Mixed hexahedron magnetic data inversion method based on random weighting

Abstract

The invention discloses a mixed hexahedron magnetic data inversion method based on random weighting, and belongs to the field of magnetic signal processing, and the method comprises the steps: carrying out the space division of an underground inversion region through employing a structure and non-structure combined mixed hexahedron grid, and discretizing an underground space into N hexahedron units; generating projection geometries with different size parameters and spatial positions through random assignment, embedding the projection geometries into the subdivided grid model, repeating N times to construct N independent N * 1-dimensional model column vectors, and then performing random sequential splicing to obtain an N * N-dimensional random weighting matrix; constructing an inversion objective function based on the random weighting matrix, and solving to obtain weighting domain magnetization intensity; and in combination with a random weighting matrix and a solving result, obtaining spatial distribution of three-dimensional magnetization intensity, and realizing construction of an inversion image. According to the invention, rapid and fine inversion of the geophysical magnetic data under the rugged topography is realized, and the inversion precision and reliability of the magnetic survey data under the complex topographic condition are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic signal processing, and in particular to a hybrid hexahedron magnetic data inversion method based on random weighting. Background Art

[0002] As a key geophysical exploration method, magnetic surveying is widely used in mineral exploration, geological mapping, and structural research due to its wide coverage, high efficiency, and low cost. Magnetic inversion aims to use surface magnetic anomalies to recover the magnetization intensity or magnetic susceptibility distribution of the subsurface medium, thereby inferring the subsurface geological structure and lithologic characteristics. However, due to the inherent non-uniqueness and pathological nature of magnetic field inversion problems, improving imaging resolution while ensuring the physical plausibility and stability of the results has always been a core challenge in magnetic data inversion research.

[0003] Traditional three-dimensional magnetic inversion mostly uses regularly structured hexahedral grids for modeling. However, the actual terrain is usually complex and undulating. Due to the rigid node arrangement limitations of the structured grid, it is difficult to accurately fit the surface morphology, which in turn affects the accuracy of physical property recovery in the near-surface area. In addition, to alleviate the "skin effect" caused by the depth attenuation of the kernel function in magnetic inversion, various forms of depth weighting or model regularization strategies have been proposed. However, traditional methods often produce a "tailing effect" in the deep part of the inversion results, making it difficult to accurately characterize deep targets. Therefore, achieving high-precision inversion of magnetic data while efficiently fitting the terrain is the current development direction. Summary of the Invention

[0004] The present invention proposes a magnetic data processing method with good modeling accuracy and inversion stability under complex terrain conditions, aiming to solve technical problems such as low inversion accuracy, insufficient deep anomaly recognition ability and complex model parameter setting in existing technologies under complex terrain conditions.

[0005] According to one aspect of the present invention, a hybrid hexahedral magnetic data inversion method based on random weighting is provided, which is characterized by comprising: spatially partitioning the underground inversion area using a hybrid hexahedral grid that combines structure and unstructure, discretizing the underground space into N hexahedral grid units; generating a projected geometric body with different size parameters and spatial positions by random assignment, and embedding the projected geometric body into the partitioned grid model, repeating N times, to construct N independent N×1-dimensional model column vectors; column-wise splicing the obtained N model column vectors in a random order to obtain an N×N-dimensional random weighted matrix; constructing an inversion objective function based on the random weighted matrix, solving the objective function, and obtaining a weighted domain magnetization intensity; and obtaining a spatial distribution of three-dimensional magnetization intensity by combining the random weighted matrix and the obtained weighted domain magnetization intensity, thereby realizing the construction of an inversion image.

[0006] Optionally, the use of a hybrid hexahedral grid combining structured and unstructured grids to spatially divide the underground inversion area and discretize the underground space into N hexahedral grid units includes: obtaining terrain elevation data of the area to be inverted, and selecting a 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; defining the area above the interface as a shallow area, and using an unstructured hexahedral grid for division, wherein the x and y directions are divided at equal intervals, the z direction is divided at equal 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 a deep area, and using a structured hexahedral grid for division, and the x, y, and z directions are all divided at equal intervals.

[0007] Optionally, a projected geometric body with different size parameters and spatial positions is generated by random assignment, and the projected geometric body is embedded in the mesh model after segmentation, and repeated N times to construct N independent N×1-dimensional model column vectors, including: in the initial state, the physical property values ​​of all grid cells in the mesh model are assigned to 0; the size parameters and spatial position of the projected geometric body are determined by random assignment, and the range of grid cells covered by the geometric body in the mesh model is determined based on the size parameters and spatial position of the generated projected geometric body; the grid cells covered by the projected geometric body are assigned non-zero physical property values, and the uncovered grid cells are kept as 0; a corresponding three-dimensional sparse array is generated according to the physical property value of each grid cell; the obtained three-dimensional sparse array is flattened into an N×1-dimensional model column vector in a predetermined order; the above process is repeated N times to obtain N independent N×1-dimensional model column vectors ,in, Indicates the randomly generated model column vectors, .

[0008] Optionally, the obtained N model column vectors are concatenated in a random order to obtain an N×N dimensional random weight matrix, which includes: using a random algorithm to generate a random permutation sequence from 1 to N , , the random permutation sequence is used to determine the splicing order of N model column vectors; according to the generated permutation sequence, the The model column vector is taken as the first column, and the The model column vector is used as the second column, and so on, until the The model column vector is used as the Nth column to obtain an N×N dimensional random weight matrix , , where represents the model column vector of the first column, represents the model column vector of the second column, Column vector representing the model for column N.

[0009] Optionally, constructing an inversion objective function based on the random weighted matrix, and solving the objective function to obtain the weighted domain magnetization intensity includes: Based on the general form of the inversion objective function: ; Take the data weight matrix is the identity matrix, and the model weight matrix is ​​taken is the random weight matrix The inverse of , , the objective function of the inversion solution is constructed as: ; ; Where, is the objective function; is the original sensitivity matrix; is the original domain magnetization parameter; is the observation data; is the regularization parameter; represents the identity matrix; is the weighted domain sensitivity matrix; is the weighted domain magnetization parameter; The fast conjugate gradient method or the least squares QR decomposition method is used to solve the weighted domain magnetization intensity parameter corresponding to the minimum of the objective function. .

[0010] Optionally, combining the random weighted matrix and the obtained weighted domain magnetization intensity to obtain a spatial distribution of three-dimensional magnetization intensity, and realizing the construction of an inversion image includes: According to the random weight matrix And the weighted domain magnetization intensity parameter corresponding to the minimum objective function , the magnetization intensity inversion results are calculated using the following formula : ; According to the magnetization intensity inversion results, the magnetization intensity is distributed to each grid unit to obtain the magnetization intensity of each grid unit 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 to construct an inversion image.

[0011] The randomly weighted hybrid hexahedral magnetic data inversion method in the present invention adopts a layered subdivision strategy to model the underground space. Unstructured hexahedral grids are introduced in the near-surface area to accurately fit the undulating terrain. Structured hexahedral grids are used in deep areas to maintain the sparsity of the forward matrix and improve computational efficiency, thereby achieving a balance between large-scale terrain modeling and inversion calculations.

[0012] During the inversion process, the present invention replaces the traditional depth weighting function by constructing a random weighting matrix of the same dimension to reconstruct the spatial distribution structure of the sensitivity kernel function. The random weighting matrix is ​​composed of multiple high-dimensional sparse perturbation model column vectors, and has good directional perturbation characteristics and spatial non-overlapping. This design not only effectively alleviates the problems of rapid weight decay and strong parameter dependence in deep areas of traditional depth weighting methods, but also simplifies the requirements for setting empirical parameters in the inversion process, thereby improving the ability to identify deep anomalies and the geological rationality of the model results.

[0013] The method of the present invention provides an effective technical means for inverting magnetic data under complex terrain, can realize fast and precise inversion of geophysical magnetic data under undulating terrain conditions, and improves the accuracy and reliability of magnetic inversion of magnetic survey data under complex terrain conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a flow chart of a hybrid hexahedral magnetic data inversion method based on random weighting according to an embodiment of the present invention; Figure 2 Schematic diagram of mixed hexahedral mesh generation for underground space; Figure 3 It is the distribution diagram of kernel function with different weighting methods; Figure 3 (a) is the unweighted kernel function distribution diagram; Figure 3 (b) is the kernel function distribution diagram of the traditional weighting method; Figure 3 (c) is the kernel function distribution diagram of random weighting method; Figure 4 Example results for inverting two prismatic magnetic data; Figure 4 (a) is a prismatic model; Figure 4 (b) Magnetic data generated for the prismatic model; Figure 4 (c) is the inversion result calculated using the traditional weighting method; Figure 4 (d) is the inversion result calculated using the random weighting method of the present invention. DETAILED DESCRIPTION

[0015] In order 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 in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only embodiments of a part of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of this application. It should be noted that, in the absence of conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0016] Secondly, the term "one embodiment" or "embodiment" 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 various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0017] The terms "comprises" and "having" and any variations thereof in the specification and claims of this application are intended to cover non-exclusive inclusions. For example, a process, method, product or apparatus that includes a series of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, product or apparatus.

[0018] Example 1: Reference Figure 1 , Figure 1 Flowchart of a hybrid hexahedral magnetic data inversion method based on random weighting according to an embodiment of the present invention. Figure 1 As shown, the method includes the following steps: S1, a hybrid hexahedral grid combining structure and unstructure is used to spatially divide the underground inversion area, discretizing the underground space into N hexahedral units; A structured hexahedron is a regular hexahedron whose side lengths and angles follow fixed geometric relationships, presenting a neat and orderly arrangement in three-dimensional space. An unstructured hexahedron is an irregular hexahedron whose side lengths and angles are not fixed and can be flexibly adjusted according to actual needs.

[0019] In order to facilitate the study of physical properties at different locations underground (such as resistivity, magnetic permeability, etc.), it is necessary to grid the underground area and divide the underground three-dimensional space into many small cubic grid units, each grid unit representing a small area underground. The embodiment of the present invention combines the characteristics of structural hexahedrons and unstructured hexahedrons. In areas with undulating terrain near the surface, unstructured hexahedrons are used for spatial division to accurately describe the complex geological conditions of the area. The geological structure of deep underground areas is relatively stable and changes little. The use of structural hexahedron grid division can improve computational efficiency while ensuring a certain degree of accuracy. This hybrid subdivision method can give full play to the advantages of the two grids and achieve more efficient and accurate modeling of underground space.

[0020] Specifically, S1 includes: S11, obtaining terrain elevation data of the area to be inverted; Terrain elevation data can be obtained through field measurements, satellite remote sensing data extraction, or existing geological exploration data. These data should have a high resolution to accurately reflect the undulations of the terrain.

[0021] S12, select the horizontal plane at a certain depth below the lowest point of the terrain as the interface between the structured grid and the unstructured grid; This interface can be flexibly set based on geological characteristics or modeling requirements (such as the target depth of geological exploration, the complexity of the underground geological structure, and the efficiency of subsequent inversion calculations). Generally speaking, in areas with relatively simple geological structures and shallow exploration targets, a smaller depth below the lowest point of the terrain can be used as the interface. In areas with complex geological structures and deeper exploration targets, the depth of this interface can be appropriately increased.

[0022] S12: The area above the interface is defined as the shallow layer and is divided using an unstructured hexahedral grid. The x and y directions (x and y are directions on the horizontal plane, which can be set according to actual conditions. Generally, the x direction is due north and the y direction is due east) are divided with equal spacing. This division method can ensure the uniformity of the grid distribution on the horizontal plane. The z direction (i.e., the direction perpendicular to the horizontal plane downward) is divided with equal layers, and the thickness of each layer in the z direction is kept consistent at each (x, y) position. S13 defines the area below the interface as the deep region and uses a structured hexahedral grid for partitioning. Equal spacing is used in the x, y, and z directions. This uniform partitioning method simplifies the calculation process and better reflects the relatively uniform geological characteristics of the deep region.

[0023] Reference Figure 2 , Figure 2The blue line section is the interface, the area above the blue line is the shallow area, and the area below the blue line is the deep area. Figure 2 As shown in the figure, the shallow area (topographic undulation area) is divided into several unstructured hexahedral grids that fit the terrain undulations. This allows for flexible adaptation to the actual terrain, adaptability to complex terrain and geological structures, and improved inversion accuracy. The deep area is divided into several structured hexahedral grids of equal size, with the same length, height, and width, to help simplify calculations and improve efficiency.

[0024] S2, generating projected geometric bodies with different size parameters and spatial positions by random assignment, and embedding the projected geometric bodies into the mesh model after segmentation, repeating N times to construct N independent N×1-dimensional model column vectors; According to the S1 underground space gridding 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. Here, X*Y*Z=N. Projected geometric bodies are randomly implanted into the discretized area. These geometric bodies can be prisms, inclined bodies, and other shapes. The size parameters and spatial position are determined by random assignment. The geometric body obtained by projection is called a "projected geometric body" (essentially, a geometric body is generated in the subdivided underground space, but the position, size, and shape of this geometric body are random). Randomness means that the position and size of each projected geometric body in space are uncertain, which increases the diversity and complexity of the model. For example, when simulating the distribution of underground ore bodies, the shape and position of the ore bodies are often unknown. Randomly projecting geometric bodies of different shapes can better simulate this uncertainty.

[0025] Specifically, S2 includes: S21, in the initial state, assign the physical property values ​​of all grid cells in the grid model to 0; The physical property of each discrete unit is assigned a value of 0, which is equivalent to a three-dimensional array of all 0s in X*Y*Z.

[0026] S22, determining the size parameters and spatial position of the projected geometric body by random assignment, and determining the range of grid cells covered by the geometric body in the grid model based on the size parameters and spatial position of the generated projected geometric body; S23, assigning non-zero physical property values ​​to the mesh cells covered by the projected geometry, and keeping the uncovered mesh cells as 0; The specific value of the non-zero physical property value can be set according to the actual situation. For example, if the projection is a prism representing an ore body, the cells inside the prism can be assigned a higher resistivity value to simulate the existence of the ore body.

[0027] S24, generating a corresponding three-dimensional sparse array according to the physical property value of each grid cell; After projecting the geometry onto the initial mesh model, non-zero physical property values ​​are assigned to the cells of the projected geometry. Based on the physical property values ​​of each mesh cell in the mesh model, a three-dimensional sparse array of X*Y*Z can be generated. A sparse array refers to an array in which most elements are 0 or the same value, and only a few elements are non-zero or non-identical values.

[0028] S25, flattening the obtained three-dimensional sparse array into an N×1-dimensional model column vector according to a predetermined order; This step is to convert the three-dimensional data into one-dimensional data. The obtained three-dimensional sparse array is expanded into a column vector in a predetermined order (such as first in the x direction, then in the y direction, and finally in the z direction), and a model column vector with a shape of N×1 is obtained.

[0029] S26, repeat the above steps S21 to S25 N times to obtain N independent N×1 dimensional model column vectors ,in, Indicates the randomly generated model column vectors, .

[0030] Projecting once onto the model domain yields a three-dimensional sparse array of X*Y*Z dimensions, which, when expanded, yields the corresponding N×1 model column vector. This projection process is repeated N times, including the steps of randomly generating the dimensions and spatial position of the projected geometry, assigning physical property values, generating a three-dimensional sparse array, and flattening it into a column vector. Each projection is performed independently, ultimately yielding N model column vectors.

[0031] S3, concatenate the obtained N model column vectors in a random order to obtain an N×N dimensional model random weight matrix; N model column vectors obtained in S2 Combined, that is, each column vector is used as a column of the matrix, forming the model weight matrix based on random projection , this N×N dimensional model random weight matrix , which is used to weight the original sensitivity. The random projection of the same dimension in step S2 is to construct this matrix.

[0032] It should be noted that, in the embodiment of the present invention, random order is used for column-wise splicing. Random order splicing means combining the obtained N N×1-dimensional model column vectors into an N×N model weight matrix in no particular order. Specifically, S3 includes: S31, using a random algorithm to generate a permutation sequence , , the permutation sequence is a random permutation from 1 to N, which is used to determine the splicing order of N model column vectors; Permutation sequence Each element in takes a value between 1 and N (a positive integer between 1 and N), and the value of each element is unique.

[0033] S32, according to the generated permutation sequence, model column vector As the first column of the concatenated matrix, model column vector As the second column of the concatenated matrix, and so on, until the model column vector As the Nth column of the concatenated matrix, we finally get an N×N dimensional random weighted matrix , .

[0034] represents the first model column vector (i.e. the model column vector of the first column) arranged in random order, represents the second model column vector (i.e. the model column vector of the second column) arranged in random order, Represents the Nth model column vector arranged in random order (that is, the model column vector of the Nth column).

[0035] It should be understandable. The data source in is the N model column vectors obtained in step S2 , just the N model column vectors obtained in order The order of the subscripts was rearranged randomly. This is to match the subscript in S2 The second generation is distinguished.

[0036] For example, suppose that in the previous S2 step, N=3 model column vectors have been obtained, which are recorded as 、 、 , if the permutation sequence 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 weight matrix is .

[0037] In regularized inversion, the shape of the model weighting matrix is ​​N×N. Traditional methods are generally based on empirical formulas to generate it, while the embodiments of the present invention generate it through geometric projection methods. Although the order of the model column vectors when they are combined into a matrix is ​​random, each model column vector itself is generated by unfolding the projected geometry that determines the spatial position in the model domain. In other words, the arrangement order of the elements inside each model column vector is fixed, and random order splicing does not change the underground physical property distribution information represented by each model column vector, but only changes the presentation order of this information. For example, a projected geometry covers specific cells in the discretized area, and the positions and values ​​of the physical property values ​​corresponding to these cells in the model column vector will not change due to changes in the arrangement order of the model column vectors in the matrix.

[0038] Compared with the conventional sequential splicing method, random sequence splicing increases the uncertainty and diversity of matrix construction. The element distribution of the matrix is ​​more random, which reduces the intuitive correlation between the model column vectors, thereby better simulating the uncertainty of the underground physical property distribution and improving the reliability of the inversion results.

[0039] S4, constructing an inversion objective function based on the random weighted matrix, solving the objective function, and obtaining a weighted domain magnetization intensity; The objective function is usually used to measure the difference between the observed magnetic data and the theoretical magnetic data calculated based on the model parameters. By solving the objective function, the weighted domain magnetization intensity that minimizes this difference is found, thereby obtaining the magnetization intensity representation of the underground model in the weighted domain that best matches the actual observed data.

[0040] In the regularized inversion system, the objective function of potential field data inversion usually consists of two parts: data fitting term and model constraint term. Its general form can be expressed as: ; Where, is the objective function; is the data weighting matrix; A is the original domain sensitivity matrix; is the original domain magnetization parameter; is the observation data; is the regularization parameter; is the model weight matrix.

[0041] Data weighting matrix It is usually constructed based on the square root of the error covariance matrix of the observation data. If the errors of the observation data at different locations or different physical quantities are different, The data fitting items can be weighted so that greater weight is given to data points with smaller errors, thereby improving the degree of fit of the inversion results to reliable data.

[0042] Model weight matrix The function of is to constrain the model parameters to address the non-uniqueness of the inversion problem. In the inversion of potential field data, because potential field data has a higher resolution for shallow anomalies and a lower resolution for deep anomalies, traditional model weighting matrices are usually constructed using depth-dependent functions, such as exponential functions or power functions. This imposes stronger constraints on the deep model parameters, thereby improving the depth resolution of the inversion results. Since the model weighting matrix is ​​used to improve depth resolution, it is sometimes also called the model depth weighting matrix, or simply the depth weighting matrix.

[0043] In the embodiment of the present invention, the random weight matrix Integrate the objective function, construct the objective function of the inversion solution, obtain the model parameter value after random weighting, and after the model random weighting matrix, the inversion objective function is constructed as follows: ; in, ; Where, is the weighted domain sensitivity matrix; is the weighted domain magnetization parameter.

[0044] The random weighted matrix constructed in the embodiment of the present invention , which is equivalent to proposing a new method for constructing the model weight matrix. Since it is constructed based on projection, the subscript is “ ” (the first letter of “projection”). Generally refers to the model weight matrix generated by various methods. Specifically refers to the model weight matrix generated based on random projection of the model domain, that is, It is a special , which does not rely on traditional empirical formulas or depth-related functions, but directly starts from the geometric projection of the model domain, and has greater flexibility and adaptability. and traditional They have similar functions and are designed 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.

[0045] The specific derivation process is as follows: Since the data weighting matrix has little influence, in the embodiment of the present invention, the data weighting matrix is ​​directly taken as is the identity matrix , take the model weight matrix is the random (projection) weight matrix The inverse of , , then according to the general form of the objective function, we can get: in, , .

[0046] In summary, the embodiment of the present invention, under the regularized inversion theory system, uses the objective function of the potential field data to Departure, take , , transforming the objective function into .

[0047] Then, the objective function is solved by using the fast conjugate gradient method or the least squares QR decomposition method, and the objective function is found through iterative optimization. The model parameters that reach the minimum value are used to obtain the corresponding weighted domain magnetization intensity parameters. ( is the magnetization intensity inversion result in the weighted domain).

[0048] S5, combining the random weighted matrix and the obtained weighted domain magnetization intensity to obtain the spatial distribution of the three-dimensional magnetization intensity, thereby realizing the construction of the inversion image.

[0049] According to the random weight matrix And the weighted domain magnetization intensity parameter corresponding to the minimum objective function , and the magnetization intensity inversion results are obtained : ; Magnetization It is an N×1 model parameter vector. According to the inversion result of the magnetization intensity, it is reshaped back into a three-dimensional array of X*Y*Z, which corresponds one-to-one to the subdivided underground space grid, thereby distributing the magnetization intensity to each grid unit and obtaining the magnetization intensity of each grid unit in the underground space. These magnetization intensities are presented in the form of images, and different intensities are mapped with different colors. This can realize the construction of the inversion image and intuitively show the distribution of underground magnetic bodies.

[0050] In addition, in magnetic data inversion, the inversion can be either magnetization or magnetic susceptibility, and there is a proportional relationship between the two. Specifically, the relationship between magnetization (M) and magnetic susceptibility (k) is: ,here represents the vacuum permeability (constant), Normal geomagnetic field. In most actual exploration work, Slowly changing is considered a constant, i.e. It can be regarded as a proportional constant. Therefore, magnetic data inversion can obtain the spatial distribution of magnetic susceptibility or the spatial distribution of magnetization intensity.

[0051] Example 2: The present invention demonstrates the application effects of different designs and different weighting methods in magnetic data inversion through specific examples, further verifying the effectiveness of the present invention.

[0052] The comparison between the random weighted matrix designed by the present invention and the traditional weighted method is as follows: Figure 3 As shown, Figure 3 is the distribution diagram of kernel functions with different weighting methods; among them, Figure 3 (a) is unweighted; Figure 3 (b) is the traditional weighting method; Figure 3 (c) is a random weighting method; Figure 3 It can be seen that the original sensitivity matrix exhibits a rapid attenuation characteristic with increasing depth, which causes the inversion results to be often limited to the vicinity of the surface, namely the well-known skin effect of potential field inversion. After weighting by the traditional method, the attenuation characteristics of the reconstructed sensitivity matrix are improved, but its weight distribution is still mainly concentrated in the shallow area. However, after the kernel function matrix is ​​reconstructed by the model random weighting matrix, its original rapid attenuation characteristics are significantly improved, and the weight distribution is reasonably reflected in both shallow and deep areas, which helps to effectively identify and recover deep anomalies. The random weighting matrix designed by the present invention is significantly superior to the traditional weighting method in terms of depth resolution and can effectively improve the depth resolution.

[0053] The inversion results of the method of the present invention and the traditional method are compared. Figure 4 As shown, Figure 4 This is an example of the effect of inverting two prism magnetic data in an embodiment of the present invention, where: Figure 4 (a) is a prismatic model; Figure 4 (b) Magnetic data generated for the prismatic model; Figure 4 (c) is the inversion result calculated using the traditional weighting method; Figure 4 (d) shows the inversion result calculated using the random weighting method of the present invention. As can be seen from the figure, traditional weighting methods are prone to blurring the boundaries of anomalies and smearing during the inversion process, affecting the interpretation accuracy. In contrast, the magnetic data inversion method based on random weighting proposed in this invention can effectively suppress such artifacts. The obtained results are highly consistent with the actual model in terms of spatial morphology and boundary position, with significantly improved resolution. The method of the present invention has higher accuracy in determining the location and physical parameters of the target body, and the computational efficiency is 2.82 times that of the traditional method.

[0054] In summary, the present invention effectively improves the depth resolution of magnetic data inversion through the design of a random weighted matrix, and can more accurately identify targets at different depths underground; compared with traditional methods, the method of the present invention has higher precision in determining the target position and physical parameters, and can more accurately describe the geometric shape and physical properties of underground targets; and the computational efficiency of the method of the present invention is 2.82 times that of traditional methods, which greatly shortens the inversion calculation time and improves work efficiency.

[0055] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A hybrid hexahedral magnetic data inversion method based on random weighting, characterized in that: include: A hybrid hexahedral grid combining structure and unstructure is used to spatially divide the underground inversion area, discretizing the underground space into N hexahedral grid units. Generate projected geometric bodies with different size parameters and spatial positions by random assignment, and embed the projected geometric bodies into the mesh model after segmentation, repeating 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 weight matrix; Constructing an inversion objective function based on the random weighted matrix, solving the objective function, and obtaining a weighted domain magnetization intensity; By combining the random weighted matrix and the obtained weighted domain magnetization intensity, the spatial distribution of the three-dimensional magnetization intensity is obtained, thereby realizing the construction of the inversion image.

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

3. The random weighted hybrid hexahedral magnetic data inversion method according to claim 1, characterized in that: Generate projected geometric bodies with different size parameters and spatial positions by random assignment, and embed the projected geometric bodies into the mesh model after segmentation. Repeat N times to construct N independent N×1-dimensional model column vectors including: In the initial state, the physical property values ​​of all grid cells in the grid model are assigned to 0; Using random assignment to determine the size parameters and spatial position of the projected geometric body, and based on the size parameters and spatial position of the generated projected geometric body, determine the range of grid cells covered by the geometric body in the grid model; The mesh cells covered by the projected geometry are assigned non-zero property values, while the uncovered mesh cells remain at 0. Generate a corresponding three-dimensional sparse array based on the physical property values ​​of each grid cell; Flatten the obtained three-dimensional sparse array 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 randomly generated model column vectors, .

4. The random weighted hybrid hexahedral magnetic data inversion method 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 weight matrix including: Use a random algorithm to generate a random sequence from 1 to N , , the random permutation sequence is used to determine the splicing order of N model column vectors; According to the generated permutation sequence, The model column vector is taken as the first column, and the The model column vector is used as the second column, and so on, until the The model column vector is used as the Nth column to obtain an N×N dimensional random weight matrix , , where represents the model column vector of the first column, represents the model column vector of the second column, Column vector representing the model for column N.

5. The random weighted hybrid hexahedral magnetic data inversion method according to claim 4, characterized in that: Constructing an inversion objective function based on the random weighted matrix, and solving the objective function to obtain the weighted domain magnetization intensity includes: Based on the general form of the inversion objective function: ； Take the data weight matrix is the identity matrix, and the model weight matrix is ​​taken is the random weight matrix The inverse of , , the objective function of the inversion solution is constructed as: ； ； Where, is the objective function; is the original sensitivity matrix; is the original domain magnetization parameter; is the observation data; is the regularization parameter; represents the identity matrix; is the weighted domain sensitivity matrix; is the weighted domain magnetization parameter; The fast conjugate gradient method or the least squares QR decomposition method is used to solve the weighted domain magnetization intensity parameter corresponding to the minimum of the objective function. .

6. The random weighted hybrid hexahedral magnetic data inversion method according to claim 5, characterized in that: Combining the random weighted matrix and the obtained weighted domain magnetization intensity to obtain the spatial distribution of the three-dimensional magnetization intensity, and realizing the construction of the inversion image includes: According to the random weight matrix And the weighted domain magnetization intensity parameter corresponding to the minimum objective function , the magnetization intensity inversion results are calculated using the following formula : ； According to the magnetization intensity inversion results, the magnetization intensity is distributed to each grid unit to obtain the magnetization intensity of each grid unit 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 to construct an inversion image.

Images