Magnetization intensity vector inversion method and device under conditions of strong residual magnetism and rugged topography
By using tetrahedral mesh division and magnetization intensity vector inversion methods under undulating terrain and strong residual magnetism, the inversion accuracy and accuracy are improved.
Patent Information
- Application Number
- CN202311754367.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-12-19
- Publication Date
- 2025-06-20
AI Technical Summary
In the case of undulating terrain and strong residual magnetism, there are errors in the existing magnetic anomaly data inversion methods, especially regular hexahedral dissection cannot effectively fit complex terrain, and residual magnetism leads to poor magnetic inversion accuracy.
The tetrahedral mesh division and magnetization intensity vector inversion methods are used to determine the sensitivity matrix through the tetrahedral magnetic anomaly forward simulation method, the objective function of the magnetization intensity vector is constructed, and the objective function is optimized to obtain the inversion result.
Through the forward simulation of magnetic anomalies of the unstructured tetrahedral mesh, the simulation accuracy of complex morphological geological bodies and undulating terrain is improved, and the problem of poor inversion accuracy of magnetism under strong residual magnetism is solved, and the three-components of the total magnetization vector are directly inverted to reduce the impact of residual magnetism on inversion.
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Abstract
Description
Technical Field
[0001] The present disclosure relates to the field of inversion technology in geophysical exploration, and particularly to a method and device for inverting magnetization intensity vector in the case of strong remanent magnetism and undulating terrain. Background Art
[0002] Three-dimensional magnetic inversion plays an important role in obtaining information on the distribution of underground magnetic susceptibility and has been applied to various geological surveys, such as mineral exploration, geological and tectonic research, etc. Remanent magnetism and undulating terrain will have an important impact on the inversion accuracy of magnetic anomalies in magnetic prospecting. Regular rectangular block dissection and magnetic susceptibility inversion will introduce errors when dealing with situations with large undulations or strong remanent magnetism.
[0003] To solve the problem of inverting magnetic anomaly data in the case of undulating terrain and strong remanent magnetism, the following problems are usually encountered. First, the topographic features and geological structures that cause magnetic anomalies usually have arbitrary and complex three-dimensional curvatures and distributions. Structured polygon meshes, such as the currently popular rectangular block meshes, cannot effectively model and invert these complex structures. Especially in the inversion of magnetic anomalies with undulating terrain and strong remanent magnetism, regular hexahedron dissection cannot well fit the terrain. Second, remanent magnetism will change the magnitude and direction of the total magnetization intensity of the magnetic body, and the magnitude and direction of remanent magnetism are very difficult to determine. Currently, it can only be obtained through laboratory measurement of the oriented specimens collected in the field. In magnetic susceptibility inversion, generally, the direction of the total magnetization intensity is used as prior information, and the error of magnetic susceptibility inversion is relatively large when dealing with magnetic anomalies with strong remanent magnetism.
[0004] In related technologies, the methods for dealing with remanent magnetism mainly include total magnetization direction estimation, magnetic anomaly modulus inversion, and magnetization intensity vector inversion. The method of total magnetization direction estimation is suitable for isolated geological bodies and cannot handle the case of superimposed anomalies. Magnetic modulus inversion depends on the selection of magnetic anomaly modulus, and all current magnetic anomaly moduli depend on the magnetization direction of the magnetic body. Magnetic vector inversion can directly invert the three components of the magnetization intensity vector, but it has high computational consumption, strong inversion non-uniqueness, and complex algorithms combined with unstructured grids. Currently, there is no application of magnetic vector inversion in unstructured grid inversion. Summary of the Invention
[0005] To solve the above technical problems or at least partially solve the above technical problems, embodiments of the present disclosure provide a method and device for inverting magnetization intensity vector in the case of strong remanent magnetism and undulating terrain.
[0006] In a first aspect, embodiments of the present disclosure provide a method for inverting magnetization intensity vector in the case of strong remanent magnetism and undulating terrain, including:
[0007] Obtain the topographic data and magnetic anomaly data of the target survey area, and perform tetrahedral mesh generation on the inversion area corresponding to the target survey area, where the inversion area is determined based on the topographic data and magnetic anomaly data;
[0008] Based on the tetrahedral magnetic anomaly forward simulation method, determine the sensitivity matrix for inverting the magnetization intensity vector;
[0009] Based on the sensitivity matrix for inverting the magnetization intensity vector, construct the objective function of the magnetization intensity vector;
[0010] Optimize the objective function of the optimized magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion area.
[0011] In a possible implementation manner, the depth of the inversion area is less than or equal to the minimum side length of the target survey area.
[0012] In a possible implementation manner, the step of determining the sensitivity matrix for inverting the magnetization intensity vector based on the tetrahedral magnetic anomaly forward simulation method includes:
[0013] According to the three magnetic anomaly components generated by different tetrahedrons in the inversion area at different observation points, construct three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system;
[0014] Based on the three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system, determine the sensitivity matrix for inverting the magnetization intensity vector.
[0015] In a possible implementation manner, through the following expressions, according to the three magnetic anomaly components generated by different tetrahedrons in the inversion area at different observation points, construct three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system, including:
[0016]
[0017]
[0018]
[0019]
[0020]
[0021]
[0022]
[0023]
[0024]
[0025]
[0026]
[0027]
[0028]
[0029]
[0030] C ij = arctanh(λ ij )
[0031] Ω ij = sign(v i )arctanh(λ ij )
[0032]
[0033]
[0034] wherein, G X , G Y and G Z are respectively the sensitivity matrices of three mutually orthogonal magnetization intensity vector components in the Cartesian coordinate system, n is the number of ground observation points, m is the number of tetrahedrons into which the underground inversion area is divided, is the unit vector in the direction of the geomagnetic field, and are respectively the three components of the magnetic anomaly generated by the p-th tetrahedron at the q-th observation point when the total magnetization intensity vector is different from , is the unit vector of the outer normal of the i-th face of the tetrahedron, b ij is the relevant integral of the j-th edge of the i-th face of the tetrahedron, is the unit vector of the tangent of the j-th edge of the i-th face of the tetrahedron, r1 is the direction vector from the observation point to the first point of the j-th edge of the i-th face of the tetrahedron, L ij is the length of the j-th edge of the i-th face of the tetrahedron, and r1 and r2 are respectively the distances from the first point and the second point of the j-th edge of the i-th face of the tetrahedron to the observation point.
[0035] In a possible implementation manner, based on the sensitivity matrices of three mutually orthogonal magnetization intensity vector components in the Cartesian coordinate system, the sensitivity matrix for inverting the magnetization intensity vector is determined through the following expression:
[0036] G = [G X G Y G Z
[0037] where G is the sensitivity matrix for inverting the magnetization vector, G X , G Y and G Z are respectively the sensitivity matrices of three mutually orthogonal components of the magnetization vector in the Cartesian coordinate system.
[0038] In one possible implementation, based on the sensitivity matrix for inverting the magnetization vector, a target function of the magnetization vector is constructed through the following expression, including:
[0039] φ = (d - Gm) T W(d - Gm)
[0040] where φ is the value of the target function of the magnetization vector, G is the sensitivity matrix for inverting the magnetization vector, σ m is the standard deviation of the error of the m-th observed data, d is the forward magnetic anomaly of the observed data, and m is the inversion model.
[0041] In one possible implementation, optimizing the target function of the optimized magnetization vector to obtain the inversion result of the magnetization vector in the inversion region includes:
[0042] Let minimize the target function value φ to obtain the following linear equations:
[0043] G T WGm = G T W d
[0044] where G is the sensitivity matrix for inverting the magnetization vector, σ m is the standard deviation of the error of the m-th observed data, d is the forward magnetic anomaly of the observed data, and m is the inversion model,
[0045] Multiply both sides of the above linear equations by the preconditioning matrix P to obtain the following difference expression:
[0046] PG T WGΔm = PG T WΔd
[0047]
[0048] where Δm and Δd are respectively the correction amounts of the model parameters and the observed data in the iteration, C = 1, E is the identity matrix, ΔL is the distance between the model unit and the observed data point, and β = 1.0,
[0049] Solve the inversion model m in the difference expression.
[0050] In a second aspect, an embodiment of the present disclosure provides a magnetization intensity vector inversion device in the case of strong remanent magnetism and undulating terrain, including:
[0051] A meshing module, configured to obtain terrain data and magnetic anomaly data of a target survey area, and perform tetrahedral mesh meshing on an inversion area corresponding to the target survey area, where the inversion area is determined based on the terrain data and the magnetic anomaly data;
[0052] A determination module, configured to determine a sensitivity matrix for inverting the magnetization intensity vector based on the tetrahedral magnetic anomaly forward simulation method;
[0053] A construction module, configured to construct an objective function of the magnetization intensity vector based on the sensitivity matrix for inverting the magnetization intensity vector;
[0054] An optimization module, configured to optimize the objective function of the optimized magnetization intensity vector to obtain an inversion result of the magnetization intensity vector of the inversion area.
[0055] In a third aspect, an embodiment of the present disclosure provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, where the processor, the communication interface, and the memory complete mutual communication through the communication bus;
[0056] The memory is used to store a computer program;
[0057] The processor is configured to implement the above-mentioned magnetization intensity vector inversion method in the case of strong remanent magnetism and undulating terrain when executing the program stored on the memory.
[0058] In a fourth aspect, an embodiment of the present disclosure provides a computer-readable storage medium, on which a computer program is stored, and characterized in that the computer program implements the above-mentioned magnetization intensity vector inversion method when executed by a processor.
[0059] The above technical solutions provided by the embodiments of the present disclosure have at least some or all of the following advantages compared with the prior art:
[0060] The magnetization intensity vector inversion method under the conditions of strong remanent magnetism and undulating terrain in the embodiments of the present disclosure obtains the terrain data and magnetic anomaly data of the target survey area, and performs tetrahedral mesh division on the inversion area corresponding to the target survey area, wherein the inversion area is determined based on the terrain data and magnetic anomaly data; based on the tetrahedral magnetic anomaly forward simulation method, a sensitivity matrix for inverting the magnetization intensity vector is determined; based on the sensitivity matrix for inverting the magnetization intensity vector, an objective function of the magnetization intensity vector is constructed; the objective function for optimizing the magnetization intensity vector is optimized to obtain the inversion result of the magnetization intensity vector in the inversion area. The numerical forward simulation of magnetic anomalies using unstructured tetrahedral meshes can solve the problems of rectangular body meshes for complex-shaped geological bodies, undulating terrain, and simulation accuracy. The inversion of the magnetization intensity vector based on unstructured mesh division can solve the problem of poor inversion accuracy of magnetic susceptibility when the total magnetization direction deviates from the geomagnetic field direction under the condition of strong remanent magnetism. The influence of remanent magnetism on magnetic anomaly inversion is solved by directly inverting the three components of the total magnetization vector. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present disclosure and used together with the specification to explain the principles of the present disclosure.
[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure or the prior art, the following will briefly introduce the accompanying drawings required for use in the description of the embodiments or related technologies. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.
[0063] Figure 1 Schematically shows a schematic flow chart of the magnetization intensity vector inversion method under the conditions of strong remanent magnetism and undulating terrain according to an embodiment of the present disclosure;
[0064] Figure 2 Schematically shows a schematic diagram of the terrain and the positions of magnetic anomaly bodies of an experimental model according to an embodiment of the present disclosure;
[0065] Figure 3 Schematically shows a schematic diagram of the magnetic anomalies generated by the experimental model according to an embodiment of the present disclosure;
[0066] Figure 4 Schematically shows a schematic diagram of the tetrahedral division of the inversion area according to an embodiment of the present disclosure;
[0067] Figure 5 Schematically shows a schematic diagram of the inversion magnetization intensity scalar result of the experimental model according to an embodiment of the present disclosure;
[0068] Figure 6Schematic diagram showing the result of the inverted magnetization intensity vector of the experimental model according to an embodiment of the present disclosure;
[0069] Figure 7 Schematic block diagram showing the structure of a magnetization intensity vector inversion device in the case of strong remanence and undulating terrain according to an embodiment of the present disclosure;
[0070] Figure 8 Schematic block diagram showing the structure of an electronic device according to an embodiment of the present disclosure. Detailed implementation manners
[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure. Apparently, the described embodiments are some, but not all, of the embodiments of the present disclosure. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present disclosure without creative efforts shall fall within the scope of protection of the present disclosure.
[0072] Refer to Figure 1 , embodiments of the present disclosure provide a method for inverting the magnetization intensity vector in the case of strong remanence and undulating terrain, including the following steps:
[0073] S1. Obtain the terrain data and magnetic anomaly data of the target survey area, and perform tetrahedral mesh subdivision on the inversion area corresponding to the target survey area, where the inversion area is determined based on the terrain data and magnetic anomaly data.
[0074] In this embodiment, the depth of the inversion area is less than or equal to the minimum side length of the target survey area.
[0075] In this embodiment, the terrain data of the target survey area includes the geographical location information of the target survey area, including the eastward (X), northward (Y), and elevation (Z) coordinates, and the magnetic anomaly data is ΔT magnetic anomaly data with the unit of nT.
[0076] S2. Based on the tetrahedral magnetic anomaly forward simulation method, determine the sensitivity matrix for inverting the magnetization intensity vector.
[0077] S3. Based on the sensitivity matrix for inverting the magnetization intensity vector, construct the objective function of the magnetization intensity vector.
[0078] S4. Optimize the objective function for optimizing the magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion area.
[0079] In this embodiment, in step S2, when there is remanent magnetism, the total magnetization intensity vector and the direction of the geomagnetic field They are different, and it is necessary to construct a sensitivity matrix for inverting the magnetization intensity vector under the condition of strong remanent magnetism. The method for forward simulation of tetrahedral magnetic anomalies is used to determine the sensitivity matrix for inverting the magnetization intensity vector, including:
[0080] Construct three mutually orthogonal sensitivity matrices of magnetization intensity vector components in the Cartesian coordinate system according to the three magnetic anomaly components generated by different tetrahedrons in different observation points in the inversion area;
[0081] Based on the three mutually orthogonal sensitivity matrices of magnetization intensity vector components in the Cartesian coordinate system, determine the sensitivity matrix for inverting the magnetization intensity vector.
[0082] In this embodiment, through the following expressions, three mutually orthogonal sensitivity matrices of magnetization intensity vector components in the Cartesian coordinate system are constructed according to the three magnetic anomaly components generated by different tetrahedrons in different observation points in the inversion area, including:
[0083]
[0084]
[0085]
[0086]
[0087]
[0088]
[0089]
[0090]
[0091]
[0092]
[0093]
[0094]
[0095]
[0096]
[0097] C ij = arctanh(λ ij )
[0098] Ω ij = sign(vi ) arctanh(λ ij )
[0099]
[0100]
[0101] where G X , G Y and G Z are the sensitivity matrices of the three mutually orthogonal magnetization vector components in the Cartesian coordinate system, n is the number of ground observation points, m is the number of tetrahedrons into which the underground inversion region is divided, is the unit vector of the geomagnetic field direction, and are the three components of the magnetic anomaly generated by the p-th tetrahedron at the q-th observation point when the total magnetization vector is different from , is the unit vector of the outer normal of the i-th face of the tetrahedron, b ij is the relevant integral of the j-th edge of the i-th face of the tetrahedron, is the unit vector of the tangent of the j-th edge of the i-th face of the tetrahedron, r1 is the direction vector from the observation point to the first point of the j-th edge of the i-th face of the tetrahedron, L ij is the length of the j-th edge of the i-th face of the tetrahedron, r1 and r2 are the distances from the first point and the second point of the j-th edge of the i-th face of the tetrahedron to the observation point respectively, and the total magnetization vector is set to and
[0102] In this embodiment, through the following expression, based on the sensitivity matrices of the three mutually orthogonal magnetization vector components in the Cartesian coordinate system, the sensitivity matrix for inverting the magnetization vector is determined:
[0103] G = [G X G Y G Z
[0104] where G is the sensitivity matrix for inverting the magnetization vector, and G X , G Y and G Z are the sensitivity matrices of the three mutually orthogonal magnetization vector components in the Cartesian coordinate system respectively.
[0105] In this embodiment, in step S3, through the following expression, based on the sensitivity matrix for inverting the magnetization vector, the objective function of the magnetization vector is constructed, including:
[0106] φ = (d - Gm) T W(d - Gm)
[0107] Where φ is the objective function value of the magnetization intensity vector, G is the sensitivity matrix for inverting the magnetization intensity vector, σ m is the standard deviation of the error of the m-th observed data, d is the forward magnetic anomaly of the observed data, and m is the inversion model.
[0108] In this embodiment, in step S4, the optimization of the objective function of the optimized magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion area includes:
[0109] Let Minimize the objective function value φ to obtain the following linear equations:
[0110] G T WGm = G T W d
[0111] Where G is the sensitivity matrix for inverting the magnetization intensity vector, σ m is the standard deviation of the error of the m-th observed data, d is the forward magnetic anomaly of the observed data, and m is the inversion model,
[0112] Multiply both sides of the above linear equations by the preconditioning matrix P to obtain the following difference expression:
[0113] PG T WGΔm = PG T WΔd
[0114]
[0115] Where Δm and Δd are the correction amounts of the model parameters and the observed data in the iteration, C = 1, E is the unit matrix, ΔL is the distance between the model unit and the observed data point, and β = 1.0,
[0116] Solve for the inversion model m in the difference expression.
[0117] In this embodiment, the solution for the inversion model m in the difference expression includes:
[0118] First step, calculate G, let i = 0, m i = 0, where m i is a 3m×1 zero matrix;
[0119] Second step, d i = Gm i , Δd i = d - d i ;
[0120] Step 3: If ||Δd i || ≤ ε, then output the optimal solution m i , and the inversion ends; otherwise, proceed to Step 4;
[0121] Step 4: Let Δm i = 0, j = 0, r j = G T W T WΔd i ;
[0122] Step 5: z j = Pr j . If j = 0, then p j = z j , otherwise p j = z j + β j-1 p j-1 ;
[0123] Step 6: H j = G T W T WGp j , Δm i = Δm i + t j p j , r j+1 = r j - t j H j ;
[0124] Step 7: If ||p j || ≤ ε PCG , execute Step 9; otherwise, execute Step 8;
[0125] Step 8: j = j + 1, and execute Step 5;
[0126] Step 9: m i+1 = m i + Δm i ;
[0127] Step 10: If m i+1，n < m min，n , m i+1，n = m min，n ; if m i+1，n > m max，n , m i+1，n = m max，n , where n = 1, 2,..., N;
[0128] Step 11: i = i + 1, and execute Step 2.
[0129] This disclosure adopts unstructured grid magnetization intensity vector inversion. The selected preconditioning matrix must be applicable to both undulating terrain and magnetic anomaly data. When solving the linear equations by inversion, a preconditioning matrix is constructed using distance-weighted model constraints, that is, the distance between the measurement points and the model is negatively correlated with the contribution of the model to the anomaly, so as to avoid the inversion result from skinning or clustering near the measurement points. Therefore, the preconditioning matrix P is obtained through the following steps:
[0130] Assume the coefficient matrix G T WG decays according to the square of the distance between the field source and the measurement point, that is β
[0131] diag(G T WG) = CΔL -2β E
[0132] Use the preconditioning factor to offset the attenuation of the magnetic anomaly, then the preconditioning matrix is:[[]]END]]
[0133]
[0134] where C is a value used to adjust the amplitude of the preconditioning factor, and C = 1 is set in both theoretical models and practical applications. E is the identity matrix, ΔL is the distance between the model element and the observation data point, and β is a constant related to the magnetic anomaly attenuation rate. In the inversion of this disclosure, β = 1.0 is selected. This weighting function combines the distance characteristics of depth weighting and the generality of the sensitivity-based weighting function, and is not affected by the magnetization direction.
[0135] The magnetization intensity vector inversion method in the case of strong remanence and undulating terrain of this disclosure solves large-scale linear equations through the preconditioned conjugate gradient method. Using the preconditioning matrix can improve the condition number of the coefficient matrix in the linear equations and improve the convergence speed and convergence effect.
[0136] Taking Figure 2 the terrain data and the underground magnetic body model of the target survey area shown as an example, the application steps of the magnetization intensity vector inversion method in the case of strong remanence and undulating terrain of this disclosure are as follows:
[0137] In the first step, use the analytical forward modeling method to simulate the geophysical magnetic measurement data generated by the underground magnetic body. As Figure 2 shown, the central burial depth of the underground magnetic body is 300 meters, the shape is a cuboid, the length and width are both 500 meters, the height is 400 m, the total magnetization intensity is 1 A / m, the geomagnetic inclination is 45°, the geomagnetic declination is 0°, and the total magnetization inclination and total magnetization declination are 60° and 0° respectively. The terrain data is a three-dimensional view of the terrain, with a total of 2000 ground measurement points, and the entire survey area ranges from 2000 m × 2000 m. Figure 3 is the magnetic anomaly generated by the underground magnetic body model, and is the geophysical magnetic measurement data ΔT in actual work.
[0138] In the second step, unstructured tetrahedral mesh generation is performed on the inversion area, and the generated mesh generation result is as Figure 4 shown;
[0139] In the third step, the tetrahedral magnetic anomaly forward simulation method is adopted to calculate the sensitivity matrix G required for the inversion of the magnetization intensity vector;
[0140] In the fourth step, an objective function for the inversion of the magnetization intensity vector is constructed;
[0141] In the fifth step, the objective function is optimized, and the inversion results are as Figure 5 and 6 shown, Figure 5 is the magnitude of the scalar magnetization intensity obtained, and the areas with high magnetization intensity basically coincide with the positions of the forward model. Figure 6 is the result of the magnetization intensity vector obtained, and the direction of the magnetization intensity obtained by inversion is close to the true direction.
[0142] The magnetization intensity vector inversion method in the case of strong remanence and undulating terrain of the present disclosure adopts unstructured tetrahedral meshing and magnetization intensity vector inversion method, and can solve the magnetic anomaly inversion problem in the case of strong remanence and undulating terrain.
[0143] Referring to Figure 7 , the embodiment of the present disclosure provides a magnetization intensity vector inversion device in the case of strong remanence and undulating terrain, including:
[0144] A meshing module 11, configured to obtain terrain data and magnetic anomaly data of a target survey area, and perform tetrahedral meshing on an inversion area corresponding to the target survey area, where the inversion area is determined based on the terrain data and the magnetic anomaly data;
[0145] A determination module 12, configured to determine a sensitivity matrix for inverting the magnetization intensity vector based on the tetrahedral magnetic anomaly forward simulation method;
[0146] A construction module 13, configured to construct an objective function of the magnetization intensity vector based on the sensitivity matrix for inverting the magnetization intensity vector;
[0147] An optimization module 14, configured to optimize the objective function of the magnetization intensity vector to obtain an inversion result of the magnetization intensity vector of the inversion area.
[0148] The implementation processes of the functions and roles of each unit in the above device are specifically described in detail in the implementation processes of the corresponding steps in the above method, and will not be elaborated here.
[0149] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the descriptions in the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present invention. Those of ordinary skill in the art can understand and implement it without creative work.
[0150] In the above embodiments, any combination of the dissection module 11, the determination module 12, the construction module 13, and the optimization module 14 can be combined and implemented in one module, or any one of the modules can be split into multiple modules. Alternatively, at least part of the functions of one or more of these modules can be combined with at least part of the functions of other modules and implemented in one module. At least one of the dissection module 11, the determination module 12, the construction module 13, and the optimization module 14 can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on chip, a system on a substrate, a system in a package, an application specific integrated circuit (ASIC), or can be implemented by any other reasonable means such as hardware or firmware for integrating or packaging circuits, or can be implemented in any one of the three implementation modes of software, hardware, and firmware or in any appropriate combination of several of them. Alternatively, at least one of the dissection module 11, the determination module 12, the construction module 13, and the optimization module 14 can be at least partially implemented as a computer program module, and when the computer program module runs, the corresponding functions can be executed.
[0151] Referring to Figure 8 As shown, the electronic device provided by the embodiments of the present disclosure includes a processor 1110, a communication interface 1120, a memory 1130, and a communication bus 1140. Among them, the processor 1110, the communication interface 1120, and the memory 1130 communicate with each other through the communication bus 1140;
[0152] The memory 1130 is used to store a computer program;
[0153] When the processor 1110 executes the program stored in the memory 1130, it implements the magnetization intensity vector inversion method in the case of strong remanence and undulating terrain as follows:
[0154] Obtain the terrain data and magnetic anomaly data of the target survey area, and perform tetrahedral mesh dissection on the inversion area corresponding to the target survey area, where the inversion area is determined based on the terrain data and magnetic anomaly data;
[0155] Based on the tetrahedral magnetic anomaly forward simulation method, determine the sensitivity matrix for inverting the magnetization intensity vector;
[0156] Based on the sensitivity matrix for inverting the magnetization intensity vector, construct the objective function of the magnetization intensity vector;
[0157] Optimize the objective function for optimizing the magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion region.
[0158] The above communication bus 1140 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus 1140 can be divided into an address bus, a data bus, a control bus, etc. For the sake of convenience in representation, only a thick line is used in the figure, but it does not mean that there is only one bus or one type of bus.
[0159] The communication interface 1120 is used for communication between the above electronic device and other devices.
[0160] The memory 1130 can include a Random Access Memory (RAM), and can also include a non-volatile memory, such as at least one disk memory. Optionally, the memory 1130 can also be at least one storage device located far from the aforementioned processor 1110.
[0161] The above processor 1110 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.
[0162] Based on the same inventive concept, the fifth exemplary embodiment of the present disclosure also provides a computer-readable storage medium. A computer program is stored on the above-mentioned computer-readable storage medium, and when the computer program is executed by a processor, the magnetization intensity vector inversion method in the case of strong remanence and undulating terrain as described above is implemented.
[0163] The computer-readable storage medium may be included in the device / apparatus described in the above embodiments; or it may exist separately and not be assembled into the device / apparatus. The above computer-readable storage medium carries one or more programs, and when the one or more programs are executed, the magnetization intensity vector inversion method in the case of strong remanence and undulating terrain according to the embodiments of the present disclosure is implemented.
[0164] According to the embodiments of the present disclosure, the computer-readable storage medium may be a non-volatile computer-readable storage medium, for example, it may include but is not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In the present disclosure, the computer-readable storage medium may be any tangible medium that contains or stores a program, and the program can be used by or in combination with an instruction execution system, device, or device.
[0165] It should be noted that in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variation thereof is intended to cover a non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the element.
[0166] The above description is only the specific implementation manners of the present disclosure, enabling those skilled in the art to understand or implement the present disclosure. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.
Claims
1. A method for inverting the magnetization intensity vector in the case of strong remanent magnetism and undulating terrain, characterized in that, The method includes: Obtaining the topographic data and magnetic anomaly data of the target survey area, and performing tetrahedral mesh dissection on the inversion area corresponding to the target survey area, where the inversion area is determined based on the topographic data and magnetic anomaly data; Determining a sensitivity matrix for inverting the magnetization intensity vector based on the tetrahedral magnetic anomaly forward simulation method; Constructing an objective function of the magnetization intensity vector based on the sensitivity matrix for inverting the magnetization intensity vector; Optimizing the objective function for optimizing the magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion area.
2. The method according to claim 1, characterized in that, The depth of the inversion area is less than or equal to the minimum side length of the target survey area.
3. The method according to claim 1, characterized in that, The determining a sensitivity matrix for inverting the magnetization intensity vector based on the tetrahedral magnetic anomaly forward simulation method includes: Constructing three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system according to the three magnetic anomaly components generated by different tetrahedrons in the inversion area at different observation points; Determining a sensitivity matrix for inverting the magnetization intensity vector based on the three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system.
4. The method according to claim 3, characterized in that, Constructing three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system according to the three magnetic anomaly components generated by different tetrahedrons in the inversion area at different observation points through the following expressions, including: C ij = arctanh(λ ij ) Ω ij = sign(v i ) arctanh(λ ij ) Among them, G X , G Y and G Z are respectively the sensitivity matrices of three mutually orthogonal magnetization intensity vector components in the Cartesian coordinate system. n is the number of ground observation points, and m is the number of tetrahedrons into which the underground inversion region is divided. is the unit vector in the direction of the geomagnetic field. and are respectively the three components of the magnetic anomaly generated by the p-th tetrahedron at the q-th observation point when the total magnetization intensity vector is different from . is the unit vector of the outer normal of the i-th face of the tetrahedron, and b ij is the relevant integral of the j-th edge of the i-th face of the tetrahedron. is the unit vector of the tangent of the j-th edge of the i-th face of the tetrahedron. r1 is the direction vector from the observation point to the first point of the j-th edge of the i-th face of the tetrahedron. L ij is the length of the j-th edge of the i-th face of the tetrahedron. r1 and r2 are respectively the distances from the first point and the second point of the j-th edge of the i-th face of the tetrahedron to the observation point.
5. The method according to claim 1, characterized in that, Determining a sensitivity matrix for inverting the magnetization intensity vector based on the three mutually orthogonal sensitivity matrices of the magnetization intensity vector components in the Cartesian coordinate system through the following expressions: G = [G X G Y G Z Among them, G is the sensitivity matrix for inverting the magnetization vector, G X , G Y and G Z are respectively the sensitivity matrices of three mutually orthogonal components of the magnetization vector in the Cartesian coordinate system.
6. The method according to claim 1, characterized in that, Constructing an objective function of the magnetization intensity vector based on the sensitivity matrix for inverting the magnetization intensity vector through the following expressions, including: φ = (d - Gm) T W(d - Gm) where φ is the objective function value of the magnetization intensity vector, G is the sensitivity matrix for inverting the magnetization intensity vector, σ m is the standard deviation of the error of the m-th observed data, d is the forward magnetic anomaly of the observed data, and m is the inversion model.
7. According to the method described in claim 6, wherein, The optimizing the objective function for optimizing the magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion area includes: Let Minimize the objective function value φ to obtain the following system of linear equations: G T WGm = G T W d where G is the sensitivity matrix for inverting the magnetization vector, σ m is the standard deviation of the error of the m-th observed data, d is the forward magnetic anomaly of the observed data, and m is the inversion model. Multiplying both sides of the above linear equations by the preconditioning matrix P to obtain the following difference expression: PG T WGΔm = PG T WΔd where Δm and Δd are the correction amounts of the model parameters and observation data in the iteration, C = 1, E is the identity matrix, ΔL is the distance between the model unit and the observation data point, and β = 1.0, Solving for the inversion model m in the difference expression.
8. A magnetization intensity vector inversion device in the case of strong remanent magnetism and undulating terrain, characterized in that, It includes: A dissection module for obtaining the topographic data and magnetic anomaly data of the target survey area, and performing tetrahedral mesh dissection on the inversion area corresponding to the target survey area, where the inversion area is determined based on the topographic data and magnetic anomaly data; A determination module for determining a sensitivity matrix for inverting the magnetization intensity vector based on the tetrahedral magnetic anomaly forward simulation method; A construction module for constructing an objective function of the magnetization intensity vector based on the sensitivity matrix for inverting the magnetization intensity vector; An optimization module for optimizing the objective function for optimizing the magnetization intensity vector to obtain the inversion result of the magnetization intensity vector in the inversion area.
9. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete communication with each other through the communication bus; The memory is used for storing computer programs; The processor, when executing the programs stored on the memory, implements the method for inverting the magnetization intensity vector in the case of strong remanence and undulating terrain according to any one of claims 1-7.
10. A computer-readable storage medium, on which a computer program is stored, characterized in that, When the computer program is executed by a processor, it implements the method for inverting the magnetization intensity vector in the case of strong remanent magnetism and undulating terrain according to any one of claims 1-7.