A method for inverting hybrid hexahedral magnetic data based on random weighting

Abstract

This invention discloses a method for inverting geophysical magnetic data based on random weighting, belonging to the field of magnetic signal processing. The method includes: spatially partitioning the subsurface inversion area using a hybrid hexahedral mesh combining structured and unstructured elements, discretizing the subsurface space into N hexahedral units; generating projected geometries with different size parameters and spatial locations through random assignment, embedding them into the partitioned mesh model, repeating this process N times to construct N independent N×1 dimensional model column vectors, which are then randomly sequentially concatenated to obtain an N×N dimensional random weighting matrix; constructing an inversion objective function based on the random weighting matrix, and solving for the weighted domain magnetization intensity; combining the random weighting matrix and the solution results to obtain the spatial distribution of three-dimensional magnetization intensity, thus constructing the inversion image. This invention enables rapid and precise inversion of geophysical magnetic data under undulating terrain, improving the accuracy and reliability of magnetic data inversion under complex terrain conditions.

Description

Technical Field

[0001] This invention relates to the field of magnetic signal processing technology, and in particular to a method for inverting hybrid hexahedral magnetic data based on random weighting. Background Technology

[0002] Magnetic surveying, as an important method in geophysical exploration, is widely used in mineral exploration, geological mapping, and structural research due to its advantages of wide coverage, high efficiency, and low cost. Magnetic inversion aims to reconstruct the magnetization intensity or magnetic susceptibility distribution of subsurface media using surface magnetic anomalies, thereby inferring subsurface geological structures and lithological characteristics. However, due to the inherent non-uniqueness and ill-conditioned nature of the magnetic field inversion problem, ensuring the physical rationality and stability of the results while improving imaging resolution has always been a core challenge in magnetic data inversion research.

[0003] Traditional 3D magnetic inversion methods mostly employ regular hexahedral meshes for modeling. However, actual terrain is often complex and undulating, and the rigid node arrangement of structured meshes makes it difficult to accurately fit the surface morphology, thus affecting the accuracy of near-surface property recovery. Furthermore, to alleviate the "skin effect" caused by the depth decay of the kernel function in magnetic inversion, various depth-weighted or model regularization strategies have been proposed. However, traditional methods often produce a "tailing effect" in the deeper parts of the inversion results, making it difficult to accurately characterize deep objects. Therefore, achieving high-precision magnetic data inversion while efficiently fitting the terrain is the current development direction. Summary of the Invention

[0004] This invention proposes a magnetic data processing method with good modeling accuracy and inversion stability under complex terrain conditions, aiming to solve the technical problems of low inversion accuracy, insufficient deep anomaly identification capability, and complex model parameter settings in existing technologies under complex terrain conditions.

[0005] According to one aspect of the present invention, a method for inverting hybrid hexahedral magnetic data based on random weighting is provided, characterized by comprising: spatially partitioning the underground inversion area using a hybrid hexahedral mesh combining structured and unstructured elements, discretizing the underground space into N hexahedral mesh elements; generating projection geometries with different size parameters and spatial positions through random assignment, and embedding the projection geometries into the partitioned mesh model, repeating this process N times to construct N independent N×1 dimensional model column vectors; concatenating the obtained N model column vectors in a random order to obtain an N×N dimensional random weighting matrix; constructing an objective function for inversion based on the random weighting matrix, solving the objective function to obtain the weighted domain magnetization intensity; and combining the random weighting matrix and the obtained weighted domain magnetization intensity to obtain the spatial distribution of three-dimensional magnetization intensity, thereby constructing the inversion image.

[0006] Optionally, the step of spatially subdividing the underground inversion area using a hybrid hexahedral mesh combining structured and unstructured elements, and discretizing the underground space into N hexahedral mesh units, includes: acquiring topographic elevation data of the area to be inverted; selecting a horizontal plane at a certain depth below the lowest point of the topographic relief as the interface between the structured and unstructured meshes; defining the area above the interface as the shallow area, and subdividing it using an unstructured hexahedral mesh, wherein the x and y directions are divided with equal spacing, the z direction is divided with an equal number of layers, and the thickness of each layer in the z direction is kept consistent at each (x, y) position; defining the area below the interface as the deep area, and subdividing it using a structured hexahedral mesh, with equal spacing in the x, y, and z directions.

[0007] Optionally, generating projection geometries with different size parameters and spatial positions through random assignment, and embedding the projection geometries into the partitioned mesh model, repeating this process N times to construct N independent N×1 dimensional model column vectors includes: initially, assigning the physical property values ​​of all mesh cells in the mesh model to 0; determining the size parameters and spatial positions of the projection geometries through random assignment, and determining the range of mesh cells covered by the generated projection geometries in the mesh model based on the size parameters and spatial positions of the generated projection geometries; assigning non-zero physical property values ​​to the mesh cells covered by the projection geometries, and keeping the uncovered mesh cells as 0; generating a corresponding three-dimensional sparse array based on the physical property value of each mesh cell; flattening the obtained three-dimensional sparse array into an N×1 dimensional model column vector according to a predetermined order; repeating the above process N times to obtain N independent N×1 dimensional model column vectors. ,in, Indicates the first The model column vector is generated randomly once. .

[0008] Optionally, the obtained N model column vectors are concatenated in a random order to obtain an N×N dimensional random weighted matrix, which includes generating a random permutation sequence from 1 to N using a random algorithm. , The random permutation sequence is used to determine the concatenation order of the N model column vectors; based on the generated permutation sequence, the first... The nth model column vector is used as the first column, and the nth... The first model column vector is used as the second column, and so on, until the second model column vector is used as the third column. Using the model column vectors as the Nth column, we obtain an N×N dimensional random weighted matrix. , In the formula, This represents the model column vector in the first column. This represents the model column vector in the second column. This represents the model column vector of the Nth column.

[0009] Optionally, constructing an objective function for inversion based on the random weighting matrix, and solving the objective function to obtain the weighted domain magnetization includes:

[0010] Based on the general form of the inversion objective function:

[0011] ;

[0012] Take the weighted matrix of the data The identity matrix, and the model weighting matrix within it. The random weighting matrix The reverse, that is , The objective function for inversion is constructed as follows:

[0013] ;

[0014] ;

[0015] In the formula, The objective function is... This is the original sensitivity matrix; These are the original domain magnetization parameters; For observational data; For regularization parameters; Represents the identity matrix; This is the weighted domain sensitivity matrix; These are the magnetization parameters for the weighted domain;

[0016] The weighted domain magnetization parameter corresponding to the minimum objective function can be obtained by using the fast conjugate gradient method or the least squares QR decomposition method. .

[0017] Optionally, by combining the random weighting matrix and the obtained weighted domain magnetization, the spatial distribution of the three-dimensional magnetization is obtained, and the construction of the inversion image is achieved by:

[0018] According to the random weighting matrix And the weighted domain magnetization parameter corresponding to the minimum of the objective function. The magnetization inversion result is calculated using the following formula. :

[0019] ;

[0020] Based on the obtained magnetization inversion results, the magnetization intensity is allocated to each grid cell to obtain the magnetization intensity of each grid cell in the underground space;

[0021] The distribution of underground magnetic bodies is characterized by color mapping based on the magnetization intensity of each grid cell, and a corresponding image is generated, thereby realizing the construction of the inversion image.

[0022] The random weighted hybrid hexahedral magnetic data inversion method in this invention adopts a hierarchical partitioning strategy to model underground space. In the near-surface region, unstructured hexahedral meshes are introduced to accurately fit undulating terrain, while structured hexahedral meshes are used in the deep region to maintain the sparsity of the forward modeling matrix and improve computational efficiency, thereby achieving a balance between large-scale terrain modeling and inversion calculation.

[0023] In the inversion process, this invention replaces the traditional depth weighting function with a random weighting matrix of the same dimension to reconstruct the spatial distribution structure of the sensitivity kernel function. This random weighting matrix is ​​composed of multiple high-dimensional sparse perturbation model column vectors, which have good directional perturbation characteristics and spatial non-overlap. This design not only effectively alleviates the problems of rapid weight decay and strong parameter dependence in the deep region of the traditional depth weighting method, but also simplifies the requirements for setting empirical parameters in the inversion process, and improves the identification ability of deep anomalies and the geological rationality of the model results.

[0024] The method of this invention provides an effective technical means for magnetic data inversion under complex terrain, which can realize rapid and accurate inversion of geophysical magnetic data under undulating terrain conditions, and improve the accuracy and reliability of magnetic inversion of magnetic data under complex terrain conditions. Attached Figure Description

[0025] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0026] Figure 1 This is a flowchart of a method for inverting hybrid hexahedral magnetic data based on random weighting, according to an embodiment of the present invention.

[0027] Figure 2 A schematic diagram of the hybrid hexahedral mesh partitioning of underground space;

[0028] Figure 3 Distribution plots of kernel functions with different weighting methods; Figure 3 (a) is the unweighted kernel function distribution plot; Figure 3 (b) shows the kernel function distribution using the traditional weighting method; Figure 3 (c) is the distribution diagram of the kernel function with random weighting;

[0029] Figure 4 To demonstrate the effect of inverting two prism magnetic data instances; Figure 4 (a) is a prism model; Figure 4 (b) Magnetic data generated for the prism model; Figure 4 (c) shows the inversion results calculated using the traditional weighted method; Figure 4 (d) is the inversion result calculated using the random weighting method of the present invention. Detailed Implementation

[0030] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application 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 application, and not all of them. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present application can be combined with each other.

[0031] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0032] The terms “comprising” and “having”, and any variations thereof, in the specification and claims of this application are intended to cover non-exclusive inclusion, for example, a process, method, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or apparatus.

[0033] Example 1: Refer to Figure 1 , Figure 1 This is a flowchart of a method for inverting hybrid hexahedral magnetic data based on random weighting, according to an embodiment of the present invention. Figure 1 As shown, the method includes the following steps:

[0034] S1 uses a hybrid hexahedral mesh combining structured and unstructured elements to spatially partition the underground inversion region, discretizing the underground space into N hexahedral units;

[0035] Among them, a structured hexahedron refers to a regular hexahedron, where the lengths and angles of each side follow fixed geometric relationships, presenting a neat and orderly arrangement in three-dimensional space. An unstructured hexahedron refers to an irregularly shaped hexahedron, where the side lengths and angles are not subject to fixed constraints and can be flexibly adjusted according to actual needs.

[0036] To facilitate the study of physical properties (such as resistivity and magnetic permeability) at different underground locations, it is necessary to mesh the underground region, dividing the three-dimensional underground space into numerous small cubic mesh units, each representing a small portion of the underground area. This invention combines the characteristics of structured and unstructured hexahedrons. In near-surface topographical undulations, unstructured hexahedrons are used for spatial partitioning to accurately describe the complex geological conditions of the area. In deeper underground regions where the geological structure is relatively stable and less variable, structured hexahedron meshing is used, which can improve computational efficiency while maintaining a certain level of accuracy. This hybrid meshing method fully leverages the advantages of both types of meshes, achieving more efficient and accurate modeling of underground space.

[0037] Specifically, S1 includes:

[0038] S11, Obtain the topographic elevation data of the area to be inverted;

[0039] Topographic elevation data can be obtained through field measurements, extraction from satellite remote sensing data, or existing geological exploration data. This data should have high resolution to accurately reflect the undulations and changes in the terrain.

[0040] S12, select the horizontal plane at a certain depth below the lowest point of the terrain undulation as the interface between the structured grid and the unstructured grid;

[0041] This interface can be flexibly set according to geological characteristics or modeling needs (such as the target depth of geological exploration, the complexity of underground geological structures, and the efficiency of subsequent inversion calculations). Generally speaking, for areas with relatively simple geological structures and shallow exploration targets, a smaller depth below the lowest point of topographic relief can be selected as the interface; while for areas with complex geological structures and deeper exploration targets, the depth of this interface can be appropriately increased.

[0042] S12 defines the area above the interface as the shallow region and uses an unstructured hexahedral mesh for subdivision. The x and y directions (x and y are directions on the horizontal plane, which can be set according to the actual situation. Generally, the x direction is due north and the y direction is due east) are divided at equal intervals. This division method can ensure the uniformity of the mesh distribution on the horizontal plane. The z direction (i.e., the direction perpendicular to the horizontal plane downward) is divided with an equal number of layers, and the thickness of each layer in the z direction is kept consistent at each (x, y) position.

[0043] S13 defines the region below the interface as the deep region and uses a structured hexahedral mesh for subdivision. The x, y, and z directions are all divided at equal intervals. This uniform subdivision method simplifies the calculation process and can better reflect the relatively uniform geological characteristics of the deep region.

[0044] Reference Figure 2 , Figure 2 This is a schematic diagram of the hybrid hexahedral mesh generation in an embodiment of the present invention. The blue line represents the interface, with the area above the blue line being the shallow region and the area below being the deep region. Figure 2 As shown, the shallow region (topographic relief area) is divided into several unstructured hexahedral grids that conform to the topographic relief, so as to flexibly fit the actual terrain, adapt to complex terrain and geological structures, and improve the accuracy of inversion; the deep region is divided into several structured hexahedral grids of equal size with the same length, height and width dimensions, in order to simplify calculations and improve computational efficiency.

[0045] S2, generate projection geometry with different size parameters and spatial positions by random assignment, and embed the projection geometry into the mesh model after partitioning, repeat N times to construct N independent N×1 dimensional model column vectors;

[0046] According to the S1 underground space grid partitioning strategy, the area to be inverted (i.e., the underground space) is discretized into X*Y*Z units, where X, Y, and Z represent the number of units in the x, y, and z coordinate directions, respectively, and X*Y*Z=N. Projected geometries are randomly implanted into the discretized area. These geometries can be various shapes such as prisms and inclined bodies, with their size parameters and spatial positions determined by random assignment. The resulting geometry is called a "projected geometry" (essentially, a geometry is generated within the partitioned underground space, but its position, size, and shape are random). This randomness means that the position and size of the projected geometry in space are uncertain each time, increasing the diversity and complexity of the model. For example, when simulating the distribution of underground ore bodies, the shape and location of the ore bodies are often unknown; randomly projecting geometries of different shapes can better simulate this uncertainty.

[0047] Specifically, S2 includes:

[0048] S21, In the initial state, the physical property values ​​of all grid elements in the mesh model are set to 0;

[0049] Each discrete unit is assigned a property value of 0, which is equivalent to a three-dimensional array of all zeros (X*Y*Z).

[0050] S22, using random assignment, determines the size parameters and spatial position of the projected geometry, and based on the size parameters and spatial position of the generated projected geometry, determines the range of mesh cells covered by the geometry in the mesh model;

[0051] S23 assigns non-zero physical property values ​​to the mesh cells covered by the projected geometry, while keeping the uncovered mesh cells at 0;

[0052] The specific value of this non-zero physical property can be set according to the actual situation. For example, if the projection is a prism representing a ore body, then the cells inside the prism can be given a higher resistivity value to simulate the existence of the ore body.

[0053] S24, Generate a corresponding three-dimensional sparse array based on the physical property value of each grid cell;

[0054] After projecting the geometry onto the initial mesh model, non-zero property values ​​are assigned to the elements of the projected geometry. Based on the property values ​​of each mesh element in the network model, a three-dimensional sparse array of X*Y*Z can be generated. A sparse array is an array in which most elements are 0 or have the same value, and only a few elements are non-zero or have different values.

[0055] S25, flatten the obtained three-dimensional sparse array into an N×1 dimensional model column vector according to a predetermined order;

[0056] This step converts the three-dimensional data into one-dimensional data. The resulting three-dimensional sparse array is then unfolded into a column vector in a predetermined order (e.g., first the x-direction, then the y-direction, and finally the z-direction), resulting in a model column vector of shape N×1.

[0057] S26. Repeat steps S21 to S25 N times to obtain N independent N×1 dimensional model column vectors. ,in, Indicates the The model column vector is generated randomly once. .

[0058] Projecting once into the model domain yields a three-dimensional sparse array of X*Y*Z, which, when expanded, results in an N×1 model column vector. This projection process is repeated N times, including steps such as randomly generating the size parameters and spatial position of the projected geometry, assigning property values, generating the three-dimensional sparse array, and flattening it into column vectors. Each projection is performed independently, ultimately resulting in N model column vectors.

[0059] S3, concatenate the obtained N model column vectors in a random order to obtain an N×N dimensional model random weighted matrix;

[0060] The N model column vectors obtained in S2 When combined, with each column vector serving as a column of the matrix, this forms the model weighting matrix constructed based on random projection. This N×N dimensional model random weighting matrix This matrix is ​​used to weight the original sensitivity; the same-dimensional random projection in step S2 is used to construct this matrix.

[0061] It should be noted that in this embodiment of the invention, column concatenation is performed in a random order. Random order concatenation refers to combining the obtained N N×1 dimensional model column vectors into an N×N model weighted matrix without regard to order. Specifically, S3 includes:

[0062] S31, use a random algorithm to generate a permutation sequence. , This permutation sequence is a random arrangement of 1 to N, used to determine the concatenation order of the N model column vectors;

[0063] Permutation sequence Each element in the array takes a value from 1 to N (a positive integer from 1 to N), and each element takes a unique value.

[0064] S32, based on the generated permutation sequence, the first... Model column vectors As the first column of the concatenated matrix, the first... Model column vectors As the second column of the concatenated matrix, and so on, until the first column is... Model column vectors The Nth column of the concatenated matrix ultimately yields an N×N dimensional random weighted matrix. , .

[0065] This represents the first model column vector arranged in random order (i.e., the model column vector in the first column). This represents the second model column vector arranged in random order (i.e., the model column vector in the second column). This represents the Nth model column vector (i.e., the model column vector in the Nth column) arranged in random order.

[0066] That should be understandable. The data source is the N model column vectors obtained in step S2. It only involves the N model column vectors obtained in order. The order has been rearranged randomly, and the indices... In order to match the subscript in S2 The secondary generation makes a distinction.

[0067] For example, suppose that in the previous S2 step, N=3 model column vectors have been obtained, denoted as follows: , , If the permutation sequence is generated by a random algorithm Then, according to the splicing rules, As the first column, As the second column, As the third column, the final 3×3 dimensional model random weighting matrix is: .

[0068] In regularized inversion, the model weighting matrix has an N×N shape. Traditional methods typically generate it based on empirical formulas, while this invention generates it using geometric projection. Although the order in which the model column vectors are combined into the matrix is ​​random, each model column vector itself is generated by expanding a projected geometry whose spatial location is determined in the model domain. In other words, the order of elements within each model column vector is fixed. Randomly concatenating these elements does not change the subsurface property distribution information represented by each model column vector; it only changes the order in which this information is presented. For example, if a projected geometry covers specific units in a discretized region, the position and value of the property values ​​corresponding to these units in the model column vectors will not change due to the change in the arrangement order of the model column vectors in the matrix.

[0069] Compared to the conventional sequential splicing method, random sequential splicing increases the uncertainty and diversity of matrix construction. The distribution of matrix elements is more random, reducing the intuitive correlation between model column vectors, thereby better simulating the uncertainty of underground physical property distribution and improving the reliability of inversion results.

[0070] S4. Construct an inversion objective function based on the random weighting matrix, solve the objective function, and obtain the weighted domain magnetization.

[0071] Objective functions are typically used to measure the difference between observed magnetic data and theoretical magnetic data calculated based on model parameters. By solving the objective function, the weighted domain magnetization intensity that minimizes this difference is found, thus obtaining the representation of the subsurface model's magnetization intensity in the weighted domain that best matches the actual observed data.

[0072] In a regularized inversion system, the objective function for potential field data inversion typically consists of two parts: a data fitting term and a model constraint term. Its general form can be expressed as:

[0073] ;

[0074] Where, The objective function is... A is the data weighting matrix; A is the original domain sensitivity matrix; These are the original domain magnetization parameters; For observational data; For regularization parameters; This is the weighting matrix for the model.

[0075] Data weighting matrix It is usually constructed based on the square root of the error covariance matrix of the observed data. If the errors in the observed data differ at different locations or for different physical quantities, it is then... The data fitting term can be weighted, giving greater weight to data points with smaller errors, thereby improving the fit of the inversion results to reliable data.

[0076] Model weighting matrix The purpose of this is to constrain model parameters to address the non-uniqueness of the inversion problem. In potential field data inversion, since potential field data has high resolution for shallow anomalies but low resolution for deep anomalies, traditional model weighting matrices are usually constructed using depth-related functions, such as exponential or power functions. This imposes stronger constraints on deep model parameters, thereby improving the depth resolution of the inversion results. Because the model weighting matrix is ​​used to improve depth resolution, it is sometimes called the model depth weighting matrix, or simply the depth weighting matrix.

[0077] In this embodiment of the invention, the random weighting matrix is... By incorporating the objective function, we construct the objective function for inversion and obtain the model parameter values ​​after one random weighting. After the model random weighting matrix is ​​obtained, the inversion objective function is constructed as follows:

[0078] ;

[0079] in, ;

[0080] In the formula, This is the weighted domain sensitivity matrix; For the weighted domain magnetization parameters.

[0081] The random weighted matrix constructed in the embodiments of the present invention This is equivalent to proposing a new method for constructing the model weighting matrix. Since it is based on projection, the subscripts are represented by "". ("projection" is the first letter of the word). Generally refers to the model weighting matrix generated by various methods. Specifically refers to the model weighting matrix generated based on random projection of the model domain, that is, It is a special It does not rely on traditional empirical formulas or deeply related functions, but starts directly from the geometric projection of the model domain, which has greater flexibility and adaptability. and traditional They have similar functions and both aim to make the inversion results more consistent with the actual situation by weighting the model parameters, thereby improving the stability and reliability of the inversion.

[0082] The specific derivation process is as follows: Since the data weighting matrix has a very small impact, in this embodiment of the invention, the data weighting matrix is ​​directly taken. identity matrix Take the model weighting matrix For random (projected) weighted matrices The reverse, that is , Therefore, according to the general form of the objective function, we can obtain: ;in, , .

[0083] In summary, under the framework of regularized inversion theory, the embodiments of the present invention extract the objective function from potential field data. Set off, take , Transform the objective function into .

[0084] Then, the objective function is solved using methods such as the fast conjugate gradient method or the least squares QR decomposition method. Through iterative optimization, a method is found that satisfies the objective function. The model parameters that reach the minimum value are used to obtain the corresponding weighted domain magnetization parameters. ( (This is the magnetization inversion result under the weighted domain).

[0085] S5. Combining the random weighting matrix and the obtained weighted domain magnetization, the spatial distribution of three-dimensional magnetization is obtained, thereby realizing the construction of the inverted image.

[0086] According to the random weighting matrix And the weighted domain magnetization parameter corresponding to the minimum of the objective function. The magnetization inversion results were obtained. :

[0087] ;

[0088] magnetization It is an N×1 model parameter vector. Based on the obtained magnetization intensity inversion result, it is reshaped back into a three-dimensional array of X*Y*Z, which corresponds one-to-one with the subdivided underground space grid, thereby distributing the magnetization intensity to each grid cell and obtaining the magnetization intensity of each grid cell in the underground space. These magnetization intensities are presented in the form of an image, with different intensities mapped by different colors, thus realizing the construction of the inversion image and intuitively showing the distribution of underground magnetic bodies.

[0089] Furthermore, in magnetic data inversion, either magnetization or magnetic susceptibility can be inverted, and the two are directly proportional. Specifically, the relationship between magnetization (M) and magnetic susceptibility (k) is as follows: ,here It represents the vacuum permeability (constant). This is a normal geomagnetic field, and in most actual exploration work, Slow changes are considered constant, that is, It can be regarded as a proportionality constant. Therefore, magnetic data inversion can be used to obtain either the spatial distribution of magnetic susceptibility or the spatial distribution of magnetization.

[0090] Example 2: This embodiment of the invention demonstrates the application effects of different designs and weighting methods in magnetic data inversion through specific examples, further verifying the effectiveness of the invention.

[0091] A comparison of the random weighting matrix designed in this invention with traditional weighting methods. Figure 3 As shown, Figure 3 The distribution plots of kernel functions with different weighting methods are shown; among them, Figure 3 (a) is unweighted; Figure 3 (b) is the traditional weighting method; Figure 3 (c) represents a random weighting method; from Figure 3 It can be seen that the original sensitivity matrix exhibits a rapid decay characteristic with increasing depth, which often limits the inversion results to the vicinity of the surface, i.e., the well-known skin effect in potential field inversion. After traditional weighting, the decay characteristic of the reconstructed sensitivity matrix is ​​improved, but its weight distribution is still mainly concentrated in the shallower regions. However, the kernel function matrix reconstructed by the model's random weighted matrix shows a significant improvement in its original rapid decay characteristic, with the weight distribution reasonably reflected in both shallow and deep regions. This is helpful for the effective identification and recovery of deep anomalies. The random weighted matrix designed in this invention is significantly superior to the traditional weighting method in terms of depth resolution, and can effectively improve depth resolution.

[0092] Comparison of inversion results between the method of this invention and the conventional method, for example Figure 4 As shown, Figure 4 This is an example of the effect of inverting magnetic data of two prisms in an embodiment of the present invention, wherein, Figure 4 (a) is a prism model; Figure 4 (b) Magnetic data generated for the prism model; Figure 4 (c) shows the inversion results calculated using the traditional weighted method; Figure 4 (d) shows the inversion results calculated using the random weighting method of this invention. As can be seen from the figure, traditional weighting methods are prone to anomaly boundary blurring and tailing during the inversion process, affecting interpretation accuracy. In contrast, the magnetic data inversion method based on random weighting proposed in this invention can effectively suppress such artifacts. The results obtained are highly consistent with the actual model in terms of spatial morphology and boundary position, significantly improving resolution. This invention's method has higher accuracy in determining the target body position and physical property parameters, and its computational efficiency is 2.82 times that of traditional methods.

[0093] In summary, this invention effectively improves the depth resolution of magnetic data inversion through the design of a random weighting matrix, enabling more accurate identification of targets at different underground depths. Compared with traditional methods, this invention's method has higher accuracy in determining the location and physical properties of targets, and can more accurately describe the geometry and physical properties of underground targets. Furthermore, the computational efficiency of this invention's method is 2.82 times that of traditional methods, significantly shortening the inversion calculation time and improving work efficiency.

[0094] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for inverting hybrid hexahedral magnetic data based on random weighting, characterized in that, include: A hybrid hexahedral mesh combining structured and unstructured elements is used to spatially partition the underground inversion region, discretizing the underground space into N hexahedral mesh elements; Projected geometries with different size parameters and spatial positions are generated by random assignment, and the projected geometries are embedded into the mesh model after partitioning. This process is repeated N times to construct N independent N×1 dimensional model column vectors. The obtained N model column vectors are concatenated in a random order to obtain an N×N dimensional random weighted matrix; Based on the random weighting matrix, an objective function is constructed for inversion and solution. The objective function is then solved to obtain the weighted domain magnetization. By combining the random weighting matrix and the obtained weighted domain magnetization, the spatial distribution of three-dimensional magnetization is obtained, thereby realizing the construction of the inverted image.

2. The method for inverting hybrid hexahedral magnetic data based on random weighting according to claim 1, characterized in that, The method of spatially partitioning the underground inversion region using a hybrid hexahedral mesh combining structured and unstructured elements, discretizing the underground space into N hexahedral mesh elements, includes: Obtain the topographic elevation data of the area to be inverted, and select the horizontal plane at a certain depth below the lowest point of the topographic relief as the interface between the structured grid and the unstructured grid. The area above the interface is defined as the shallow region and is divided using an unstructured hexahedral mesh. The x and y directions are divided with equal spacing, and the z direction is divided with an equal number of layers. The thickness of each layer in the z direction is kept consistent at each (x, y) position. The region below the interface is defined as the deep region, and it is divided using a structured hexahedral mesh with equal spacing in the x, y, and z directions.

3. The method for inverting hybrid hexahedral magnetic data based on random weighting according to claim 1, characterized in that, Projected geometries with different size parameters and spatial positions are generated by random assignment, and these projected geometries are embedded into the meshed model. This process is repeated N times to construct N independent N×1 dimensional model column vectors, including: In the initial state, the physical property values ​​of all mesh elements in the mesh model are set to 0; The size parameters and spatial position of the projected geometry are determined by random assignment, and the range of grid cells covered by the geometry in the mesh model is determined based on the size parameters and spatial position of the generated projected geometry. Mesh cells covered by the projected geometry are assigned non-zero property values, while uncovered mesh cells are kept to 0. Generate a corresponding three-dimensional sparse array based on the physical property value of each grid cell; The obtained three-dimensional sparse array is flattened into an N×1 dimensional model column vector according to a predetermined order; Repeat the above process N times to obtain N independent N×1 dimensional model column vectors. ,in, Indicates the first The model column vector is generated randomly once. .

4. The method for inverting hybrid hexahedral magnetic data based on random weighting according to claim 3, characterized in that, The obtained N model column vectors are concatenated in a random order to obtain an N×N dimensional random weighted matrix, including: Use a random algorithm to generate a random permutation sequence from 1 to N. , The random permutation sequence is used to determine the concatenation order of the N model column vectors; Based on the generated permutation sequence, the first... The nth model column vector is used as the first column, and the nth... The first model column vector is used as the second column, and so on, until the second model column vector is used as the third column vector. Using the model column vectors as the Nth column, we obtain an N×N dimensional random weighted matrix. , In the formula, This represents the model column vector in the first column. This represents the model column vector in the second column. This represents the model column vector of the Nth column.

5. The method for inverting hybrid hexahedral magnetic data based on random weighting according to claim 4, characterized in that, Based on the aforementioned random weighting matrix, an objective function is constructed for inversion and solution. Solving the objective function yields the weighted domain magnetization, including: Based on the general form of the inversion objective function: ； Take the weighted matrix of the data The identity matrix, and the model weighting matrix within it. For the random weighting matrix The reverse, that is , The objective function for inversion is constructed as follows: ； ； In the formula, The objective function is... This is the original sensitivity matrix; These are the original domain magnetization parameters; For observational data; For regularization parameters; Represents the identity matrix; This is the weighted domain sensitivity matrix; These are the magnetization parameters for the weighted domain; The weighted domain magnetization parameter corresponding to the minimum objective function can be obtained by using the fast conjugate gradient method or the least squares QR decomposition method. .

6. The method for inverting hybrid hexahedral magnetic data based on random weighting according to claim 5, characterized in that, Combining the aforementioned random weighting matrix and the obtained weighted domain magnetization, the spatial distribution of three-dimensional magnetization is obtained, and the construction of the inversion image is achieved by including: According to the random weighting matrix And the weighted domain magnetization parameter corresponding to the minimum of the objective function. The magnetization inversion result is calculated using the following formula. : ； Based on the obtained magnetization inversion results, the magnetization intensity is allocated to each grid cell to obtain the magnetization intensity of each grid cell in the underground space; The distribution of underground magnetic bodies is characterized by color mapping based on the magnetization intensity of each grid cell, and a corresponding image is generated, thereby realizing the construction of the inversion image.

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