Magnetic anomaly efficient simulation method based on hybrid algorithm

Abstract

The invention discloses an efficient magnetic anomaly simulation method based on a hybrid algorithm, and the method comprises the steps: building a Cartesian coordinate system for a target region, and obtaining the information of any grid unit of the target region, the information of an observation point, and the magnetic field intensity; based on the information of the grid units and the information of the observation points, dividing the grid units by adopting a distance adaptive algorithm to obtain a plurality of near-field area grid units and a plurality of far-field area grid units; calculating a kernel matrix element corresponding to any far-field area grid unit by adopting a point magnetic source algorithm, and calculating a kernel matrix element corresponding to any near-field area grid unit by adopting a numerical integration method; and the kernel matrix elements corresponding to the far-field area grid units and the kernel matrix elements corresponding to the near-field area grid units are synthesized, and a magnetic anomaly vector is obtained. Through the scheme, the method has the advantages of simple logic, accuracy, reliability and the like, and has very high practical value and popularization value in the technical field of physical simulation.

Description

Technical Field

[0001] This invention relates to the field of physical simulation technology, and in particular to an efficient method for simulating magnetic anomalies based on a hybrid algorithm. Background Technology

[0002] In the field of physical simulation technology, calculating the distribution of spatial magnetic anomalies caused by magnetic media is a fundamental and crucial technique. This technique, by constructing a linear forward model of the 'magnetic source-magnetic field' response, provides explanatory basis for multiple fields, including engineering and environmental geophysics (such as unexploded ordnance detection and archaeological surveys), materials science and industrial testing (such as non-destructive testing and magnetic property imaging), and planetary science and space physics (such as inversion of planetary shell magnetic structure). To facilitate the simulation of complex magnetic media, the target region is typically divided into a series of regular (e.g., cuboid) grid cells, assuming uniform magnetic susceptibility within each grid cell. The core calculation process is as follows: based on potential field theory, the magnetic field contribution generated by each rectangular grid cell at each observation point is accurately calculated using numerical integration methods, forming a kernel function matrix; finally, the magnetic anomaly is obtained by multiplying this kernel function matrix by a vector characterizing the magnetic susceptibility distribution. For example, the publicly disclosed technologies "a self-constrained magnetic anomaly property inversion method and system based on correlation coefficient" (publication number CN119575490A) and "a geophysical gravity and magnetic anomaly source model construction and rapid forward and inverse modeling method" (publication number CN120912802A).

[0003] While the aforementioned forward modeling method based on global numerical integration can guarantee accuracy, it suffers from significant efficiency bottlenecks in large-scale practical applications. The fundamental reason lies in its high computational complexity; the calculation of each element of the kernel function matrix requires triple numerical integration over the grid cell (requiring eight evaluations). The core drawback of this method is its failure to optimize based on physical laws. It applies the same integration process to all grid cells without considering the characteristic that the far field can be approximated as a point magnetic source. This indiscriminate treatment results in a huge waste of computational resources.

[0004] Therefore, there is an urgent need to propose a simple, accurate, and reliable method for efficient simulation of magnetic anomalies based on a hybrid algorithm. Summary of the Invention

[0005] To address the above problems, the present invention aims to provide an efficient method for simulating magnetic anomalies based on a hybrid algorithm. The technical solution adopted by the present invention is as follows: An efficient method for simulating magnetic anomalies based on a hybrid algorithm includes the following steps: Establish a Cartesian coordinate system for the target area and obtain information on any grid cell, observation point, and magnetic field strength within the target area; Based on the information of the grid cells and the observation point information, and using a distance adaptive algorithm to divide the grid cells, several near-field grid cells and several far-field grid cells are obtained. The kernel matrix elements corresponding to any far-field region grid cell are calculated using the point magnetic source algorithm, and the kernel matrix elements corresponding to any near-field region grid cell are calculated using the numerical integration method. The kernel matrix elements corresponding to the far-field region grid cells and the near-field region grid cells are synthesized to obtain the magnetic anomaly vector.

[0006] Compared with the prior art, the present invention has the following beneficial effects: (1) Based on the information of the grid cells and the observation point information, the present invention uses a distance adaptive algorithm to divide the grid cells to obtain several near-field grid cells and several far-field grid cells, which are used to distinguish the point magnetic source calculation area and the integral calculation area.

[0007] (2) The present invention uses the point magnetic source algorithm to calculate the kernel matrix element corresponding to any far-field region grid cell, and uses the numerical integration method to calculate the kernel matrix element corresponding to any near-field region grid cell, which ensures both calculation accuracy and improves calculation efficiency.

[0008] (3) The present invention synthesizes the kernel matrix elements corresponding to the far-field grid cells and the kernel matrix elements corresponding to the near-field grid cells, and obtains the magnetic anomaly vector, which comprehensively considers the computational efficiency and computational accuracy.

[0009] In summary, this invention has the advantages of simple logic and high accuracy and reliability, and has high practical and promotional value in the field of physical simulation technology. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope of protection. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a logic flowchart of the present invention. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this application clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0013] In this embodiment, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0014] The terms "first" and "second," etc., used in the specification and claims of this embodiment are used to distinguish different objects, not to describe a specific order of objects. For example, "first target object" and "second target object," etc., are used to distinguish different target objects, not to describe a specific order of target objects.

[0015] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0016] In the description of the embodiments in this application, unless otherwise stated, "multiple" means two or more. For example, multiple processing units means two or more processing units; multiple systems means two or more systems.

[0017] like Figure 1 As shown, this embodiment provides an efficient simulation method for magnetic anomalies based on a hybrid algorithm, which includes the following steps: The first step is to establish a Cartesian coordinate system for the target region, where the x-axis, y-axis, and z-axis point east, north, and vertically downwards, respectively. Here, information about any grid cell, observation point, and magnetic field strength of the target region is obtained. The information of the grid cells is as follows: ;in, This represents the coordinate of the j-th grid cell in the x-direction of the Cartesian coordinate system; This represents the coordinate of the j-th grid cell in the y-direction of the Cartesian coordinate system; This represents the coordinate of the j-th grid cell in the z-direction of the Cartesian coordinate system; This represents the width of the j-th grid cell in the x-direction of the Cartesian coordinate system; This represents the width of the j-th grid cell in the y-direction of the Cartesian coordinate system; This represents the width of the j-th grid cell in the z-direction of the Cartesian coordinate system; This represents the magnetic susceptibility value of the j-th grid cell. Additionally, the observation point information is... ;in, This represents the coordinates of the i-th observation point in the x-direction of the Cartesian coordinate system; This represents the coordinates of the i-th observation point in the y-direction of the Cartesian coordinate system; Let represent the coordinates of the i-th observation point in the z-direction of the Cartesian coordinate system.

[0018] To ensure that the cuboid mesh element can be subdivided into an integer number of standard cube sub-mesh elements without remainder, the three side lengths of each mesh element are checked iteratively. , , If there is an integer multiple relationship between the values, return to the user for re-sharding; if so, proceed to the next step.

[0019] The second step involves dividing the grid cells based on the information from the grid cells and the observation points, using a distance-adaptive algorithm to obtain several near-field and far-field grid cells. Extensive simulation experiments derived mathematically demonstrate that when the rectangular object is a cube, and the distance between the observation point and the center of the cube is half the sum of the lengths of all the cube's sides, the relative error of the point magnetic source approximation is less than 0.1%. Therefore, this embodiment uses a distance-adaptive algorithm to distinguish between near-field and far-field grid cells. Specifically: When the mesh element satisfies: ,and If the condition is met, then the grid cell is a far-field grid cell; otherwise, the grid cell is classified as a near-field grid cell.

[0020] The third step involves using the point magnetic source algorithm to calculate the kernel matrix element corresponding to any far-field region grid cell, and using the numerical integration method to calculate the kernel matrix element corresponding to any near-field region grid cell.

[0021] Specifically, for the far-field region grid cells, the j-th grid cell in the far-field region grid cells is first divided into k×m×n cube cells with length a, width b, and height c. Then, the kernel matrix elements corresponding to any far-field region grid cell are calculated using the point magnetic source algorithm. The kernel matrix elements are obtained by the following formula: ;in, Represents the elements of the kernel function matrix; The magnetic field strength is represented by t; t represents the magnetic field vector of the observation point relative to the center of the unit. This represents the minimum side length of the grid cell in the far-field region in the Cartesian coordinate system.

[0022] In the above formula, the minimum side length of the far-field mesh element in the Cartesian coordinate system. The expression is: ;in, This represents the minimum side length of the grid cell in the Cartesian coordinate system for the j-th far-field region.

[0023] Furthermore, the expression for the magnetic field vector t at the observation point relative to the center of the unit is: ; ; ; ;in, This represents the unit magnetic field component in the x-direction of the Cartesian coordinate system. This represents the unit magnetic field component in the y-direction of the Cartesian coordinate system. This represents the unit magnetic field component in the z-direction of the Cartesian coordinate system. Let represent the distance between the i-th observation point and the j-th cube element in the x-direction of the Cartesian coordinate system. Let represent the distance between the i-th observation point and the j-th cube element in the y-direction of the Cartesian coordinate system. represents the distance between the i-th observation point and the j-th cube element in the z-direction of the Cartesian coordinate system; k represents the quotient of the length of the cube element in the x-direction of the Cartesian coordinate system divided by the minimum size; m represents the quotient of the length of the cube element in the y-direction of the Cartesian coordinate system divided by the minimum size; n represents the quotient of the length of the cube element in the z-direction of the Cartesian coordinate system divided by the minimum size.

[0024] For near-field mesh elements, the kernel matrix elements are obtained using the following formula: ; Where ln represents the natural logarithm; This represents the definite integral operator.

[0025] The fourth step involves synthesizing the kernel matrix elements corresponding to the far-field and near-field grid cells to obtain the magnetic anomaly vector. Here, the magnetic anomaly vector is obtained by synthesizing the information of the far-field and near-field grid cells within the target region and the observation point information. Its expression is: ;in, Represents the magnetic anomaly vector; Indicates the number of grid cells, j∈ ; Indicates the number of observation points, i∈ .

[0026] To demonstrate the computational efficiency of the hybrid algorithm, this embodiment conducted a comparative experiment with three instances of different data sizes. The specific experimental setup is as follows: Example 1: The number of observation data is 1000, the number of model elements is 100,000, and all grid elements are cube elements.

[0027] Example 2: The number of observation data is 1000, the number of model units is 100,000, and the size of all grid units is cuboid, where the length is twice the width and the height is equal to the width.

[0028] Example 3: The number of observation data is 1000, the number of model units is 100,000, and the size of all grid units is cuboid, where the length is twice the width and the height is equal to the length.

[0029] Table 1 shows a comparison of the computation time of this embodiment with that of the traditional method under different model instances: Table 1 Comparison of computation time between the method of this embodiment and the traditional method under different model instances. Example One Example Two Example Three Conventional algorithm (integration calculation method) 54.16 seconds 54.16 seconds 54.16 seconds Method of the present embodiment 11.82 seconds 21.42 seconds 32.21 seconds The comparison shows that, for Example 1, the method of this embodiment improves computational efficiency by approximately 4.6 times compared to traditional techniques. For Example 2, the method of this embodiment improves computational efficiency by approximately 2.5 times compared to traditional techniques. For Example 3, the method of this embodiment improves computational efficiency by approximately 1.7 times compared to traditional techniques.

[0030] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes made based on the design principles of the present invention, or any non-creative modifications made thereon, shall fall within the scope of protection of the present invention.

Claims

1. A method for efficient simulation of magnetic anomalies based on a hybrid algorithm, characterized in that, Includes the following steps: Establish a Cartesian coordinate system for the target area and obtain information on any grid cell, observation point, and magnetic field strength within the target area; Based on the information of the grid cells and the observation point information, and using a distance adaptive algorithm to divide the grid cells, several near-field grid cells and several far-field grid cells are obtained. The kernel matrix elements corresponding to any far-field region grid cell are calculated using the point magnetic source algorithm, and the kernel matrix elements corresponding to any near-field region grid cell are calculated using the numerical integration method. The kernel matrix elements corresponding to the far-field region grid cells and the near-field region grid cells are synthesized to obtain the magnetic anomaly vector.

2. The efficient magnetic anomaly simulation method based on a hybrid algorithm according to claim 1, characterized in that, The information of the grid cell is ;in, This represents the coordinate of the j-th grid cell in the x-direction of the Cartesian coordinate system; This represents the coordinate of the j-th grid cell in the y-direction of the Cartesian coordinate system; This represents the coordinate of the j-th grid cell in the z-direction of the Cartesian coordinate system; This represents the width of the j-th grid cell in the x-direction of the Cartesian coordinate system; This represents the width of the j-th grid cell in the y-direction of the Cartesian coordinate system; This represents the width of the j-th grid cell in the z-direction of the Cartesian coordinate system; This represents the magnetic susceptibility value of the j-th grid cell.

3. The efficient magnetic anomaly simulation method based on a hybrid algorithm according to claim 2, characterized in that, The observation point information is: ;in, This represents the coordinates of the i-th observation point in the x-direction of the Cartesian coordinate system; This represents the coordinates of the i-th observation point in the y-direction of the Cartesian coordinate system; Let represent the coordinates of the i-th observation point in the z-direction of the Cartesian coordinate system.

4. The efficient magnetic anomaly simulation method based on a hybrid algorithm according to claim 3, characterized in that, Based on the information from the grid cells and the observation points, and using a distance-adaptive algorithm to divide the grid cells, several near-field grid cells and several far-field grid cells are obtained, including: If the mesh element satisfies: ,and If the condition is met, then the grid cell is a far-field grid cell; otherwise, the grid cell is a near-field grid cell. in, This represents the distance between the i-th observation point and the center point of the j-th grid cell.

5. The efficient magnetic anomaly simulation method based on a hybrid algorithm according to claim 4, characterized in that, Also includes: The j-th grid cell in the far-field region is divided into k×m×n cube cells with length a, width b, and height c. The kernel matrix element corresponding to any far-field region grid cell is calculated using the point magnetic source algorithm, and its expression is: ； in, Represents the elements of the kernel function matrix; The magnetic field strength is represented by t; t represents the magnetic field vector of the observation point relative to the center of the unit. This represents the minimum side length of the far-field region grid cell in the Cartesian coordinate system; The minimum side length of the far-field region grid cell in the Cartesian coordinate system The expression is: ;in, This represents the minimum side length of the grid cell in the Cartesian coordinate system for the j-th far-field region. The expression for the magnetic field vector t at the observation point with respect to the unit center is: ; ;in, This represents the unit magnetic field component in the x-direction of the Cartesian coordinate system. This represents the unit magnetic field component in the y-direction of the Cartesian coordinate system. This represents the unit magnetic field component in the z-direction of the Cartesian coordinate system. Let represent the distance between the i-th observation point and the j-th cube element in the x-direction of the Cartesian coordinate system. Let represent the distance between the i-th observation point and the j-th cube element in the y-direction of the Cartesian coordinate system. represents the distance between the i-th observation point and the j-th cube element in the z-direction of the Cartesian coordinate system; k represents the quotient of the length of the cube element in the x-direction of the Cartesian coordinate system divided by the minimum size; m represents the quotient of the length of the cube element in the y-direction of the Cartesian coordinate system divided by the minimum size; n represents the quotient of the length of the cube element in the z-direction of the Cartesian coordinate system divided by the minimum size.

6. The efficient magnetic anomaly simulation method based on a hybrid algorithm according to claim 5, characterized in that, The kernel matrix elements corresponding to any near-field region grid cell are calculated using the numerical integration method, and their expression is as follows: ;in, This represents the unit magnetic field component in the x-direction of the Cartesian coordinate system. This represents the unit magnetic field component in the y-direction of the Cartesian coordinate system. ln represents the unit magnetic field component in the z-direction of the Cartesian coordinate system; ln represents the natural logarithm. This represents the definite integral operator.

7. The efficient magnetic anomaly simulation method based on a hybrid algorithm according to claim 6, characterized in that, The kernel matrix elements corresponding to the far-field grid cells and the near-field grid cells are synthesized to obtain the magnetic anomaly vector, which is expressed as follows: ;in, Represents the magnetic anomaly vector; Indicates the number of grid cells, j∈ ; Indicates the number of observation points, i∈ .

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