A magnetic anomaly inversion method, device, medium and product

Abstract

The present application discloses a magnetic anomaly inversion method, equipment, medium and product, and relates to the field of data processing. The method comprises: arranging nodes in a parameterized background grid to determine a mapping matrix; constructing an inversion model using a hybrid radial basis function; using the parameter value of the node as the inversion model parameter, and obtaining a background model based on the mapping matrix; performing focused inversion on the background model to obtain a focused inversion result; adaptively adding nodes based on the focused inversion result to obtain a new mapping matrix and background model, returning to perform focused inversion on the background model to obtain a focused inversion result, until no more nodes can be added, and a gridless inversion result is obtained; mapping the gridless inversion result back to the space of the inversion model to obtain a magnetic anomaly inversion result. The present application can avoid the complex grid generation and operation in the known methods, and solve the problem of discretization of unstructured nodes; at the same time, it can effectively utilize known information to improve the accuracy and stability of magnetic anomaly inversion.

Description

Technical Field

[0001] The present application relates to the field of data processing, and in particular to a magnetic anomaly inversion method, device, medium and product. Background Art

[0002] The meshless method (Mesh less Method or Mesh free Method) is a numerical method based on node approximation. It constructs interpolation function discrete control equations according to some arbitrarily distributed coordinate points to simulate physical fields of various complex shapes. It avoids cumbersome mesh division and can completely abandon mesh reconstruction when dealing with discontinuity and large deformation problems. It is easy to implement and has a wider range of applicability.

[0003] As a pure meshless method, the radial basis function method can overcome the dependence of known numerical methods on the mesh. It has the advantages of accuracy and stability for interpolation and fitting of scattered data. It has infinite smoothness plus the derivative of the function about a certain coordinate direction, which can be expressed as a weighted linear combination of the function values ​​at all discrete points along this direction. The parameter selection of the radial basis function is a difficulty that has always existed with the development of the radial basis.

[0004] The application of meshless methods, especially radial basis functions, in gravity and magnetic exploration and all geophysical methods is quite rare, but the corresponding finite element method has made great progress. The known finite element method is often difficult to obtain good results in dealing with many practical problems. For example, in the numerical solution of high-dimensional geophysical inversion, it is almost impossible to construct a discrete point model, which gives the meshless method an opportunity to develop. In addition, the known finite difference method discretizes the underground space into regular grid units, and the size ratio of the grid units will have a greater impact on accuracy and efficiency, and the two cannot be achieved at the same time.

[0005] Gridless gravity forward modeling has been developed to a certain extent, but the gridless method is still in a nearly blank situation in magnetic methods. Summary of the invention

[0006] The purpose of this application is to provide a magnetic anomaly inversion method, equipment, medium and product, which can avoid the complex grid generation and operation in the known methods, solve the problem of unstructured node discretization, and at the same time, improve the accuracy and stability of magnetic anomaly inversion.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides a magnetic anomaly inversion method, comprising:

[0009] Setting a background grid and performing parameterization processing on the background grid;

[0010] Arranging nodes in the parameterized background grid, and determining a mapping matrix based on the nodes;

[0011] The inversion model is constructed using hybrid radial basis function;

[0012] Using the parameter values ​​of the nodes as parameters of the inversion model, and obtaining a background model based on the mapping matrix;

[0013] Performing focusing inversion on the background model to obtain a focusing inversion result;

[0014] Adaptively adding nodes to the parameterized background grid based on the focused inversion result, determining a new mapping matrix based on the adaptively added nodes, and obtaining a new background model based on the new mapping matrix, returning to the step of performing focused inversion on the background model to obtain a focused inversion result, until the condition for adaptively adding nodes is not met, and obtaining a gridless inversion result;

[0015] The gridless inversion result is mapped back to the space of the inversion model to obtain a magnetic anomaly inversion result.

[0016] Optionally, taking the parameter values ​​of the nodes as parameters of the inversion model and obtaining a background model based on the mapping matrix comprises:

[0017] Using the parameter values ​​of the nodes as parameters of the inversion model, and obtaining an initial background model based on the mapping matrix;

[0018] The maximum number of iterations is set, and constraints are imposed on the minimum and maximum values ​​of the parameters of the initial background model to obtain the background model.

[0019] Optionally, the inversion model is expressed as:

[0020]

[0021] In the formula, φ is the objective function, λ is the regularization factor, and m s is a vector in the subspace, (m s ) ref is the reference model, W s is the modal weighting matrix, W d is the data weighting matrix, L is the mapping matrix, d is the weighted distance of the hybrid radial basis function, and G is the sensitivity matrix.

[0022] Optionally, adaptively adding nodes to the parameterized background grid based on the focusing inversion result comprises:

[0023] A node whose inversion value in the focused inversion result is greater than a set threshold is determined in the parameterized background grid, and a plurality of new nodes are added within a set range centered on the node.

[0024] Optionally, add 4 new nodes within a set range centered on this node.

[0025] Optionally, the hybrid radial basis function used is a hybrid basis function after adjusting the distance weight.

[0026] Optionally, the hybrid basis function is obtained based on a combination of a radial basis function and a cubic kernel function.

[0027] In a second aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any one of the magnetic anomaly inversion methods described above.

[0028] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any one of the magnetic anomaly inversion methods described above.

[0029] In a fourth aspect, the present application provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of any one of the magnetic anomaly inversion methods described above.

[0030] According to the specific embodiments provided in this application, this application has the following technical effects:

[0031] The present application provides a magnetic anomaly inversion method, device, medium and product. By adopting a gridless discretization strategy of arranging nodes in a parameterized background grid to determine a mapping matrix, the complex grid generation and operation in the known method can be avoided, and the problem of unstructured node discretization can be solved. By adopting a hybrid radial basis function to construct an inversion model, on this basis, based on the mapping matrix, a background model is obtained to perform focused inversion, which can improve the accuracy and stability of magnetic anomaly inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 A schematic diagram of a flow chart of a magnetic anomaly inversion method provided in one embodiment of the present application;

[0034] Figure 2 A hybridization basis function array diagram provided in one embodiment of the present application;

[0035] Figure 3 A relationship diagram between the root mean square error and the shape parameter provided in an embodiment of the present application;

[0036] Figure 4 A relationship diagram between the condition number and the shape parameter provided in an embodiment of the present application;

[0037] Figure 5 A relationship diagram between the condition number and the degree of freedom provided in an embodiment of the present application;

[0038] Figure 6 A relationship diagram between the root mean square error and the degree of freedom provided in an embodiment of the present application;

[0039] Figure 7 A diagram showing the influence of various parameters on the RBF shape provided in an embodiment of the present application;

[0040] Figure 8 A schematic diagram of adding an adaptive node provided in an embodiment of the present application;

[0041] Fig. 9 A schematic diagram of a model provided for an embodiment of the present application;

[0042] Fig.10 A diagram of the forward modeling results provided by an embodiment of the present application;

[0043] Fig.11 A diagram showing the first focusing inversion result provided in an embodiment of the present application;

[0044] Fig.12 A post-inversion node addition diagram provided in an embodiment of the present application;

[0045] Fig.13 A meshless method inversion result diagram provided in an embodiment of the present application;

[0046] Fig.14 A focusing inversion result diagram of a known method provided in an embodiment of the present application;

[0047] Fig.15 A RBF node distribution diagram of a gridless inversion result provided in an embodiment of the present application;

[0048] Fig.16 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0050] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0051] In an exemplary embodiment, the present application provides a magnetic anomaly inversion method, which adopts a meshless method of hybrid radial basis function, uses a meshless discretization strategy to establish a mapping of subspace grid cells to discrete point clouds, adaptively refines nodes during the inversion process, and then inverts the background field obtained after the adaptation, thereby improving the accuracy and stability of the inversion. Based on this, Figure 1 As shown, the magnetic anomaly inversion method includes:

[0052] Step 100: Set a background grid and perform parameterization on the background grid.

[0053] Step 101: Arrange nodes in the parameterized background grid, and determine a mapping matrix based on the nodes.

[0054] Step 102: construct an inversion model using a hybrid radial basis function. For example, a suitable evaluation method is used to select suitable parameters of the hybrid radial basis function, where the selected parameters of the hybrid radial basis function are the weights of each component and the smoothness of the radial basis function components, and an inversion objective function is constructed to obtain an inversion model.

[0055] The inversion model is expressed as:

[0056]

[0057] In the formula, φ is the objective function, λ is the regularization factor, and m s is a vector in the subspace, (m s ) ref is the reference model, W s is the modal weighting matrix, W d is the data weighting matrix, L is the mapping matrix, d is the weighted distance of the hybrid radial basis function, and G is the sensitivity matrix.

[0058] Step 103: Using the parameter values ​​of the nodes as parameters of the inversion model, and obtaining a background model based on the mapping matrix.

[0059] Step 104: Perform focus inversion on the background model to obtain a focus inversion result.

[0060] Step 105: Adaptively add nodes to the parameterized background grid based on the focused inversion result, determine a new mapping matrix based on the adaptively added nodes, and obtain a new background model based on the new mapping matrix, then return to execute step 104 until the condition for adaptively adding nodes is not met, and obtain a gridless inversion result.

[0061] Step 106: Map the gridless inversion result back to the space of the inversion model to obtain the magnetic anomaly inversion result. The obtained magnetic anomaly inversion result is the predicted magnetization intensity model parameter. In the actual application process, a subspace is established in the inversion model, the initial nodes are arranged in the subspace, and the obtained subspace parameters are returned to the inversion model space by calculating the mapping matrix.

[0062] Based on the above description, the purpose of using hybrid radial basis function is to control the node spacing and correlation coefficient of the basis function to achieve high-precision modeling. In addition, the model space is subdivided from sparse nodes into refined nodes to make the inversion process more stable. First, the overall trend of the density model is inverted on a large scale using sparse node parameters, and the obtained node parameter distribution is adaptively added as the inversion parameter of the next scale inversion, and then the final inversion is performed, which can effectively improve the efficiency and accuracy of the inversion.

[0063] In another exemplary embodiment of the present application, in order to further improve the accuracy and stability of the inversion, in this embodiment, the implementation process of the above step 103 may include:

[0064] (1) The parameter values ​​of the nodes are used as the parameters of the inversion model, and based on the mapping matrix, the initial background model is obtained.

[0065] (2) Setting the maximum number of iterations, imposing constraints on the minimum and maximum values ​​of the parameters of the initial background model, and obtaining the background model.

[0066] In another exemplary embodiment of the present application, the gridless method is a node-based method, and the adaptive optimization strategy for the nodes is crucial to the calculation. The role of node adaptive optimization is to determine the area with large errors in the problem domain based on the known data model, and then adjust the nodes to achieve the purpose of improving the accuracy of the calculation results. The nodes are initially evenly and sparsely distributed, and the gridless node parameters obtained by inversion are locally encrypted according to the node parameter values, and finally inverted according to the new node distribution. The encryption of nodes draws on the ideas of quadtrees and octrees. Based on this, the process of adaptively adding nodes in the parameterized background grid based on the focused inversion results in step 105 can be described as:

[0067] In the parameterized background grid, a node whose inversion value in the focused inversion result is greater than a set threshold is determined, and multiple (e.g., 4) new nodes are added within a set range centered on the node. That is, the adaptive node adding strategy assumes that the inversion value of a node is greater than a certain threshold, and multiple new nodes are added around the node.

[0068] In actual application, the strategy of adding adaptive nodes is as follows: Figure 8 As shown, the first level decomposition divides the area into four sub-blocks and arranges nodes R1, R2, R3 and R4 in the centers of the four sub-blocks. If R1 is greater than the threshold standard, the area R1 is further decomposed into four sub-blocks and nodes R11, R12, R13 and R14 are added in the centers of the sub-blocks. Then all nodes are inverted again until a satisfactory result is achieved.

[0069] In addition, there is no limit to the number of nodes added. Too many nodes added may make the solution unstable and increase the error. In two-dimensional inversion, usually a high-precision result can be obtained by adding a node once.

[0070] In another exemplary embodiment of the present application, the hybrid radial basis function used may be a hybrid basis function after adjusting the distance weight. The hybrid basis function may be obtained based on a combination of a radial basis function and a cubic kernel function, and the specific form of its application is:

[0071]

[0072] Where φ(r) is the hybrid basis function value, r I is the distance norm between the calculated point and the node. α determines the proportion of the radial basis function in the hybrid basis function and the extreme value of the center. β determines the proportion of the cubic kernel function in the hybrid basis function. ε is the shape parameter of the radial basis function. The larger its value, the sharper the radial basis function. Figure 2 shown.

[0073] For the hybrid radial basis function, there are problems such as too many parameters and not knowing how to choose. The common method for parameter selection is the leave-one-out cross validation (LOOCV) method in statistics. In this method, the optimal value of the shape parameter is generally selected by minimizing the loss function. This application uses a simplified loss function construction method based on the very regular spatial division of geophysical inversion problems, that is, most of the known information points are used for construction points, and the remaining parts are used as verification points. The general loss function takes the root mean square error, and the root mean square error E 2 The expression is:

[0074]

[0075] In the formula, is the interpolation function s at the verification point x i The interpolation result is Verify point x i The true value at , N is the number of verification points.

[0076] The stability of the hybrid radial basis function is related to the position of the nodes. Factors that need to be considered include the degree of freedom and the condition number of the coefficient matrix. The condition number of the coefficient matrix A represents the sensitivity of the solution of a linear equation system to data errors, and its expression is:

[0077]

[0078] The smaller the condition number is, that is, closer to 1, the closer the problem is to being well-conditioned. To illustrate how to select shape parameters, this application considers the following linear function f(x, y) for numerical experiments:

[0079] f(x,y)=xy(1-x)(1-y),(x,y)∈[0,1]×[0,1] (5)

[0080] In the formula, x and y represent the two variables in the linear function.

[0081] Based on the above description, the experimental results are:

[0082] 1. The relationship between shape parameters and root mean square error is as follows Figure 3 As shown. Figure 3 It can be seen that for the optimal selection of shape parameters, there is no difference between the IMQ kernel function and the hybrid basis kernel function. When corresponding to the problem, the nodes and shape parameters can be selected first. Moreover, the hybrid basis function used in this application will be significantly lower than the known method in terms of overall error.

[0083] 2. The relationship between shape parameters and condition numbers is as follows Figure 4 As shown. Figure 4 As can be seen from the figure, as long as the shape parameter does not approach zero too closely, thus causing the radial basis kernel function to be too flat, the coefficient matrix is ​​a good solution to the interpolation problem, and the value can be selected so that both the root mean square error and the singularity of the equation are small.

[0084] 3. The relationship between degrees of freedom and condition number is as follows Figure 5 As shown. Figure 5 It can be seen that when the degree of freedom is small, the condition number in the known method increases significantly with the increase of the degree of freedom, and then tends to be stable. The hybrid basis function obviously performs better than the known method in terms of the influence of the degree of freedom. At the same time, it shows that the more nodes, the better. Too many nodes will make the solution unstable.

[0085] 4. The relationship between degrees of freedom and root mean square error is as follows Figure 6 As shown. Figure 6 It can be seen that when the degrees of freedom are small, the three methods can reduce their RMS error as the degrees of freedom increase. This also shows that too many nodes cannot reduce the interpolation error but will increase the error, but the range of error reduction is wider in comparison.

[0086] Furthermore, in actual underground geological bodies, especially in the field of metal minerals, ore bodies often have obvious structural characteristics. In order to solve this problem, a distance weighted method can be used. The known isotropic radial basis function is difficult to express the continuity of the spatial distribution of anomalies. In order to capture the important geometric details of the ore body, a local anisotropic radial basis function, also known as a modified radial basis function, is used. The known radial basis function uses Euclidean distance as the unit of measurement in space, so the calculated values ​​of each neighborhood point and the center point of the radial basis function are isotropic. In order to obtain anisotropic radial basis functions, the weight of the distance needs to be adjusted. Reweighted distance The specific form is:

[0087]

[0088]

[0089] In the formula, δ is the scaling parameter, R is the stretching matrix, θ is the rotation parameter, ρ is the stretching parameter, and G′ is the rotation matrix. The scaling parameter δ is used to change the flatness of the basis function, the stretching matrix ρ is used to match the estimated approximate shape of the ore body, and the rotation matrix θ is used to estimate the approximate inclination of the ore body. The influence of each parameter on the RBF shape is as follows: Figure 7 As shown. Among them, Figure 7 Part (a) is a schematic diagram of the RBF shape. Figure 7 Part (b) is a schematic diagram of the rotated RBF shape. Figure 7 Part (c) is a schematic diagram of the stretched RBF shape.

[0090] In another exemplary embodiment of the present application, an example is taken to establish an underground area with a length of 1000 meters and a depth of 500 meters, in which a unit grid is 25 meters long, and to establish a hypothetical geological ore body, to illustrate the implementation process of the magnetic anomaly inversion method provided by the present application. In this embodiment, the geological ore body model is a square with a side length of 125 meters, a top burial depth of 225 meters, a magnetization intensity of 50A / m, a geomagnetic inclination of 35°, and a geomagnetic declination of 90°, specifically represented as follows: Fig. 9 shown.

[0091] The forward modeling formula for magnetic anomaly at each point in the calculation area is:

[0092]

[0093] Where △T is the magnetic anomaly, H ax and Z a is the component of magnetic anomaly, is a constant, μ0=4π×10 -7 H / m, G is the gravitational constant, σ is the density difference, M x and M z is the component of the total magnetization vector M, V xz and V zz is the second-order partial derivative of the gravitational potential, I0 and D0 are the inclination and declination of the normal geomagnetic field direction.

[0094] According to formula (9), the forward value of the model can be calculated as follows: Fig.10 As shown. Fig.10 It can be seen that the forward modeling results are consistent with the basic distribution law. At the same time, due to the large burial depth of the ore body and insufficient lateral extension, the difficulty of inversion is increased.

[0095] This application uses gridless discrete focusing inversion. The focusing matrix depends on the model (i.e., the density distribution function M), and the approximate L0 norm stabilizer is selected to obtain a sparse solution, which is expressed as:

[0096]

[0097] In the formula, is the model depth weighting function, is the kth element in the model parameters, ε is a very small constant to avoid division by 0, and σ ensures that the objective function is close to zero norm. The parameter of σ is expressed as:

[0098] σ (i+1) =ρσ (i) (11)

[0099] The traditional target inversion function is:

[0100]

[0101] In the formula, φ is the objective function, λ is the regularization factor, G is the sensitivity matrix, m is the model parameter vector, and m ref is the reference model, W m and W d are the modal matrix and data weighting matrix respectively.

[0102] In general, the spatial density distribution can be projected into a related interpolation subspace, which can use the parameters in the subspace to reflect some properties that are difficult to directly represent in the spatial domain. Many types of basis functions can be used mathematically for subspace representation, and RBF is used to construct the subspace because its shape is easier to adjust. Any density distribution m in the original high-dimensional underground space can be uniquely represented by a specific set of RBF (radial basis functions), as shown below:

[0103] m=Lm s (13)

[0104] In the formula, m s represents a vector in the subspace, whose elements are defined discretely at the nodes. L is a matrix composed of RBFs (i.e., a mapping matrix), which is controlled by the form of the RBFs and the positions of the nodes. Therefore, before inversion, the initial nodes must be arranged and the mapping matrix L is calculated. L has a certain effect on the vector m. s The role of involves resampling the model to the corresponding grid.

[0105] Based on the above description, the objective function of the gridless inversion adopted in this embodiment is the inversion model represented by the above formula (1).

[0106] Comparing the gridless inversion objective function [i.e., formula (1)] with the traditional inversion objective function [i.e., formula (12)], the difference is that the inversion model parameters are changed to nodes. The difference is that the depth weighting object is changed from the underground grid to the node, and the focusing matrix also acts on the node. Therefore, the gridless magnetic anomaly inversion algorithm uses the framework of the focusing inversion algorithm to change the depth weighting matrix and the focusing matrix.

[0107] After calculating the mapping matrix L, the inversion result (i.e., the magnetization intensity of the underground metal body) obtained by the first focused inversion is as follows: Fig.11 As shown. Then, based on the results of focused inversion, adaptive node addition is performed, and the mapping matrix L is calculated again according to the results obtained after the node addition to obtain a new background model, and then focused inversion is performed again. Then, based on the result, it is determined whether the conditions for adaptive node addition are met. If not, the result can be mapped back to the model space as a gridless inversion result, and finally the predicted model parameters are obtained.

[0108] The results of the adaptive node addition after the first focused inversion are as follows Fig.12 .from Fig.12 It can be seen that due to the larger anomaly in the shallow part, more nodes are added during adaptive node addition, resulting in the result in the shallow part being more accurate than the deep part. This is because the present application uses the condition of judging whether the inversion value of a certain node is greater than a certain threshold.

[0109] The inversion results obtained by meshless inversion are as follows Fig.13 As shown in Figure 2, the inversion results obtained using traditional focusing inversion are as follows: Fig.14 As shown. By comparing and analyzing the results of traditional focused inversion with those of gridless inversion, it can be found that the results obtained by focused inversion can indicate the spatial position of the model, and the distribution of physical properties is also relatively concentrated, but compared with the results of gridless inversion, the location of the block indicated by gridless inversion is more accurate. The size of the block in the result of gridless inversion is basically consistent with the actual model, and the physical properties are concentrated at the geometric center of the ore body and then decrease toward the surrounding areas, indicating that the gridless inversion results have higher horizontal and vertical resolutions. However, compared with the real model, a ring with a small density value will be formed in the outer layer where the model is located. The main reason for this phenomenon is that the radial basis function is a function that has the largest value at the center and decreases in the direction away from the center.

[0110] To explain the principle of meshless inversion, Fig.15 As shown in Figure 1, the central node distribution of the meshless inversion is given. Fig.15 It can be seen that the adaptive nodes of the inversion results are concentrated inside the model, indicating that the adaptive strategy of meshless inversion is effective. Fig.15 It can also be seen that the distribution of nodes is basically around the center of the model, which corresponds to the distribution of the gridless inversion results around the center of the model.

[0111] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Fig.16 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store magnetic anomaly inversion data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a magnetic anomaly inversion method is implemented.

[0112] Those skilled in the art will understand that Fig.16The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components. In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0113] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0114] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0115] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0116] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0117] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0118] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0119] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A magnetic anomaly inversion method, characterized in that: The magnetic anomaly inversion method comprises: Setting a background grid and performing parameterization processing on the background grid; Arranging nodes in the parameterized background grid, and determining a mapping matrix based on the nodes; The inversion model is constructed using hybrid radial basis function; Using the parameter values ​​of the nodes as parameters of the inversion model, and obtaining a background model based on the mapping matrix; Performing focusing inversion on the background model to obtain a focusing inversion result; Adaptively adding nodes to the parameterized background grid based on the focused inversion result, determining a new mapping matrix based on the adaptively added nodes, and obtaining a new background model based on the new mapping matrix, returning to the step of performing focused inversion on the background model to obtain a focused inversion result, until the condition for adaptively adding nodes is not met, and obtaining a gridless inversion result; The gridless inversion result is mapped back to the space of the inversion model to obtain a magnetic anomaly inversion result.

2. The magnetic anomaly inversion method according to claim 1, characterized in that: The parameter values ​​of the nodes are used as the parameters of the inversion model, and a background model is obtained based on the mapping matrix, including: Using the parameter values ​​of the nodes as parameters of the inversion model, and obtaining an initial background model based on the mapping matrix; The maximum number of iterations is set, and constraints are imposed on the minimum and maximum values ​​of the parameters of the initial background model to obtain the background model.

3. The magnetic anomaly inversion method according to claim 1, characterized in that: The inversion model is expressed as: In the formula, φ is the objective function, λ is the regularization factor, and m s is a vector in the subspace, (m s ) ref is the reference model, W s is the modal weighting matrix, W d is the data weighting matrix, L is the mapping matrix, d is the weighted distance of the hybrid radial basis function, and G is the sensitivity matrix.

4. The magnetic anomaly inversion method according to claim 1, characterized in that: Adaptively adding nodes to the parameterized background grid based on the focused inversion result, including: A node whose inversion value in the focused inversion result is greater than a set threshold is determined in the parameterized background grid, and a plurality of new nodes are added within a set range centered on the node.

5. The magnetic anomaly inversion method according to claim 4, characterized in that: Adds 4 new nodes within the set range centered on this node.

6. The magnetic anomaly inversion method according to claim 1, characterized in that: The hybrid radial basis function used is the hybrid basis function after adjusting the distance weight.

7. The magnetic anomaly inversion method according to claim 6, characterized in that: The hybrid basis function is obtained based on a combination of a radial basis function and a cubic kernel function.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the magnetic anomaly inversion method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the magnetic anomaly inversion method described in any one of claims 1 to 7 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the magnetic anomaly inversion method described in any one of claims 1 to 7 is implemented.

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