Aerial magnetic field iteration method and exploration system for ferromagnetic body with arbitrary distribution of magnetic susceptibility

Abstract

The invention relates to an aviation magnetic field iteration method and exploration system for a ferromagnetic body with arbitrary distribution of magnetic susceptibility. The method comprises the following steps: respectively constructing a field source grid, an underground observation grid and an aviation observation grid, wherein the grid discretization is more flexible; constructing an arc tangent function and a logarithmic function related to cuboid units of the field source and the underground observation point according to the field source grid and the underground observation grid, and determining a kernel function coefficient of each cuboid of the underground observation grid according to the arc tangent function, the logarithmic function and a three-dimensional difference operator; firstly, a kernel function coefficient compression matrix is constructed through three-dimensional discrete convolution to quickly calculate an underground observation grid magnetic field, and then a two-dimensional compression kernel matrix is constructed through a vertical two-dimensional convolution accumulation mode to quickly calculate three components of an aviation observation grid magnetic field. The method has the advantages of high flexibility, high calculation precision and high efficiency, solves the problem of low iteration efficiency of an existing ferromagnetic body model method, and can meet the requirements of ferromagnetic body aviation exploration.

Description

Technical Field

[0001] This application relates to the field of airborne geophysical exploration technology, and in particular to an iterative method and exploration system for airborne magnetic fields of strongly magnetic bodies with arbitrary magnetic susceptibility distribution. Background Technology

[0002] Magnetic exploration is one of the most mature geophysical exploration methods. Especially with the development of instrument technology, airborne magnetic surveying instruments have become increasingly sophisticated. Compared with ground-based magnetic surveying, airborne magnetic surveying has significant advantages such as high efficiency, low cost, and no need for ground personnel to approach the exploration area, making it very suitable for mineral resource exploration in the vast western regions of my country. At the same time, the need to study rapid forward modeling methods and inversion imaging software that match large-scale airborne magnetic survey data has become increasingly urgent. Furthermore, in magnetic exploration, the influence of demagnetization is usually ignored, assuming that the magnetization direction is parallel to the local geomagnetic field, and that the effective magnetization intensity is the product of the local geomagnetic field and the magnetic susceptibility. This assumption is valid when the magnetic susceptibility is less than 0.1 SI. However, as the magnetic susceptibility increases, not only will the external magnetic field cause magnetization of the magnetic body, but it will also be affected by the magnetic field generated inside the magnetic body and by other surrounding magnetic bodies. This phenomenon is commonly referred to as the "demagnetization effect." The demagnetization effect can change the amplitude and direction of the external geomagnetic field, leading to distortion of the magnetic anomaly morphology. In particular, when the magnetic susceptibility is greater than 1.0 SI, the effect of demagnetization, whether considered or not, reaches 30%, which poses a great challenge to the processing and interpretation of magnetic measurement data.

[0003] Currently, numerical simulations based on airborne magnetic anomaly exploration methods using strong magnetic shapes suffer from problems such as large memory usage and low efficiency. Summary of the Invention

[0004] Therefore, it is necessary to provide an iterative method, system, computer equipment, and storage medium for airborne magnetic fields of strongly magnetic bodies with arbitrary magnetic susceptibility distribution, which can reduce the memory footprint of numerical simulation and improve computational efficiency, in order to address the above-mentioned technical problems.

[0005] An iterative method for the airborne magnetic field of a strongly magnetic body with arbitrary magnetic susceptibility distribution, the method comprising:

[0006] Information on the exploration target area and the distribution information of strongly magnetic geological bodies is obtained. The field source area and the underground observation area are uniformly discretized into several cuboid units along the x, y, and z directions, respectively, to obtain the corresponding field source grid and underground observation grid. The field source grid and the underground observation grid are independent of each other and have the same size.

[0007] Obtain aerial observation altitude information, and uniformly discretize the corresponding aerial observation area along the x and y directions into several rectangular units to obtain the aerial observation grid;

[0008] The magnetic susceptibility of each cuboid cell in the field source grid is assigned a value to establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution. The initial effective magnetization information is obtained based on the complex strong magnetic body model.

[0009] Based on the field source grid and the underground observation grid, an arctangent function and a logarithmic function related to the cuboid elements of the field source and the underground observation point are constructed. Based on the arctangent function, the logarithmic function, and the three-dimensional difference operator, the kernel function coefficients of each cuboid of the underground observation grid are determined. The values ​​of the kernel function coefficients can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size.

[0010] The expression for the three components of the magnetic field of the underground observation grid is obtained by three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration.

[0011] The expressions for the three components of the magnetic field of the airborne observation grid are obtained by vertical two-dimensional convolutional addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the airborne observation grid are quickly calculated, and the airborne magnetic field information is output.

[0012] An airborne magnetic field exploration system for strongly magnetic bodies with arbitrary magnetic susceptibility distribution, the system comprising:

[0013] The grid setting module is used to acquire information on the exploration target area and the distribution information of strongly magnetic geological bodies. It uniformly discretizes the field source area and the underground observation area into several cuboid units along the x, y, and z directions, respectively, to obtain the field source grid and the underground observation grid. The field source grid and the underground observation grid are independent of each other and have the same size. It acquires the aerial observation altitude information and uniformly discretizes the aerial observation area at the corresponding altitude into several rectangular units along the x and y directions to obtain the aerial observation grid.

[0014] The complex strong magnetic body model construction module is used to assign a value to the magnetic susceptibility of each cuboid unit of the field source grid, establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution, and obtain the initial effective magnetization intensity information based on the complex strong magnetic body model.

[0015] The kernel function coefficient determination module is used to construct arctangent and logarithmic functions related to the cuboid elements of the field source and the underground observation grid based on the field source grid and the underground observation grid, and to determine the kernel function coefficients of each cuboid of the underground observation grid based on the arctangent and logarithmic functions and the three-dimensional difference operator; the values ​​of the kernel function coefficients can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size;

[0016] The three-dimensional convolution module is used to obtain the expression of the three components of the magnetic field of the underground observation grid through three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration.

[0017] The two-dimensional convolution module is used to obtain the expression of the three components of the magnetic field of the airborne observation grid by vertical two-dimensional convolution addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively, and then the three components of the magnetic field of the airborne observation grid are quickly calculated to output the airborne magnetic field information.

[0018] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0019] Information on the exploration target area and the distribution information of strongly magnetic geological bodies is obtained. The field source area and the underground observation area are uniformly discretized into several cuboid units along the x, y, and z directions, respectively, to obtain the corresponding field source grid and underground observation grid. The field source grid and the underground observation grid are independent of each other and have the same size.

[0020] Obtain aerial observation altitude information, and uniformly discretize the corresponding aerial observation area along the x and y directions into several rectangular units to obtain the aerial observation grid;

[0021] The magnetic susceptibility of each cuboid cell in the field source grid is assigned a value to establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution. The initial effective magnetization information is obtained based on the complex strong magnetic body model.

[0022] Based on the field source grid and the underground observation grid, an arctangent function and a logarithmic function related to the cuboid elements of the field source and the underground observation point are constructed. Based on the arctangent function, the logarithmic function, and the three-dimensional difference operator, the kernel function coefficients of each cuboid of the underground observation grid are determined. The values ​​of the kernel function coefficients can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size.

[0023] The expression for the three components of the magnetic field of the underground observation grid is obtained by three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration.

[0024] The expressions for the three components of the magnetic field of the airborne observation grid are obtained by vertical two-dimensional convolutional addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the airborne observation grid are quickly calculated, and the airborne magnetic field information is output.

[0025] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0026] Information on the exploration target area and the distribution information of strongly magnetic geological bodies is obtained. The field source area and the underground observation area are uniformly discretized into several cuboid units along the x, y, and z directions, respectively, to obtain the corresponding field source grid and underground observation grid. The field source grid and the underground observation grid are independent of each other and have the same size.

[0027] Obtain aerial observation altitude information, and uniformly discretize the corresponding aerial observation area along the x and y directions into several rectangular units to obtain the aerial observation grid;

[0028] The magnetic susceptibility of each cuboid cell in the field source grid is assigned a value to establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution. The initial effective magnetization information is obtained based on the complex strong magnetic body model.

[0029] Based on the field source grid and the underground observation grid, an arctangent function and a logarithmic function related to the cuboid elements of the field source and the underground observation point are constructed. Based on the arctangent function, the logarithmic function, and the three-dimensional difference operator, the kernel function coefficients of each cuboid of the underground observation grid are determined. The values ​​of the kernel function coefficients can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size.

[0030] The expression for the three components of the magnetic field of the underground observation grid is obtained by three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration.

[0031] The expressions for the three components of the magnetic field of the airborne observation grid are obtained by vertical two-dimensional convolutional addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the airborne observation grid are quickly calculated, and the airborne magnetic field information is output.

[0032] The aforementioned iterative method and exploration system for airborne magnetic fields of strongly magnetic bodies with arbitrary magnetic susceptibility distribution constructs source grids, underground observation grids, and airborne observation grids, respectively, allowing for more flexible grid discretization. Based on the source grid and underground observation grid, arctangent and logarithmic functions related to the cuboid elements of the source and underground observation points are constructed. Kernel function coefficients for each cuboid in the underground observation grid are determined using the arctangent and logarithmic functions, along with a three-dimensional difference operator. These kernel function coefficients can be directly merged using the subtraction theorem of the arctangent and logarithmic functions, effectively reducing the number of arctangent and logarithmic functions in the integral of a single cuboid element. This significantly improves the computational efficiency of element integral coefficients while ensuring analytical solution accuracy in forward modeling. First, a kernel function coefficient compression matrix is ​​constructed through three-dimensional discrete convolution to quickly calculate the magnetic field of the underground observation grid. Then, a two-dimensional compression kernel matrix is ​​constructed through vertical two-dimensional convolution addition to quickly calculate the three components of the airborne observation grid's magnetic field. This obtains the airborne magnetic field distribution without requiring grid discretization in the air layer. The combination of three-dimensional and two-dimensional convolution improves computational efficiency. This invention has the advantages of high flexibility, high computational accuracy and high efficiency, and solves the problem of low iteration efficiency of existing strong magnetic body model methods, and can meet the needs of airborne exploration of strong magnetic bodies. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating an iterative method for an airborne magnetic field of a strongly magnetic body with arbitrary magnetic susceptibility distribution in one embodiment.

[0034] Figure 2 A schematic diagram of a sphere model designed in a specific embodiment;

[0035] Figure 3This is a schematic diagram comparing the analytical and numerical solutions of magnetic anomalies in a specific embodiment, where (a), (b), and (c) are schematic diagrams of the numerical solution, analytical solution, and absolute error in the x-direction, respectively; (d), (e), and (f) are schematic diagrams of the numerical solution, analytical solution, and absolute error in the y-direction, respectively; and (g), (h), and (i) are schematic diagrams of the numerical solution, analytical solution, and absolute error in the z-direction, respectively.

[0036] Figure 4 This is a structural block diagram of an airborne magnetic field exploration system for a strongly magnetic body with arbitrary magnetic susceptibility distribution, as shown in one embodiment.

[0037] Figure 5 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0039] In one embodiment, such as Figure 1 As shown, an iterative method for the airborne magnetic field of a strongly magnetic body with arbitrary magnetic susceptibility distribution is provided, including the following steps:

[0040] Step 102: Obtain information on the exploration target area and the distribution information of strong magnetic geological bodies. Discrete the source area and the underground observation area uniformly into several cuboid units along the x, y, and z directions, respectively, to obtain the source grid and the underground observation grid.

[0041] Existing technologies typically establish grids directly based on the target area, meaning the source and observation grids are integrated. In contrast, this application establishes separate grids for the source region and the underground observation region, with the source and observation grids being independent and of equal size. This allows the number of discrete grids in the source region and the underground observation region to be the same or different, making grid discretization more flexible.

[0042] Step 104: Obtain the aerial observation altitude information, and uniformly discretize the aerial observation area at the corresponding altitude into several rectangular units along the x and y directions to obtain the aerial observation grid.

[0043] The aerial observation area can be located directly above the source region or diagonally above the source region, making the observation area independent of the source region grid.

[0044] Step 106: Assign a value to the magnetic susceptibility of each cuboid cell in the field source grid, establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution, and obtain the initial effective magnetization information based on the complex strong magnetic body model.

[0045] The magnetic susceptibility of each small cuboid cell in the field source grid is assigned a value based on the magnetic susceptibility distribution characteristics of the exploration area, and the magnetic susceptibility within each cuboid cell is set to a constant. The magnetic susceptibility of each cuboid cell can be the same or different, thus characterizing a complex strong magnetic body model with arbitrary magnetic susceptibility distribution.

[0046] Effective magnetization calculation

[0047]

[0048] in, This indicates the magnetic susceptibility of a magnetic material. For the total magnetic field, It is the Earth's main magnetic field. It is a magnetic anomaly field.

[0049] Step 108: Construct arctangent and logarithmic functions related to the cuboid units of the field source and underground observation points based on the field source grid and the underground observation grid. Determine the kernel function coefficients of each cuboid of the underground observation grid based on the arctangent and logarithmic functions and the three-dimensional difference operator.

[0050] Based on the source grid and the underground observation grid, the arctangent function related to the cuboid elements of the source and underground observation points is constructed as follows:

[0051]

[0052] The logarithmic function associated with the cuboid elements of the field source and underground observation points is as follows:

[0053]

[0054] in, , , This represents the constructed arctangent function. Indicates the arctangent operation; , , Represents the constructed logarithmic function, Represents logarithmic operations; , , , , , , , ; Indicates the number is The center coordinates of the cuboid cells of the underground observation grid. , , , , , This represents the number of grid cells in the x, y, and z directions of the underground observation grid; Indicates the number is The center coordinates of the cuboid elements of the field source mesh. , , , , , This represents the number of grid cells in the x, y, and z directions of the field source grid; , and These represent the dimensions of the discrete cuboid element in the x, y, and z directions, respectively.

[0055] Based on the arctangent function, logarithmic function, and three-dimensional difference operator, the kernel function coefficients of each cuboid in the underground observation grid are determined as follows:

[0056]

[0057] in, , , , , , This represents the kernel function coefficients of each cuboid cell in the underground observation grid. Represents a three-dimensional difference operator. It represents pi (π).

[0058] The values ​​of the kernel function coefficients can be determined by the cuboid cell numbers of the source grid, the cuboid cell numbers of the underground observation grid, and the grid size, as inferred below:

[0059] According to the subtraction theorem of the arctangent function, we can obtain , , It can be represented as:

[0060]

[0061]

[0062]

[0063] The two-dimensional difference operator for the arctangent function can be expressed as:

[0064]

[0065]

[0066]

[0067] According to the recursive relation, , and It can be done , , Calculation, where

[0068]

[0069]

[0070]

[0071] Similarly, , and It can be done , , get:

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] In the formula

[0079]

[0080]

[0081] sign represents the sign function, and its specific expression is:

[0082]

[0083] Similar to the method of combining like terms in the arctangent function, the logarithmic function... , , The specific expressions for the three-dimensional difference operators are as follows:

[0084]

[0085]

[0086]

[0087] The arctangent and logarithmic functions constructed in this invention can be directly combined based on the subtraction theorem of arctangent and logarithmic functions, effectively reducing the number of arctangent and logarithmic functions in a single cuboid unit integral. Since the computational cost of arctangent and logarithmic functions in a computer is far greater than that of addition, subtraction, multiplication, and division, reducing the number of arctangent and logarithmic functions in a single cuboid unit integral effectively improves the efficiency of unit integration.

[0088] The method described in this application can effectively improve the calculation efficiency of the integral coefficients of cuboid elements while ensuring the accuracy of the analytical solution.

[0089] Step 110: The expression of the three components of the underground observation grid magnetic field is obtained by three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the underground observation grid magnetic field are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration.

[0090] The expression for the three components of the underground observation grid magnetic field obtained by three-dimensional discrete convolution is as follows:

[0091]

[0092]

[0093]

[0094] in, , , For the number Anomaly magnetic field of cuboid unit of underground observation grid The three components, , , The effective magnetization has three components;

[0095] The three-dimensional compressed kernel matrix is ​​constructed based on the kernel function coefficients as follows:

[0096]

[0097] in, The superscript indicates the rectangular cell number of the field source, and the subscript indicates the rectangular cell number of the underground observation point; given both the superscript and subscript numbers, the cell integral can be quickly calculated using the kernel function. Corresponding matrix element.

[0098] Based on the initial effective magnetization information, the three-dimensional effective magnetization matrix is ​​constructed as follows:

[0099]

[0100] in, The superscript indicates the number of the cuboid element of the field source;

[0101] Rapid calculation of the three components of the magnetic field of the underground observation grid:

[0102]

[0103] in, and These represent the three-dimensional forward and inverse Fourier transforms, respectively. Indicates the first part of the extracted matrix Each element.

[0104] The values ​​of the kernel function coefficients can be determined by the cuboid cell number of the source grid, the cuboid cell number of the underground observation grid, and the grid size.

[0105] The underground magnetic field information is obtained and iterative judgment is performed. The iterative formula is as follows:

[0106]

[0107]

[0108]

[0109] in, The background magnetic field value. For the first The magnetic anomaly value of the sub-forward modeling Through compact operator iteration The total magnetic field value of the second forward modeling It is iteration The total magnetic field value of the second forward modeling The magnetic susceptibility of a magnetic material. , It is an intermediate variable.

[0110] In this embodiment, the termination condition for iterative convergence can be expressed as:

[0111]

[0112] if If the convergence condition is met, the effective magnetization of the last iteration is output. Otherwise, update the effective magnetization and restart the cycle until the convergence condition is met.

[0113] Step 112: The expressions for the three components of the magnetic field of the airborne observation grid are obtained by vertical two-dimensional convolutional addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the airborne observation grid are quickly calculated, and the airborne magnetic field information is output.

[0114] At a given observation altitude The effective magnetization obtained by the above iterative process The expression for the three components of the magnetic field of the airborne observation grid is obtained by vertical two-dimensional convolutional summation:

[0115]

[0116]

[0117]

[0118] in, Indicates the number as aviation altitude The above number is The center coordinates of the rectangular cells in the aerial observation grid; , , For aviation altitude The above number is Anomalous magnetic field of rectangular unit in aerial observation grid The three components;

[0119] The two-dimensional compressed kernel matrix is ​​constructed based on the kernel function coefficients as follows:

[0120]

[0121] in, The superscript of the matrix element represents the cuboid cell number of the field source, and the subscript represents the cuboid cell number of the underground observation point. Given the superscript and subscript numbers, the values ​​can be quickly calculated from the kernel function coefficients.

[0122] Based on the effective magnetization information from the last iteration, a two-dimensional effective magnetization matrix is ​​constructed as follows:

[0123]

[0124] in, , , They represent dimensions as follows: , , Two-dimensional zero matrix; two-dimensional effective magnetization matrix The two-dimensional effective magnetization matrix has the same size as the two-dimensional compression kernel matrix. It is an extended matrix formed by the effective magnetization.

[0125] Rapid calculation of the three components of the magnetic field of the airborne observation grid yields the number of source layers for a given condition. Magnetic field of the airborne observation grid:

[0126]

[0127] in, and These represent two-dimensional forward and inverse Fourier transforms, respectively. Indicates the first part of the extracted matrix lines and Column elements.

[0128] The given observation height is obtained by accumulation. Total magnetic field observed from air:

[0129]

[0130] Will As output airborne magnetic field information.

[0131] This invention combines three-dimensional and two-dimensional convolution to obtain the distribution of airborne magnetic fields without requiring mesh discretization in the air layer, thereby improving computational efficiency and enabling the calculation of magnetic anomalies at any altitude.

[0132] In the aforementioned iterative method for airborne magnetic fields of strongly magnetic bodies with arbitrary magnetic susceptibility distribution, source grids, underground observation grids, and airborne observation grids are constructed separately, allowing for more flexible grid discretization. Based on the source grid and underground observation grid, arctangent and logarithmic functions related to the cuboid elements of the source and underground observation points are constructed. Kernel function coefficients for each cuboid in the underground observation grid are determined using the arctangent and logarithmic functions, along with a three-dimensional difference operator. These kernel function coefficients can be directly merged using the subtraction theorem of the arctangent and logarithmic functions, effectively reducing the number of arctangent and logarithmic functions in the integral of a single cuboid element. This significantly improves the computational efficiency of element integral coefficients while ensuring analytical solution accuracy in forward modeling. First, a kernel function coefficient compression matrix is ​​constructed using three-dimensional discrete convolution to quickly calculate the magnetic field of the underground observation grid. Then, a two-dimensional compression kernel matrix is ​​constructed using vertical two-dimensional convolution addition to quickly calculate the three components of the airborne observation grid's magnetic field. This method obtains the airborne magnetic field distribution without requiring grid discretization in the air layer. The combination of three-dimensional and two-dimensional convolution improves computational efficiency. This invention has the advantages of high flexibility, high computational accuracy and high efficiency, and solves the problem of low iteration efficiency of existing strong magnetic body model methods, and can meet the needs of airborne exploration of strong magnetic bodies.

[0133] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0134] In one specific embodiment, the following is designed: Figure 2 The spherical model shown is detailed below: The target region extends from -100m to 100m in both the x and y directions, and from 0m to 100m in the z direction. There are 200 prisms in both the x and y directions, and 100 prisms in the z direction. The center coordinates of the sphere are (0m, 0m, 50m). The sphere radius is 25m, the inner radius of the shell is 15m, and the magnetic susceptibility is 7.3SI. The source region is uniformly discretized into 25 × 25 × 25 cuboid units. The local geomagnetic field magnitude is 50000 nT, and the geomagnetic tilt angle is... Magnetic declination is .

[0135] The method for calculating aero-magnetic anomalies of strongly magnetic bodies implemented in this invention is programmed using the Fortran language. Figure 3 To compare the analytical and numerical solutions for magnetic anomalies, it was found that the analytical and numerical interpretations are identical in shape. Therefore, the absolute error between the analytical and numerical solutions was calculated. The maximum absolute error is less than two orders of magnitude of the field value, which can effectively measure the numerical accuracy of the present invention.

[0136] In one embodiment, such as Figure 4 As shown, an airborne magnetic field exploration system for strongly magnetic bodies with arbitrary magnetic susceptibility distribution is provided, including: a grid setting module 402, a complex strongly magnetic body model construction module 404, a kernel function coefficient determination module 406, a three-dimensional convolution module 408, and a two-dimensional convolution module 410, wherein:

[0137] The grid setting module 402 is used to acquire information on the exploration target area and the distribution information of strongly magnetic geological bodies. It uniformly discretizes the source area and the underground observation area into several cuboid units along the x, y, and z directions, respectively, to obtain the source grid and the underground observation grid. The source grid and the underground observation grid are independent of each other and have the same size. It acquires the aerial observation altitude information and uniformly discretizes the aerial observation area at the corresponding altitude into several rectangular units along the x and y directions to obtain the aerial observation grid.

[0138] The complex strong magnetic body model construction module 404 is used to assign the magnetic susceptibility of each cuboid element of the field source grid, establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution, and obtain the initial effective magnetization information based on the complex strong magnetic body model.

[0139] The kernel function coefficient determination module 406 is used to construct the arctangent function and logarithmic function related to the cuboid elements of the field source and underground observation points based on the field source grid and the underground observation grid. Based on the arctangent function, logarithmic function, and three-dimensional difference operator, the kernel function coefficient of each cuboid of the underground observation grid is determined. The value of the kernel function coefficient can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size.

[0140] The three-dimensional convolution module 408 is used to obtain the expression of the three components of the magnetic field of the underground observation grid through three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and perform iterative judgment to obtain the effective magnetization information of the last iteration.

[0141] The two-dimensional convolution module 410 is used to obtain the expression of the three components of the magnetic field of the airborne observation grid by vertical two-dimensional convolution addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively, and then the three components of the magnetic field of the airborne observation grid are quickly calculated to output the airborne magnetic field information.

[0142] The kernel function coefficient determination module 406 is also used to construct the arctangent function related to the cuboid elements of the field source and underground observation points based on the field source grid and the underground observation grid:

[0143]

[0144] The logarithmic function associated with the cuboid elements of the field source and underground observation points is as follows:

[0145]

[0146] in, , , It is the arctangent function. Indicates the arctangent operation; , , It is a logarithmic function. Represents logarithmic operations; , , , , , , , ; Indicates the number is The center coordinates of the cuboid cells of the underground observation grid. , , , , , This represents the number of grid cells in the x, y, and z directions of the underground observation grid; Indicates the number is The center coordinates of the cuboid elements of the field source mesh. , , , , , This represents the number of grid cells in the x, y, and z directions of the field source grid; , and These represent the dimensions of the discrete cuboid element in the x, y, and z directions, respectively.

[0147] The kernel function coefficient determination module 406 is also used to determine the kernel function coefficients of each cuboid of the underground observation grid based on the arctangent function, the logarithmic function, and the three-dimensional difference operator:

[0148]

[0149] in, , , , , , This represents the kernel function coefficients of each cuboid cell in the underground observation grid. Represents a three-dimensional difference operator. It represents pi (π).

[0150] The 3D convolution module 408 is also used to obtain the expression for the three components of the underground observation grid magnetic field through 3D discrete convolution, which is:

[0151]

[0152]

[0153]

[0154] in, , , For the number Anomaly magnetic field of cuboid unit of underground observation grid The three components, , , The effective magnetization has three components;

[0155] The three-dimensional compressed kernel matrix is ​​constructed based on the kernel function coefficients as follows:

[0156]

[0157] in, Superscripts indicate the cuboid cell number of the field source, and subscripts indicate the rectangular cell number of the underground observation point.

[0158] Based on the initial effective magnetization information, the three-dimensional effective magnetization matrix is ​​constructed as follows:

[0159]

[0160] in, The superscript indicates the number of the rectangular cuboid element of the field source;

[0161] Rapid calculation of the three components of the magnetic field of the underground observation grid:

[0162]

[0163] in, and These represent the three-dimensional forward and inverse Fourier transforms, respectively. Indicates the first part of the extracted matrix Each element.

[0164] The 3D convolution module 408 is also used to obtain underground magnetic field information and perform iterative judgments. The iterative formula is as follows:

[0165]

[0166]

[0167]

[0168] in, The background magnetic field value. For the first The magnetic anomaly value of the sub-forward modeling Through compact operator iteration The total magnetic field value of the second forward modeling It is iteration The total magnetic field value of the second forward modeling The magnetic susceptibility of a magnetic material. , As an intermediate variable;

[0169] The termination condition for iterative convergence is:

[0170]

[0171] if If the convergence condition is met, the effective magnetization of the last iteration is output. Otherwise, update the effective magnetization and recycle.

[0172] The two-dimensional convolution module 410 is also used to obtain the expression for the three components of the magnetic field of the airborne observation grid by vertical two-dimensional convolution addition:

[0173]

[0174]

[0175]

[0176] in, Indicates the number as aviation altitude The above number is The center coordinates of the rectangular cells in the aerial observation grid; , , For aviation altitude The above number is Anomalous magnetic field of rectangular unit in aerial observation grid The three components;

[0177] The two-dimensional compressed kernel matrix is ​​constructed based on the kernel function coefficients as follows:

[0178]

[0179] in, The superscript of the matrix element indicates the cuboid cell number of the field source, and the subscript indicates the cuboid cell number of the underground observation point.

[0180] Based on the effective magnetization information from the last iteration, a two-dimensional effective magnetization matrix is ​​constructed as follows:

[0181]

[0182] in, , , They represent dimensions as follows: , , A two-dimensional zero matrix;

[0183] Rapid calculation of the three components of the magnetic field of the airborne observation grid yields the number of source layers for a given condition. Magnetic field of the airborne observation grid:

[0184]

[0185] in, and These represent two-dimensional forward and inverse Fourier transforms, respectively. Indicates the first part of the extracted matrix lines and Column elements.

[0186] The two-dimensional convolution module 410 is also used to obtain the total airborne magnetic field at a given observation altitude by accumulation:

[0187]

[0188] Will As output airborne magnetic field information.

[0189] Specific limitations regarding the airborne magnetic field exploration system for strongly magnetic bodies with arbitrary magnetic susceptibility distribution can be found in the limitations of the iterative method for airborne magnetic fields of strongly magnetic bodies with arbitrary magnetic susceptibility distribution mentioned above, and will not be repeated here. Each module in the aforementioned airborne magnetic field exploration system for strongly magnetic bodies with arbitrary magnetic susceptibility distribution can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0190] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 5As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage medium. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements an iterative method for the airborne magnetic field of a strongly magnetic body with arbitrary magnetic susceptibility distribution. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0191] Those skilled in the art will understand that Figure 5 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0192] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps in the above method embodiment.

[0193] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0194] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0195] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0196] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An iterative method for the airborne magnetic field of a strongly magnetic body with arbitrary magnetic susceptibility distribution, characterized in that, The method includes: Information on the exploration target area and the distribution information of strongly magnetic geological bodies is obtained. The field source area and the underground observation area are uniformly discretized into several cuboid units along the x, y, and z directions, respectively, to obtain the corresponding field source grid and underground observation grid. The field source grid and the underground observation grid are independent of each other and have the same size. Obtain aerial observation altitude information, and uniformly discretize the corresponding aerial observation area along the x and y directions into several rectangular units to obtain the aerial observation grid; The magnetic susceptibility of each cuboid cell in the field source grid is assigned a value to establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution. The initial effective magnetization information is obtained based on the complex strong magnetic body model. Based on the field source grid and the underground observation grid, an arctangent function and a logarithmic function related to the cuboid elements of the field source and the underground observation point are constructed. Based on the arctangent function, the logarithmic function, and the three-dimensional difference operator, the kernel function coefficients of each cuboid of the underground observation grid are determined. The values ​​of the kernel function coefficients can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size. The expression for the three components of the magnetic field of the underground observation grid is obtained by three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration. The expressions for the three components of the magnetic field of the airborne observation grid are obtained by vertical two-dimensional convolutional addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the airborne observation grid are quickly calculated, and the airborne magnetic field information is output.

2. The method according to claim 1, characterized in that, Based on the source grid and the underground observation grid, construct the arctangent function and logarithmic function related to the cuboid elements of the source and underground observation points, including: Based on the source grid and the underground observation grid, the arctangent function related to the cuboid elements of the source and underground observation points is constructed as follows: The logarithmic function associated with the cuboid elements of the field source and underground observation points is as follows: in, , , This represents the constructed arctangent function. Indicates the arctangent operation; , , Represents the constructed logarithmic function, Represents logarithmic operations; , , , , , , , ; Indicates the number is The center coordinates of the cuboid cells of the underground observation grid. , , , , , The number of grid cells in the x, y, and z directions of the underground observation grid; Indicates the number is The center coordinates of the cuboid elements of the field source mesh. , , , , , The number of grid cells in the x, y, and z directions of the field source grid; , and These represent the dimensions of the discrete cuboid element in the x, y, and z directions, respectively.

3. The method according to claim 2, characterized in that, The kernel function coefficients of each cuboid in the underground observation grid are determined based on the arctangent function, the logarithmic function, and the three-dimensional difference operator, including: Based on the arctangent function, the logarithmic function, and the three-dimensional difference operator, the kernel function coefficients of each cuboid in the underground observation grid are determined as follows: in, , , , , , This represents the kernel function coefficients of each cuboid cell in the underground observation grid. Represents a three-dimensional difference operator. It represents pi (π).

4. The method according to claim 3, characterized in that, The expressions for the three components of the underground observation grid magnetic field are obtained through three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the underground observation grid magnetic field are rapidly calculated, including: The expression for the three components of the underground observation grid magnetic field obtained by three-dimensional discrete convolution is as follows: in, , , For the number Anomaly magnetic field of cuboid unit of underground observation grid The three components, , , The effective magnetization has three components; Based on the kernel function coefficients, the three-dimensional compressed kernel matrix is ​​constructed as follows: in, Superscripts indicate the cuboid cell number of the field source, and subscripts indicate the rectangular cell number of the underground observation point. Based on the initial effective magnetization information, a three-dimensional effective magnetization matrix is ​​constructed as follows: in, The superscript indicates the number of the rectangular cuboid element of the field source; The three components of the magnetic field of the underground observation grid are calculated quickly: in, and These represent the three-dimensional forward and inverse Fourier transforms, respectively. Indicates the first part of the extracted matrix Each element.

5. The method according to claim 4, characterized in that, The underground magnetic field information is obtained and iteratively evaluated to obtain the effective magnetization information for the last iteration, including: The underground magnetic field information is obtained and iterative judgment is performed. The iterative formula is as follows: in, The background magnetic field value. For the first The magnetic anomaly value of the sub-forward modeling Through compact operator iteration The total magnetic field value of the second forward modeling It is iteration The total magnetic field value of the second forward modeling The magnetic susceptibility of a magnetic material. , As an intermediate variable; The termination condition for iterative convergence is: if If the convergence condition is met, the effective magnetization of the last iteration is output. Otherwise, update the effective magnetization and recycle.

6. The method according to claim 5, characterized in that, The expressions for the three components of the magnetic field of the airborne observation grid are obtained by vertical two-dimensional convolutional summation. Based on the kernel function coefficients and the effective magnetization information from the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the airborne observation grid are rapidly calculated, including: The expression for the three components of the magnetic field of the airborne observation grid is obtained by vertical two-dimensional convolutional summation: in, Indicates the number as aviation altitude The above number is The center coordinates of the rectangular cells in the aerial observation grid; , , For aviation altitude The above number is Anomalous magnetic field of rectangular unit in aerial observation grid The three components; Based on the kernel function coefficients, a two-dimensional compressed kernel matrix is ​​constructed as follows: in, The superscript of the matrix element indicates the cuboid cell number of the field source, and the subscript indicates the cuboid cell number of the underground observation point. Based on the effective magnetization information from the last iteration, a two-dimensional effective magnetization matrix is ​​constructed as follows: in, , , They represent dimensions as follows: , , A two-dimensional zero matrix; The three components of the magnetic field of the airborne observation grid are quickly calculated to obtain the given number of source layers. Magnetic field of the airborne observation grid: in, and These represent two-dimensional forward and inverse Fourier transforms, respectively. Indicates the first part of the extracted matrix lines and Column elements.

7. The method according to claim 6, characterized in that, By rapidly calculating the three components of the magnetic field of the aforementioned airborne observation grid, a given number of source layers can be obtained. Following the magnetic field of the airborne observation grid, it also includes: The total magnetic field observed from air at a given observation altitude is obtained by summing: Will As output airborne magnetic field information.

8. An airborne magnetic field exploration system for strongly magnetic bodies with arbitrary magnetic susceptibility distribution, characterized in that, The system includes: The grid setting module is used to acquire information on the exploration target area and the distribution information of strongly magnetic geological bodies. It uniformly discretizes the field source area and the underground observation area into several cuboid units along the x, y, and z directions, respectively, to obtain the field source grid and the underground observation grid. The field source grid and the underground observation grid are independent of each other and have the same size. It acquires the aerial observation altitude information and uniformly discretizes the aerial observation area at the corresponding altitude into several rectangular units along the x and y directions to obtain the aerial observation grid. The complex strong magnetic body model construction module is used to assign a value to the magnetic susceptibility of each cuboid unit of the field source grid, establish a complex strong magnetic body model with arbitrary magnetic susceptibility distribution, and obtain the initial effective magnetization intensity information based on the complex strong magnetic body model. The kernel function coefficient determination module is used to construct arctangent and logarithmic functions related to the cuboid elements of the field source and the underground observation grid based on the field source grid and the underground observation grid, and to determine the kernel function coefficients of each cuboid of the underground observation grid based on the arctangent and logarithmic functions and the three-dimensional difference operator; the values ​​of the kernel function coefficients can be determined by the cuboid element number of the field source grid, the cuboid element number of the underground observation grid, and the grid size; The three-dimensional convolution module is used to obtain the expression of the three components of the magnetic field of the underground observation grid through three-dimensional discrete convolution. Based on the kernel function coefficients and the initial effective magnetization information, a three-dimensional compressed kernel matrix and a three-dimensional effective magnetization matrix are constructed respectively. Then, the three components of the magnetic field of the underground observation grid are quickly calculated to obtain the underground magnetic field information and iteratively judged to obtain the effective magnetization information of the last iteration. The two-dimensional convolution module is used to obtain the expression of the three components of the magnetic field of the airborne observation grid by vertical two-dimensional convolution addition. Based on the kernel function coefficients and the effective magnetization information of the last iteration, a two-dimensional compressed kernel matrix and a two-dimensional effective magnetization matrix are constructed respectively, and then the three components of the magnetic field of the airborne observation grid are quickly calculated to output the airborne magnetic field information.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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