A gravity and magnetic inversion method based on grid merging and BTTB matrix fast forward

Abstract

The application discloses a gravity and magnetic inversion method based on grid merging and BTTB matrix fast forward, relates to the technical field of gravity and magnetic exploration, and comprises the following steps: establishing a basic forward and inversion grid and a basic grid kernel function matrix; initializing a coarse grid model and a conversion matrix; coarse grid inversion; adaptive grid subdivision based on a model gradient and establishment of a new conversion matrix; fine grid inversion; iterative convergence and output. The application has the beneficial effects that the BTTB kernel function matrix is calculated based on the basic grid in advance, the conversion from fine scale model parameters to coarse scale model parameters is realized through the conversion matrix, the iterative closed loop process of coarse grid inversion, adaptive grid subdivision and fine grid inversion is adopted, the criterion of adaptive grid subdivision is to compare the gradient eigenvalue of the current inversion model parameters with a preset threshold value, and in the grid inversion of different scales, the BTTB kernel function matrix generated by the same set of basic grid in advance is used to realize fast forward through the processing of the conversion matrix.

Description

Technical Field

[0001] This invention relates to the field of gravity and magnetic exploration technology, and in particular to a gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix. Background Technology

[0002] Gravity and magnetic exploration is an important tool in geophysics. Its core principle is to invert the distribution of physical properties (density, magnetic susceptibility) in subsurface space using gravity or magnetic field data observed at the Earth's surface, thereby identifying geological structures or mineral resources. Three-dimensional inversion is the mainstream method for interpreting gravity and magnetic data, but it has long faced two major technical bottlenecks:

[0003] Computational efficiency and memory consumption issues: Refined 3D inversion requires dividing the underground space into a massive number of basic grid cells. Traditional forward modeling calculations (such as direct integration methods) have a time complexity of up to [missing information - likely a number]. ( (This refers to the number of grid cells), and the storage of the kernel function matrix also requires... The spatial limitations make large-scale 3D inversion difficult to run on ordinary computers. Although Fast Fourier Transform (FFT) methods (such as those utilizing the BTTB matrix structure) can reduce the computational complexity of forward modeling to... However, the inversion process still requires processing model parameters equal to the number of grids, resulting in a huge computational and memory burden.

[0004] The problem of multiple solutions in inversion: Gravity and magnetic data themselves have volume effects, and physical anomalies of different depths and shapes may produce similar data responses. When the number of model parameters far exceeds the number of data, the inversion problem becomes highly ill-conditioned and has a strong multiple solution problem. Conventional smoothing constraint regularization methods (such as Tikhonov regularization) can provide stable solutions, but they often lead to blurred and overly smoothed boundaries in the inversion results, making it difficult to accurately characterize the sharp boundaries of geological bodies.

[0005] Existing adaptive mesh refinement techniques mostly dynamically add meshes during forward or inverse modeling, but there is a lack of a method that can both take advantage of the fast forward modeling of the BTTB matrix and systematically achieve an efficient iterative closed loop between fast global optimization of coarse meshes and fine boundary characterization of fine meshes. Summary of the Invention

[0006] To address the technical challenges of low computational efficiency, severe multiple solutions, and low resolution in gravity and magnetic field 3D inversion, this invention discloses a gravity and magnetic field inversion method based on mesh merging and rapid forward modeling of the BTTB matrix. This method organically combines the rapid and high-precision forward modeling of the BTTB matrix with an adaptive mesh merging or subdivision strategy, forming a rapid iterative inversion framework that "focuses progressively from coarse to fine." Only a few fine iterations are performed in key regions, resulting in overall efficiency far exceeding that of direct high-resolution inversion, significantly improving inversion accuracy and resolution.

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

[0008] A gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix includes the following steps:

[0009] Step S1: Establish the basic forward and inverse mesh and the basic mesh kernel function matrix.

[0010] S11. Set the range of the basic forward and inverse grid according to the size of the study area, and set the size of the basic forward and inverse grid cell according to the data point spacing or the minimum target size to establish the basic forward and inverse grid.

[0011] S12. The BTTB matrix fast forward modeling algorithm is used to calculate and store the kernel function matrix at the basic grid scale as the basis for subsequent inversion calculations.

[0012] Step S2: Initialize the coarse mesh model and transformation matrix

[0013] S21. Set the initial regular coarse mesh model The coarse mesh size is 3 to 5 times the size of the basic forward and inverse mesh elements in step S1, and the number of coarse meshes is much smaller than the parameters of the basic mesh model. Quantity;

[0014] S22. Calculate the merging or subdivision matrix based on the spatial inclusion relationship between the coarse mesh and the basic mesh. This matrix defines the linear mapping relationship from the parameters of the coarse mesh model to the parameters of the basic mesh model.

[0015] S23. Establish the transformation matrix from the parameter space of the coarse mesh model to the parameter space of the basic mesh model.

[0016] Step S3: Perform coarse mesh inversion to obtain preliminary results.

[0017] Based on the basic forward and inverse mesh from step S1, establish the model constraint matrix. An objective function for gravity and magnetic inversion is established, and an optimization algorithm is used for iterative inversion to obtain the update amount of the model under coarse grid. The model is then updated to obtain a coarse-grid model result, which is a preliminary result with lower resolution.

[0018] Step S4: Adaptive mesh subdivision based on model gradient features and establishment of a new transformation matrix.

[0019] S41. Using the coarse mesh model and model transformation matrix obtained from step S3, calculate the gradient value of the basic mesh, and use the transformation matrix to calculate the gradient spatial distribution characteristics of the coarse mesh model.

[0020] S42. For regions where the gradient of the coarse mesh model changes drastically, they are identified as boundary regions of abnormal physical properties. The coarse mesh is then divided into smaller sub-mesh sizes, with the sub-mesh size being an integer multiple of the basic mesh size. For regions where the physical properties change gradually, the current mesh size is maintained.

[0021] S43. Based on the new meshing scheme, recalculate the new transformation matrix and establish a new transformation matrix from the new mesh model parameters to the basic mesh model parameters. .

[0022] Step S5: Perform fine-grid inversion to obtain high-resolution results.

[0023] S51. Based on the coarse mesh model obtained in step S3, generate the inversion initial values ​​of the current subdivided mesh model through the transformation matrix;

[0024] S52. Following the inversion calculation method in step S3, perform inversion calculations in the current finer mesh model parameter space to obtain a model with clearer physical property boundaries and higher resolution.

[0025] Step S6: Convergence condition judgment and output of final result

[0026] First, determine whether the preset termination condition is met. If the termination condition is not met, return to step S4 and continue to subdivide the physical property anomaly boundary region grid based on the model gradient value characteristics, establish a new transformation matrix, and perform a new round of fine inversion.

[0027] If the termination condition is met, the final result, i.e., the high-resolution physical property model, is output.

[0028] Furthermore, in step S12, the process of fast forward modeling of the BTTB matrix is ​​as follows:

[0029] The gravity and magnetic forward modeling formula is expressed as:

[0030] (1);

[0031] Among them, gravity and magnetic forward modeling data for Vectors are distributed at a height of On a plane Observations on regular grid nodes; kernel matrix for Model parameter vector for , which are also basic mesh model parameters; , , They are respectively , , The number of grids in the three directions, of which , The number of directional grids is the same as the number of observation point grids;

[0032] Using the BTTB matrix fast forward modeling algorithm, formula (1) can be expressed as:

[0033] (2);

[0034] in, for Forward coefficient matrix; 3D formal model parameters express matrix; This is a convolution operation.

[0035] Furthermore, in step S12, the convolution calculation result is obtained using Fast Fourier Transform, realizing fast forward modeling of large-scale data; the calculation process is as follows:

[0036] (3);

[0037] in, For the first Layer forward modeling data ; For the first Layer forward modeling coefficient matrix; for After expansion Layer property values; This is a two-dimensional fast Fourier transform; It is a two-dimensional inverse fast Fourier transform;

[0038] Extract The former The element is obtained. The forward modeling results of all layers are summed to obtain the forward modeling results of all layers.

[0039] Furthermore, in step S23, the matrix transformation formula is used to transform the parameter space of the coarse mesh model to the parameter space of the basic mesh model:

[0040] (4);

[0041] Among them, the basic mesh model parameters for vector ; for The transformation matrix; The parameter space of the coarse mesh model is The vector, ;

[0042] The formula for the inverse transformation is obtained as follows:

[0043] (5);

[0044] in, Represents the transpose of a matrix;

[0045] Transformation matrix It can achieve subdivision from coarse mesh model to basic mesh model, and the matrix It can merge basic mesh models into coarse mesh models.

[0046] Furthermore, taking a two-dimensional model as an example, the calculation... The process involves transforming the 9 model parameters in the regular mesh into 5 merged model parameters, with the following relationship:

[0047] (6);

[0048] Based on the above relationship, it can be easily obtained that:

[0049] (7).

[0050] Further, in step S3, an optimization algorithm is used for iterative inversion to solve the following equations to obtain the update amount of the model under the coarse mesh. The equation is:

[0051] (8);

[0052] in, The observed data vector is the first... The result of the next iteration; For regularization parameters, It is a reference model.

[0053] Furthermore, step S3 involves calculating the kernel matrix. and When multiplying with a vector, the BTTB matrix fast forward multiplication algorithm from step S1 is used for calculation; solving equation (8) yields... Update the model to obtain the coarse mesh model result, which is the preliminary result with lower resolution;

[0054] (9);

[0055] Among them, step size It was obtained using the Armijo linear search method.

[0056] Further, in step S6, the termination condition is one of the following:

[0057] (1) The current grid size has reached the basic grid size;

[0058] (2) The data fit difference is less than the preset threshold, and the fit difference changes very little between the two fine inversions;

[0059] (3) The changes in model parameters during the two fine inversions are less than the preset threshold;

[0060] (4) Achieve the maximum number of fine inversion iterations.

[0061] The beneficial effects of this invention are that, compared with the prior art, its advantages are:

[0062] (1) Significantly improved computational efficiency: In the initial stage, a coarse-grid model with very few parameters is used for inversion, resulting in a decrease in computational load and memory requirements by orders of magnitude. The pre-calculated BTTB kernel function matrix is ​​reused throughout the process, avoiding the overhead of repeatedly recalculating the kernel function in traditional adaptive encryption. A progressive inversion from coarse to fine is achieved, with most of the computation concentrated on rapid iteration at low resolution, and only a few fine iterations performed in key areas. The overall efficiency far exceeds that of directly performing high-resolution inversion, significantly improving the accuracy and resolution of the inversion.

[0063] (2) Reduced ambiguity: The initial coarse grid inversion model has fewer parameters, the inversion problem is highly stable, and it can quickly converge to the approximate range of the global optimum, providing an excellent initial model for subsequent subdivision and effectively avoiding local minima and ambiguity.

[0064] (3) Focus on boundary characterization: The adaptive subdivision strategy directly targets the gradient region of drastic changes in physical properties (i.e., geological boundary), automatically focusing computing resources on the edge of the anomaly, avoiding uniform densification indiscriminately throughout the space, thereby obtaining extremely high resolution at the boundary while maintaining the smoothness and stability of the internal region.

[0065] (4) Avoid over-smoothing: Traditional smoothing constraints can blur the boundaries, while the adaptive subdivision of the mesh boundaries in this invention essentially allows the model to produce abrupt changes in the subdivided regions, which can more realistically reproduce sharp geological interfaces.

[0066] (5) Reduced memory requirements: Throughout the iteration process, the number of inversion model parameters is always kept at a low level appropriate to the current resolution. It may only approach the total number of basic grids in the final stage, but by then the model is highly optimized and the number of iterations is minimal. At the same time, the inherent storage advantages of BTTB and the fast forward modeling algorithm, combined with this invention, result in extremely low memory usage. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the process of the present invention;

[0068] Figure 2 This is a schematic diagram of the model parameter transformation in this embodiment. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] This invention discloses a gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix, such as... Figure 1 As shown, the BTTB (Block-Toeplitz-Toeplitz-Block) kernel function matrix is ​​first pre-calculated based on the basic grid. The transformation matrix is ​​used to convert the model parameters from the fine-scale (basic grid) to the coarse-scale (coarse grid) model parameters. Then, an iterative closed-loop process of "coarse grid inversion → adaptive grid subdivision based on model features → fine grid inversion" is adopted. The method of constructing the transformation matrix is ​​based on the spatial topological relationship between the coarse grid and the basic grid, and defines the linear mapping of physical property parameters between grids of different scales. The criterion for adaptive grid subdivision is based on the comparison of the gradient eigenvalues ​​of the current inversion model parameters with a preset threshold, and only local densification is performed in areas with drastic changes. In the grid inversion at different scales, the same set of BTTB kernel function matrices (or their Fourier forms) pre-generated from the basic grid are used to achieve fast forward modeling through the processing of the transformation matrix, avoiding repeated calculation of the kernel function.

[0071] The specific process of this method is as follows:

[0072] Step 1: Establish the basic forward and inverse grids and the basic grid kernel function matrix.

[0073] (11) Set the range of the basic forward and inverse grid according to the size of the study area, set the size of the basic forward and inverse grid cell according to the data point spacing or the minimum target size, and establish the basic forward and inverse grid.

[0074] (12) The BTTB matrix fast forward modeling algorithm is used to calculate and store the kernel function matrix (or its Fourier transform form) at the basic grid scale. This matrix accurately describes the contribution of each basic unit to the observation data and serves as the basis for subsequent inversion calculations.

[0075] The process of fast forward modeling of the BTTB matrix.

[0076] The gravity and magnetic forward modeling formula is expressed as:

[0077] (1);

[0078] Among them, gravity and magnetic forward modeling data for Vectors are distributed at a height of On a plane Observations on regular grid nodes; kernel matrix for Model parameter vector for , which are also basic mesh model parameters; , , They are respectively , , The number of grids in the three directions, of which , The number of directional grids is the same as the number of observation point grids.

[0079] Using the BTTB matrix fast forward modeling algorithm, formula (1) can be expressed as:

[0080] (2);

[0081] in, for Forward coefficient matrix; 3D formal model parameters express matrix; This is a convolution operation.

[0082] The convolution calculation result can be obtained using the Fast Fourier Transform, enabling fast forward modeling of large-scale data; the calculation process is as follows:

[0083] (3);

[0084] in, For the first Layer forward modeling data, ; For the first Layer forward modeling coefficient matrix; for After expansion Layer property values; This is a two-dimensional fast Fourier transform; This is a two-dimensional inverse fast Fourier transform.

[0085] Extract The former The element is obtained. The forward modeling results of all layers are summed to obtain the forward modeling results of all layers.

[0086] Step 2: Initialize the coarse mesh model and transformation matrix.

[0087] (21) Set the initial regular coarse mesh model The coarse mesh size is 3 to 5 times the size of the basic forward and inverse mesh elements in step S1, and the number of coarse meshes is much smaller than the parameters of the basic mesh model. This significantly reduces the number of parameters required for inversion.

[0088] (22) Calculate the merging or subdivision matrix based on the spatial inclusion relationship between the coarse mesh and the basic mesh. This matrix defines the linear mapping relationship from the coarse mesh model parameters (coarse-scale properties) to the basic mesh model parameters (fine-scale properties) (e.g., all basic meshes within a coarse mesh have the same property values).

[0089] (23) Establish the transformation matrix from the coarse mesh model parameter space to the basic mesh model parameter space.

[0090] This method employs a mesh merging / subdivision approach. While preserving the original computational framework, it merges regions belonging to the same coarse mesh model within the basic mesh into one, and uses matrix transformation formulas to convert the parameter space of the coarse mesh model to the parameter space of the basic mesh model.

[0091] (4);

[0092] Among them, the basic mesh model parameters for vector ; for The transformation matrix; The parameter space of the coarse mesh model is The vector.

[0093] Obviously, This yields the formula for the inverse transformation (matrix transformation):

[0094] (5);

[0095] in, This represents the transpose of a matrix; if the transformation matrix is ​​obtained... Then, substitute formula (4) into the regularization inversion to perform the calculation.

[0096] Transformation matrix It can achieve subdivision from coarse mesh model to basic mesh model, and the matrix It can merge basic mesh models into coarse mesh models.

[0097] How to calculate The following is a simple two-dimensional model for illustration.

[0098] Figure 2 The transformation of 9 model parameters in the regular grid into 5 merged model parameters shows the following relationship between the model parameters at corresponding positions:

[0099] (6);

[0100] Based on the above relationship, it can be easily obtained that:

[0101] (7).

[0102] Step S3: Perform coarse mesh inversion to obtain preliminary results.

[0103] Based on the basic forward and inverse mesh from step S1, establish the model constraint matrix. (Including model minimum constraints and gradient constraints), establish the objective function for gravity and magnetic inversion (including data fit difference and model constraint terms), and use optimization algorithms (such as conjugate gradient method, Gauss-Newton method, etc.) for iterative inversion. Solve the following equations to obtain the model update amount under coarse grid. By updating the model, we can obtain the coarse mesh model result, which is the preliminary result with lower resolution.

[0104] An optimization algorithm is used for iterative inversion, and the following equations are solved to obtain the update amount of the model under the coarse mesh. ;

[0105] The equation is:

[0106] (8);

[0107] in, The observed data vector is the first... The result of the next iteration; For regularization parameters, It is a reference model.

[0108] In calculating the kernel matrix and When multiplying with vectors, the BTTB matrix fast forward multiplication algorithm from step 1 is used for calculation;

[0109] Solving equation (8) yields Update the model to obtain the coarse mesh model result, which is the preliminary result with lower resolution;

[0110] (9);

[0111] Among them, step size It was obtained using the Armijo linear search method.

[0112] Step 4: Adaptively subdivide the grid based on the model gradient features and establish a new transformation matrix.

[0113] (41) Using the coarse mesh model and model transformation matrix obtained in step 3, calculate the gradient value of the basic mesh, and use the transformation matrix to calculate the gradient spatial distribution characteristics of the coarse mesh model.

[0114] (42) For regions where the gradient of the coarse mesh model changes drastically (exceeding the preset threshold), it is determined to be a boundary region of abnormal physical properties. The coarse mesh is divided into smaller sub-mesh (for example, each dimension is divided into two). The size of the sub-mesh is an integer multiple of the basic mesh. For regions where the physical properties change gently, the current mesh size is maintained.

[0115] (43) Based on the new meshing scheme, recalculate the new transformation matrix and establish a new transformation matrix from the new mesh model parameters to the basic mesh model parameters. .

[0116] Step 5: Perform fine-grid inversion to obtain high-resolution results.

[0117] (51) Based on the coarse mesh model obtained in step 3, the inversion initial value of the current subdivided mesh model is generated by the transformation matrix.

[0118] (52) Following the inversion calculation method in step 3, perform inversion calculation in the current finer mesh model parameter space to obtain a model with clearer physical property boundaries and higher resolution.

[0119] Step 6: Determine convergence conditions and output the final result.

[0120] First, determine whether the preset termination condition is met. If the termination condition is not met, return to step 4 and continue to subdivide the physical property anomaly boundary region grid based on the model gradient value characteristics, establish a new transformation matrix, and perform a new round of fine inversion.

[0121] If the termination condition is met, the final result, i.e., the high-resolution physical property model, is output.

[0122] Furthermore, in step 6, the termination condition is one of the following:

[0123] (1) The current grid size has reached the basic grid size;

[0124] (2) The data fit difference is less than the preset threshold, and the fit difference changes very little between the two fine inversions;

[0125] (3) The changes in model parameters during the two fine inversions are less than the preset threshold;

[0126] (4) Achieve the maximum number of fine inversion iterations.

[0127] In addition, this method does not limit the specific inversion optimization algorithm. In addition to the conjugate gradient method, stochastic gradient descent, quasi-Newton methods (such as L-BFGS) can be used, as long as they can quickly realize the inversion calculation of physical properties.

[0128] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for gravity and magnetic inversion based on grid merging and fast forward of BTTB matrix, characterized in that, Includes the following steps: Step S1: Establish the basic forward and inverse mesh and the basic mesh kernel function matrix. S11. Set the range of the basic forward and inverse grid according to the size of the study area, and set the size of the basic forward and inverse grid cell according to the data point spacing or the minimum target size to establish the basic forward and inverse grid. S12. The BTTB matrix fast forward modeling algorithm is used to calculate and store the kernel function matrix at the basic grid scale as the basis for subsequent inversion calculations; Step S2: Initialize the coarse mesh model and transformation matrix S21. Set the initial rule coarse grid model , the coarse grid size is 3~5 times of the basic forward and inverse grid cell size in step S1, and the number of coarse grids is much smaller than the number of basic grid model parameters ; S22. Calculate the merging or subdivision matrix based on the spatial inclusion relationship between the coarse mesh and the basic mesh. This matrix defines the linear mapping relationship from the parameters of the coarse mesh model to the parameters of the basic mesh model. S23. Establish the transformation matrix from the coarse mesh model parameter space to the basic mesh model parameter space; Step S3: Perform coarse mesh inversion to obtain preliminary results. According to the basic forward and inverse grid of step S1, a model constraint matrix is established , a target function of gravity and magnetic inversion is established, an optimization algorithm is used for iterative inversion, and an update amount of the model under the coarse grid is obtained , the model is updated, and the coarse grid model result, i.e. the preliminary result with lower resolution, is obtained; Step S4: Adaptive mesh subdivision based on model gradient features and establishment of a new transformation matrix. S41. Using the coarse mesh model and model transformation matrix obtained from step S3, calculate the gradient value of the basic mesh, and use the transformation matrix to calculate the gradient spatial distribution characteristics of the coarse mesh model. S42. For regions where the gradient of the coarse mesh model changes drastically, they are identified as boundary regions of abnormal physical properties. The coarse mesh is then divided into smaller sub-mesh sizes, with the sub-mesh size being an integer multiple of the basic mesh size. For regions where the physical properties change gradually, the current mesh size is maintained. S43. According to the new grid division scheme, a new conversion matrix is recalculated to establish a new conversion matrix from the new grid model parameters to the basic grid model parameters ; Step S5: Perform fine-grid inversion to obtain high-resolution results. S51. Based on the coarse mesh model obtained in step S3, generate the inversion initial values ​​of the current subdivided mesh model through the transformation matrix; S52. Following the inversion calculation method in step S3, perform inversion calculations in the current finer mesh model parameter space to obtain a model with clearer physical property boundaries and higher resolution; Step S6: Convergence condition judgment and output of final result First, determine whether the preset termination condition is met. If the termination condition is not met, return to step S4 and continue to subdivide the physical property anomaly boundary region grid based on the model gradient value characteristics, establish a new transformation matrix, and perform a new round of fine inversion. If the termination condition is met, the final result, i.e., the high-resolution physical property model, is output. In step S12, the process of fast forward modeling of the BTTB matrix is ​​as follows: The gravity and magnetic forward modeling formula is expressed as: （1）； Wherein, the gravity and magnetic forward data is The vector is the observation value distributed on the regular grid nodes on the plane with the height The kernel matrix is ; The model parameter vector is ; The model parameter vector is also the basic grid model parameter; , , The number of grid in three directions respectively is , , Wherein, the number of grid in the direction , is consistent with the number of observation point grid. Using the BTTB matrix fast forward modeling algorithm, formula (1) can be expressed as: （2）； in, for Forward coefficient matrix; 3D formal model parameters express matrix; This is a convolution operation; In step S12, the convolution calculation result is obtained using Fast Fourier Transform, realizing fast forward modeling of large-scale data; the calculation process is as follows: （3）； in, For the first Layer forward modeling data; For the first Layer forward modeling coefficient matrix; for After expansion Layer property values; This is a two-dimensional fast Fourier transform; It is a two-dimensional inverse fast Fourier transform; Extract The former The element is obtained. The forward modeling results of all layers are summed to obtain the forward modeling results of all layers.

2. The gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix as described in claim 1, characterized in that, In step S23, the matrix transformation formula is used to transform the parameter space of the coarse mesh model to the parameter space of the basic mesh model: （4）； Among them, the basic mesh model parameters for vector ; for The transformation matrix; The parameter space of the coarse mesh model is The vector, ; The formula for the inverse transformation is obtained as follows: （5）； in, Represents the transpose of a matrix; Transformation matrix It can achieve subdivision from coarse mesh model to basic mesh model, and the matrix It can merge basic mesh models into coarse mesh models.

3. The gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix as described in claim 2, characterized in that, Taking a two-dimensional model as an example for calculation The process involves transforming the 9 model parameters in the regular mesh into 5 merged model parameters, with the following relationship: （6）； Based on the above relationship, we get: （7）。 4. The gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix as described in claim 3, characterized in that, Step S3: Use an optimization algorithm for iterative inversion, and solve the following equation to obtain the update amount of the model under the coarse mesh. ; The equation is: （8）； in, For the observed data vector, It is the first The result of the next iteration; For regularization parameters, It is a reference model.

5. The gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix as described in claim 4, characterized in that, Step S3 involves calculating the kernel matrix. and When multiplying with a vector, the BTTB matrix fast forward multiplication algorithm from step S1 is used for calculation; solving equation (8) yields... Update the model to obtain the coarse mesh model result, which is the preliminary result with lower resolution; （9）； Among them, step size It is obtained by the Armijo linear search method.

6. The gravity and magnetic inversion method based on grid merging and fast forward modeling of the BTTB matrix as described in claim 5, characterized in that, Step S6, the termination condition is one of the following: (1) The current grid size has reached the basic grid size; (2) The data fit difference is less than the preset threshold, and the fit difference changes very little between the two fine inversions; (3) The changes in model parameters during the two fine inversions are less than the preset threshold; (4) Achieve the maximum number of fine inversion iterations.

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