding to the complex three-dimensional stratigraphic model.

[0160] This invention provides a symmetric field drilling electromagnetic wave resistivity half-spectral domain simulation method, which has the following advantages compared with the prior art:

[0161] (1) Based on the symmetry characteristics of the spectral field in the complex formation model, the present invention proposes a 2.5D half-spectral field fast calculation method, which can effectively improve the efficiency of drilling electromagnetic wave logging simulation.

[0162] (2) This invention reduces the number of 2D problems that need to be calculated to half that of traditional methods by using a semi-spectral domain calculation method, thereby improving the calculation efficiency by nearly 50%.

[0163] (3) The present invention has a wide coverage and can be used in different types of drilling electromagnetic wave logging instruments, including but not limited to drilling electromagnetic wave resistivity logging and drilling azimuth electromagnetic wave logging.

[0164] (4) This invention has strong applicability and is applicable to any complex formation model, including but not limited to fault, fold, unconformity and other models. It can be used to analyze the logging response and influencing factors in different complex formations.

[0165] The present invention provides a method for rapid dimensionality reduction calculation of complex models of electromagnetic waves during drilling, and a method for semi-spectral domain simulation of resistivity of electromagnetic waves during drilling with symmetric fields. This method can also be used in conjunction with a computer-readable storage medium storing a computer program. Executing the computer program runs the method for rapid dimensionality reduction calculation of complex models of electromagnetic waves during drilling, and the method for semi-spectral domain simulation of resistivity of electromagnetic waves during drilling with symmetric fields. The computer program can execute computer instructions, which include computer program code. The computer program code can be in the form of source code, object code, executable files, or some intermediate form.

[0166] Computer-readable storage media may include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0167] It should be noted that the contents of computer-readable storage media may be appropriately added to or subtracted from the contents according to the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable storage media may not include electrical carrier signals and telecommunication signals.

[0168] It should be understood that the embodiments disclosed herein are not limited to the specific structures, processing steps, or materials disclosed herein, but should be extended to equivalent substitutions of these features as understood by those skilled in the art. It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

[0169] In the description of this invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front end," "rear end," "head," "tail," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0170] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0171] Certain terms are used throughout this application to refer to specific system components. As those skilled in the art will recognize, the same components may often be referred to by different names, and therefore this application is not intended to distinguish those components that differ only in name and not in function. In this application, the terms “comprise,” “include,” and “have” are used in an open-ended manner and should therefore be interpreted as meaning “including, but not limited to…”. Furthermore, the terms “substantially,” “materially,” or “approximately” as used herein refer to industry-accepted tolerances for the corresponding terms. The term “coupling,” as may be used herein, includes direct coupling and indirect coupling via additional components, elements, circuits, or modules, wherein, for indirect coupling, the intermediate component, element, circuit, or module does not alter the information of the signal but may adjust its current level, voltage level, and / or power level. Inferred coupling (e.g., one element is inferredly coupled to another element) includes direct and indirect coupling between two elements in the same manner as “coupling.”

[0172] The phrase "an embodiment" or "an embodiment" used in this specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" or "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0173] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and to design various embodiments with various modifications suitable for a particular purpose.

[0174] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, characterized in that, The method includes: For complex three-dimensional stratigraphic models, a series of two-dimensional stratigraphic models are constructed based on instrument parameters and stratigraphic distribution characteristics; In the complex three-dimensional stratigraphic model, the background stratigraphic layers are subjected to three-dimensional meshing to obtain a three-dimensional meshed model; Based on the three-dimensional meshed model, a series of spectral background electric fields corresponding to different wave numbers in the two-dimensional plane are calculated. Based on the three-dimensional electric field wave equation in the spatial domain, the two-dimensional electric field wave equation in the spectral domain is obtained, and the electric field in the finite difference scheme in the spectral domain is derived. By combining the background electric field in the spectral domain and the electric field of the finite difference scheme in the spectral domain, a system of linear equations with sparse matrices in the spectral domain is constructed. Solve the linear equations of the sparse matrix in the spectral domain to obtain the two-dimensional electric field in the spectral domain.

2. The method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling as described in claim 1, characterized in that, The complex three-dimensional stratigraphic model includes: heterogeneous, faulted, folded, and multi-layered interface three-dimensional stratigraphic models. The two-dimensional stratigraphic model is obtained through the following steps: The frequency and source distance of the drilling electromagnetic wave instrument are obtained as the instrument parameters; The spatial distribution characteristics of formation resistivity are obtained as the formation distribution characteristics; Based on the instrument parameters and the stratigraphic distribution characteristics, a series of two-dimensional stratigraphic models are constructed, in which the stratigraphic properties remain constant along the Y direction and vary along the XOZ plane.

3. The method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, as described in any one of claims 1-2, is characterized in that... The three-dimensional meshed model is obtained through the following steps: In the complex three-dimensional formation model, the formation where the current logging point is located is used as the background formation; The skin depth of the background formation is calculated based on the resistivity of the background formation and the frequency of the drilling electromagnetic wave instrument. A cubic region is established with the instrument's launch point as the center, wherein the size of the cubic region is determined based on the skin depth of the background strata; The cube region is divided into uniform meshes in the Y direction and into finer non-uniform meshes in the X and Z directions to obtain the three-dimensional meshed model.

4. A method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, as described in any one of claims 1-3, characterized in that, The background electric field in the spectral domain is obtained through the following steps: Based on Maxwell's theory, the spatial domain background electric field is calculated according to the spatial coordinates of the grid nodes in the three-dimensional meshed model. For the spatial domain background electric field, a Fourier transform is applied in the Y direction to obtain a series of spectral domain background electric fields corresponding to different wavenumbers in the XOZ two-dimensional plane.

5. A method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, as described in any one of claims 1-4, characterized in that, The two-dimensional electric field wave equation in the spectral domain is obtained through the following steps: Based on Maxwell's equations in the spatial domain, the three-dimensional electric field wave equation in the spatial domain is obtained. By applying a Fourier transform in the Y direction to the three-dimensional electric field wave equation in the spatial domain, the two-dimensional electric field wave equation in the spectral domain is obtained.

6. A method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, as described in any one of claims 1-5, characterized in that, The electric field of the finite difference scheme in the spectral domain is obtained through the following steps: The two-dimensional electric field wave equation in the spectral domain is discretized using an interleaved grid in the X and Z directions respectively to obtain the electric field in the finite difference scheme of the spectral domain.

7. A method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, as described in any one of claims 1-6, characterized in that, The linear equations of the spectral domain sparse matrix: Ax = b Where: A represents the sparse matrix, obtained according to the electric field of the finite difference scheme in the spectral domain; x represents the electric field value to be solved; b represents the source term, obtained according to the background electric field in the spectral domain.

8. A method for rapid dimensionality reduction calculation of complex electromagnetic wave models during drilling, as described in any one of claims 1-7, characterized in that, The two-dimensional spectral domain electric field is obtained through the following steps: Set the initial wavenumber and maximum wavenumber corresponding to the solution range, and set a series of sampling points within the solution range; Input the wavenumber corresponding to the current sampling point into the linear equation system of the sparse matrix in the spectral domain, and solve to obtain the corresponding two-dimensional electric field in the spectral domain. Determine whether the wavenumber of the current sampling point has reached the maximum wavenumber. If the determination result is yes, the solution ends; if the determination result is no, input the wavenumber corresponding to the next sampling point.

9. A storage medium, characterized in that, It contains instructions for performing the method as described in any one of claims 1-8.

10. A fast calculation system for dimensionality reduction of complex electromagnetic wave models during drilling, characterized in that, The system, which performs the method as described in any one of claims 1-8, comprises: The two-dimensional stratigraphic module is designed for complex three-dimensional stratigraphic models. Based on instrument parameters and stratigraphic distribution characteristics, it constructs a series of two-dimensional stratigraphic models. The three-dimensional meshing module performs three-dimensional meshing processing on the background strata in the complex three-dimensional stratigraphic model to obtain a three-dimensional meshed model; The spectral background module, based on the three-dimensional meshed model, calculates a series of spectral background electric fields corresponding to different wavenumbers in a two-dimensional plane. The finite difference module derives the two-dimensional electric field wave equation in the spectral domain from the three-dimensional electric field wave equation in the spatial domain, thereby deriving the electric field in the finite difference scheme in the spectral domain. The equation module combines the background electric field in the spectral domain with the finite difference scheme in the spectral domain to construct a sparse matrix linear equation system in the spectral domain. The solver module solves the linear equations of the sparse matrix in the spectral domain to obtain the two-dimensional electric field in the spectral domain.

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