A physical property inversion method for large-area aeromagnetic modulus data

Abstract

The present invention provides a method for inverting the physical properties of large-area aeromagnetic modulus data, and relates to the technical field of data processing. The method comprises: irregularly partitioning the underground space to obtain a recursive hierarchical subdivision schematic diagram, constructing a multi-resolution grid structure through the recursive hierarchical subdivision schematic diagram to obtain a grid unit schematic diagram under spherical triangulation, and deriving an analytical formula for calculating the modulus response of recursive hierarchical spherical aeromagnetic data according to the grid unit schematic diagram under spherical triangulation to obtain an analytical expression for calculating the tetrahedral magnetic response, and obtaining the magnetic response of the spherical triangular prism unit. The present invention can obtain a stable inversion result by iteratively solving the total objective function of the physical property inversion of the magnetic modulus data, and overcomes the problem of constructing the magnetic structure of the entire large-scale study area under the influence of residual magnetism.

Description

Technical Field

[0001] The invention relates to the technical field of data processing, and in particular to a physical property inversion method for large-area aeromagnetic modulus data. Background Art

[0002] Aeromagnetic modulus data is weakly sensitive to magnetization direction. Physical property inversion can effectively overcome the influence of residual magnetism in the study area and accurately construct the magnetic distribution characteristics of underground space, thereby achieving the purpose of finding the target geological body. When performing physical property inversion of large-area aeromagnetic modulus data, in order to overcome the influence of the earth's curvature, the inversion problem is usually constructed and solved in spherical coordinates.

[0003] The current mainstream approach is to divide the spherical space into a regular grid using longitude and latitude grids and radial scales in spherical coordinates, and divide the spherical space into a combination of spherical prisms, namely, Tesseroid unit cell grids. However, in order to meet the needs of high-precision physical property inversion of large-area aeromagnetic modulus data, the existing methods have the following defects:

[0004] Based on the spherical coordinate gridding of the Tesseroid unit, the terrain corresponding to the grid center represents the terrain of the entire grid. Therefore, it is impossible to continuously fit the undulating terrain and there are gaps between adjacent grids. Due to the geometric characteristics of the Tesseroid unit itself, there is no strict analytical expression for its modulus response in external space, and a complex numerical integration method is required for approximate calculation. It is impossible to construct a multi-resolution or constant-resolution grid structure under the Tesseroid gridding, and it is difficult to meet the grid accuracy required for inversion. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a physical property inversion method for large-area aeromagnetic modulus data, which can more finely fit complex terrain and improve the terrain fitting accuracy.

[0006] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0007] In a first aspect, a method for inverting physical properties of large-area aeromagnetic modulus data comprises:

[0008] The underground space is irregularly divided to obtain a recursive hierarchical subdivision schematic diagram;

[0009] By recursively dividing the schematic diagram into subdivisions, a multi-resolution grid structure is constructed to obtain a schematic diagram of grid units under spherical triangulation;

[0010] According to the schematic diagram of the grid unit under the spherical triangulation, the analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data is derived to obtain the analytical expression for calculating the tetrahedral magnetic response, and the magnetic response of the spherical triangular prism unit is obtained;

[0011] According to the analytical expression of tetrahedral magnetic response calculation, the inversion equation of magnetic modulus data under recursive hierarchical spherical triangulation is constructed to obtain the analytical calculation formula of magnetic modulus data response under spherical triangulation;

[0012] The magnetic modulus data is obtained through the analytical calculation formula of the magnetic modulus data response under spherical triangulation, and the linear relationship between the magnetic modulus data and the effective magnetic susceptibility is constructed to obtain the overall objective function of the physical property inversion of the magnetic modulus data;

[0013] By iterating the total objective function of the inversion of the physical properties of the magnetic modulus data, the iterative solution of the inversion equation of the physical properties of the magnetic modulus data under the recursive graded spherical triangulation is obtained.

[0014] Preferably, the underground space is irregularly divided to obtain a recursive hierarchical detailed division schematic diagram, including:

[0015] The irregular subdivision of underground space is carried out by adopting the recursive hierarchical spherical triangulation method;

[0016] Place the icosahedron in spherical coordinates, with the north and south poles corresponding to a vertex of the icosahedron respectively, align one edge of the icosahedron with the meridian, and align it with the prime meridian to obtain an aligned icosahedron;

[0017] The 20 basic equilateral triangles of the aligned regular icosahedron are taken as the 0th level, and the midpoints of each side of the equilateral triangle of the previous level are connected to form 4 equilateral triangles of the next level, and recursive hierarchical subdivision is performed to obtain a recursive hierarchical subdivision schematic diagram.

[0018] Preferably, a multi-resolution grid structure is constructed by recursively and hierarchically subdividing the schematic diagram to obtain a grid unit schematic diagram under spherical triangulation, including:

[0019] Through the recursive hierarchical subdivision diagram, the geocentric radius of the small triangle facet vertices on the sphere, ground, and interface is mapped to the sphere, ground, and interface, and a primary resolution grid structure is constructed at the same level of subdivision;

[0020] Based on the primary resolution grid structure, the region is recursively and hierarchically subdivided to construct a multi-resolution grid structure, and a schematic diagram of the grid unit under spherical triangulation is obtained.

[0021] Preferably, according to the schematic diagram of the grid unit under the spherical triangulation, an analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data is derived to obtain an analytical expression for calculating the tetrahedral magnetic response, and the magnetic response of the spherical triangular prism unit is obtained, including:

[0022] According to the schematic diagram of the grid unit under spherical triangulation, the grid unit is a spherical triangular prism with triangular surface elements on the upper and lower surfaces, and through T ABC-AB'C' =T OABC -T OAB'C' Get the magnetic response of the grid unit; where: T OABC -T OAB'C' is the difference between the magnetic responses of two tetrahedrons with the same center, T ABC-AB'C' is the magnetic response of the grid cell;

[0023] In Cartesian coordinates, with point O as the origin, the Z axis pointing vertically upward, an object with a volume of v and uniform density, passes through The gravitational potential of the observation point P in the external space is calculated, where G is the gravitational constant, ρ is the density, and r is the distance between the density volume element and the observation point P;

[0024] Through Derivation is performed to obtain the external gravitational potential V and gravitational potential gradient of the tetrahedron and its gradient tensor The analytical formula of where r f 、r e are the vector from point P to a face ABC of the tetrahedron and the vector from point P to an edge CA of the tetrahedron, respectively. f 、E e are the tensor products of faces and edges, ω f , L e are two coefficients determined by the relative positions of point P and the surface and edge. where r i 、r j 、r k are the vectors from point P to vertices C, A, and B, and their magnitudes are r i 、r j 、r k , d ij is the length of side CA; n f is the external normal vector of face ABC; n1 and n2 are the two external normal vectors of edge CA, located on face ABC and face ACD respectively; n 1f 、n 2f are the external normal vectors of n1 and n2 on the surface ABC and surface ACD respectively;

[0025] According to the Poisson formula between gravitational potential and magnetic potential, we can get And combined with the gradient tensor The expression gives the tetrahedral magnetic component B x , B y , Bz The analytical expression of the tetrahedron magnetic response in spherical coordinates is obtained by coordinate transformation to obtain the magnetic response of the spherical triangular prism unit.

[0026] Preferably, according to the tetrahedron magnetic response calculation analytical expression, a recursive hierarchical spherical triangulation magnetic modulus data physical property inversion equation is constructed to obtain an analytical calculation formula for the magnetic modulus data response under spherical triangulation, including:

[0027] The analytical expression is calculated based on the tetrahedron magnetic response, through The analytical calculation formula of the magnetic modulus data response under spherical triangulation is obtained, where T a Represents magnetic anomaly vector data T a The modulus, B x , B y , B z The magnetic component data can be calculated by the analytical expression of the tetrahedron magnetic response calculation;

[0028] Preferably, the magnetic modulus data is obtained by an analytical calculation formula of the magnetic modulus data response under spherical triangulation, and a linear relationship between the magnetic modulus data and the effective magnetic susceptibility is constructed to obtain the overall objective function of the physical property inversion of the magnetic modulus data, including:

[0029] The magnetic modulus data is obtained by the analytical calculation formula of the magnetic modulus data response under spherical triangulation;

[0030] The effective magnetic susceptibility is obtained by X=μ0M / T0, where M is the effective magnetization intensity, T0 is the geomagnetic field intensity, and μ0 is the vacuum permeability;

[0031] By constructing a linear relationship between magnetic modulus data and effective magnetic susceptibility obs =F(m), where dobs is the data vector constructed from the magnetic modulus data, and F(m) represents the nonlinear forward operator;

[0032] According to the linear relationship, The total objective function of the inversion of the physical properties of magnetic modulus data is obtained, where W d is the data weighting matrix, W m is the model weight matrix, m apr is the initial model vector, and λ is used to balance the data fitting term φ d With the regularization term φ m The regularization parameter, W m Multiply three diagonal matrices: W m =W·W e Z, where W is a diagonal weight matrix; W eis the diagonal focusing constraint matrix considering the volume, which is used to generate non-smooth, focused inversion results; Z is the depth weighting matrix related to the radial depth in spherical coordinates, which is used to improve the resolution of the inversion results in radial depth. apr Can be constructed from prior information, and is set to m when there is no prior information apr =0.001.

[0033] Preferably, the total objective function of the inversion of the physical properties of the magnetic modulus data is iterated to obtain an iterative solution to the inversion equation of the physical properties of the magnetic modulus data under the recursive hierarchical spherical triangulation, including:

[0034] The total objective function of the inversion of the physical properties of the magnetic modulus data is linearized. When k iterations are performed, let m apr k =m k-1 , F(m) is linearized by Taylor series approximation, F(m k )≈F(m k-1 )+J k (m k -m k-1 ), where J k is the Jacobian matrix at the kth iteration,

[0035] pass The iterative solution form is: m k =m k-1 +Δm k , Where F(m) represents the nonlinear forward operator of magnetic modulus data, T a is the modulus data, B x , B y , B z are magnetic component data in different directions, W a is the data weighting matrix, W n is the model weight matrix, m apr is the initial model vector, λ is the regularization parameter, k is the current iteration number, m is the model vector to be calculated, k-1 is the previous iteration number, G x is the kernel matrix corresponding to the x component, G y is the kernel matrix corresponding to the y component, J k is the Jacobian matrix of the kth iteration, d as is the data vector, m qr is the reference model vector, Δm k is the k-th iteration model disturbance term, T is the transposition symbol, φ a is the data fitting term, φ m is the model constraint, is the k-1th iteration prediction data, G z , is the data weighted diagonal matrix, is the model weighted diagonal matrix, m k-1 is the k-1th model disturbance term.

[0036] In a second aspect, a physical property inversion device for large-area aeromagnetic modulus data comprises:

[0037] The acquisition module is used to perform irregular division of underground space to obtain a recursive hierarchical division schematic diagram; construct a multi-resolution grid structure through the recursive hierarchical division schematic diagram to obtain a grid unit schematic diagram under spherical triangulation; derive an analytical formula for calculating the modulus response of recursive hierarchical spherical aeromagnetic data according to the grid unit schematic diagram under spherical triangulation to obtain an analytical expression for calculating the tetrahedral magnetic response, and obtain the magnetic response of the spherical triangular prism unit;

[0038] The processing module is used to calculate the analytical expression of the tetrahedral magnetic response and construct the inversion equation of the physical property of the magnetic modulus data under the recursive hierarchical spherical triangulation to obtain the analytical calculation formula of the magnetic modulus data response under the spherical triangulation; obtain the magnetic modulus data through the analytical calculation formula of the magnetic modulus data response under the spherical triangulation, and construct the linear relationship between the magnetic modulus data and the effective magnetic susceptibility to obtain the total objective function of the inversion of the physical property of the magnetic modulus data; iterate the total objective function of the inversion of the physical property of the magnetic modulus data to obtain the iterative solution of the inversion equation of the physical property of the magnetic modulus data under the recursive hierarchical spherical triangulation

[0039] According to a third aspect, a computing device includes:

[0040] one or more processors;

[0041] The storage device is used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0042] In a fourth aspect, a computer-readable storage medium stores a program, and the program implements the above method when executed by a processor.

[0043] The above solution of the present invention includes at least the following beneficial effects:

[0044] By recursively hierarchical spherical triangulation of underground space, complex terrain can be fitted more finely and the accuracy of terrain fitting can be improved. The constructed multi-resolution grid structure allows the physical properties of underground space to be analyzed at different scales, improving the multi-resolution analysis capability. The analytical formula for calculating the modulus response of recursively hierarchical spherical aeromagnetic data is derived, which can provide accurate calculation of tetrahedral magnetic response and improve the accuracy of magnetic modulus data calculation. Efficient physical property inversion: The physical property parameters of underground materials can be efficiently inverted through the constructed magnetic modulus data physical property inversion equation. The constructed linear relationship between magnetic modulus data and effective magnetic susceptibility simplifies the complexity of the inversion problem, making the solution process more intuitive and efficient. By iteratively solving the total objective function of the physical property inversion of magnetic modulus data, stable inversion results can be obtained, overcoming the problem of constructing the magnetic structure of the entire large-scale study area under the influence of residual magnetism. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of a method for inverting physical properties of large-area aeromagnetic modulus data provided by an embodiment of the present invention.

[0046] Figure 2 It is a schematic diagram of a control device of a physical property inversion method of large-area aeromagnetic modulus data according to the present invention.

[0047] Figure 3 A regular icosahedron of the present invention is placed in spherical coordinates, with the north and south poles corresponding to a vertex of the regular icosahedron respectively. With reference to the study area, one edge of the regular icosahedron is aligned with a suitable meridian, or directly aligned with the prime meridian.

[0048] Figure 4 It is a schematic diagram of a grid unit under spherical triangulation of the present invention.

[0049] Figure 5 It is a schematic diagram of the magnetic response calculation of the spherical triangular prism unit of the present invention.

[0050] Figure 6 It is a schematic diagram of a tetrahedron under Cartesian coordinates of the present invention.

[0051] Figure 7 The present invention uses 20 basic equilateral triangles of a regular icosahedron as the 0th level, connects the midpoints of each side of the equilateral triangles of the previous level to form 4 equilateral triangles of the next level, and performs recursive hierarchical subdivision.

[0052] Figure 8 It is a schematic diagram of the present invention mapping all small triangular face element vertices onto a spherical surface, the ground or an interface based on the geocentric radius of the vertices on the spherical surface, the ground or the interface. DETAILED DESCRIPTION

[0053] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0054] like Figure 1 As shown, an embodiment of the present invention provides a method for inverting physical properties of large-area aeromagnetic modulus data, the method comprising:

[0055] Step 11, irregularly dividing the underground space to obtain a recursive hierarchical detailed division schematic diagram;

[0056] Step 12, constructing a multi-resolution grid structure by recursively and hierarchically subdividing the schematic diagram to obtain a grid unit schematic diagram under spherical triangulation;

[0057] Step 13, according to the schematic diagram of the grid unit under the spherical triangulation, derive the analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data to obtain the analytical expression for calculating the tetrahedral magnetic response, and obtain the magnetic response of the spherical triangular prism unit;

[0058] Step 14, based on the tetrahedron magnetic response calculation analytical expression, construct a recursive hierarchical spherical triangulation magnetic modulus data physical property inversion equation to obtain an analytical calculation formula for the magnetic modulus data response under spherical triangulation;

[0059] Step 15, obtaining magnetic modulus data through an analytical calculation formula of the magnetic modulus data response under spherical triangulation, and constructing a linear relationship between the magnetic modulus data and the effective magnetic susceptibility to obtain the overall objective function of the physical property inversion of the magnetic modulus data;

[0060] Step 16, iterating the total objective function of the inversion of the physical properties of the magnetic modulus data to obtain an iterative solution to the inversion equation of the physical properties of the magnetic modulus data under the recursive graded spherical triangulation.

[0061] In the embodiment of the present invention, by performing irregular subdivision of the underground space, the actual geological structure, especially the complex terrain and geological structure, can be simulated more accurately, and an accurate basic model is provided for the subsequent calculation of magnetic modulus data and physical property inversion; constructing a multi-resolution grid structure can realize detailed analysis of different scales of the underground space, and improve the spatial resolution and analysis accuracy of the model; deriving an analytical formula for the modulus response of recursively graded spherical aeromagnetic data, and obtaining the magnetic response of the spherical triangular prism unit, is helpful to accurately simulate and analyze the magnetic field distribution of the underground space; by constructing a magnetic field under recursive graded spherical triangulation, The modulus data physical property inversion equation can accurately link the observed magnetic modulus data with the physical property parameters of underground materials, and accurately infer the distribution and properties of underground materials; construct a linear relationship between magnetic modulus data and effective magnetic susceptibility, simplify the complexity of the physical property inversion problem, and help optimize the solution by obtaining the total objective function of the magnetic modulus data physical property inversion; by iteratively solving the total objective function, the exact solution of the magnetic modulus data physical property inversion equation under recursive graded spherical triangulation can be obtained, and stable inversion results can be obtained, overcoming the influence of residual magnetism and constructing the magnetic structure of the entire large-scale study area.

[0062] In a preferred embodiment of the present invention, the underground space is irregularly divided to obtain a recursive hierarchical detailed division schematic diagram, including:

[0063] The irregular subdivision of underground space is carried out by adopting the recursive hierarchical spherical triangulation method;

[0064] Place the icosahedron in spherical coordinates, with the north and south poles corresponding to a vertex of the icosahedron respectively, align one edge of the icosahedron with the meridian, and align it with the prime meridian to obtain an aligned icosahedron;

[0065] The 20 basic equilateral triangles of the aligned regular icosahedron are taken as the 0th level, and the midpoints of each side of the equilateral triangle of the previous level are connected to form 4 equilateral triangles of the next level, and recursive hierarchical subdivision is performed to obtain a recursive hierarchical subdivision schematic diagram.

[0066] In the embodiment of the present invention, Figure 3 , place a regular icosahedron in spherical coordinates, with the north and south poles corresponding to a vertex of the regular icosahedron respectively. Referring to the study area, align one edge of the regular icosahedron with a suitable meridian, or directly with the prime meridian; aligning the regular icosahedron with the spherical coordinates allows the entire segmentation process to be carried out in a unified coordinate system, simplifying the data processing and analysis process and avoiding the complexity and errors caused by coordinate system conversion, such as Figure 7, take the 20 basic equilateral triangles of the regular icosahedron as the 0th level, connect the midpoints of each side of the equilateral triangle of the previous level to form 4 equilateral triangles of the next level for recursive hierarchical subdivision. Through recursive hierarchical subdivision, the fineness of the subdivision can be gradually increased as needed. The recursive hierarchical spherical triangulation method is used for irregular subdivision of underground space, which can more accurately fit the complex underground terrain and geological structure.

[0067] In a preferred embodiment of the present invention, a multi-resolution grid structure is constructed by recursively and hierarchically subdividing the schematic diagram to obtain a grid unit schematic diagram under spherical triangulation, including:

[0068] Through the recursive hierarchical subdivision diagram, the geocentric radius of the small triangle facet vertices on the sphere, ground, and interface is mapped to the sphere, ground, and interface, and a primary resolution grid structure is constructed at the same level of subdivision;

[0069] Based on the primary resolution grid structure, the region is recursively and hierarchically subdivided to construct a multi-resolution grid structure, and a schematic diagram of the grid unit under spherical triangulation is obtained.

[0070] In the embodiment of the present invention, Figure 8 , according to the geocentric radius of all small triangular face vertices on the sphere, ground or interface, they are mapped to the sphere, ground or interface, which can accurately map and locate. At the same level of subdivision, a nearly constant resolution grid structure can be constructed; in order to meet the needs of fine physical property inversion in the study area, users can perform deeper recursive hierarchical subdivision of a certain area to construct a multi-resolution grid structure that meets the requirements, with flexible multi-resolution analysis.

[0071] In a preferred embodiment of the present invention, according to the schematic diagram of the grid unit under the spherical triangulation, an analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data is derived to obtain an analytical expression for calculating the tetrahedral magnetic response, and the magnetic response of the spherical triangular prism unit is obtained, including:

[0072] According to the schematic diagram of the grid unit under spherical triangulation, the grid unit is a spherical triangular prism with triangular surface elements on the upper and lower surfaces, and through T ABC-AB'C' =T OABC -T OAB'C' Get the magnetic response of the grid unit; where: T OABC -T OAB'C' is the difference between the magnetic responses of two tetrahedrons with the same center, T ABC-AB'C' is the magnetic response of the grid cell;

[0073] In Cartesian coordinates, with point O as the origin, the Z axis pointing vertically upward, an object with a volume of v and uniform density, passes through The gravitational potential of the observation point P in the external space is calculated, where G is the gravitational constant, ρ is the density, and r is the distance between the density volume element and the observation point P;

[0074] Through Derivation is performed to obtain the external gravitational potential V and gravitational potential gradient of the tetrahedron and its gradient tensor The analytical formula of where r f 、r e are the vector from point P to a face ABC of the tetrahedron and the vector from point P to an edge CA of the tetrahedron, respectively. f 、E e are the tensor products of faces and edges, ω f , L e are two coefficients determined by the relative positions of point P and the surface and edge. where r i 、r j 、r k are the vectors from point P to vertices C, A, and B, and their magnitudes are r i 、r j 、r k , d ij is the length of side CA; n f is the external normal vector of face ABC; n1 and n2 are the two external normal vectors of edge CA, located on face ABC and face ACD respectively; n 1f 、n 2f are the external normal vectors of n1 and n2 on the surface ABC and surface ACD respectively;

[0075] According to the Poisson formula between gravitational potential and magnetic potential, we can get And combined with the gradient tensor The expression gives the tetrahedral magnetic component B x , B y , B z The analytical expression of the tetrahedron magnetic response in spherical coordinates is obtained by coordinate transformation to obtain the magnetic response of the spherical triangular prism unit.

[0076] In the embodiment of the present invention, under spherical triangulation, the grid unit is a series of spherical triangular prisms, and the upper and lower surfaces are triangular face elements such as Figure 4 The magnetic response of the grid cell can be expressed as Figure 5 As shown in , it is obtained by the difference in the magnetic responses of two tetrahedrons with the same sphere center: T ABC-AB'C' =T OABC -T OAB'C' ,like Figure 6 In Cartesian coordinates, point O is the origin of coordinates, the Z axis is vertically upward, and the gravitational potential V of a uniform object with a volume of v at the observation point P in the external space is: Where G is the gravitational constant, ρ is the density, and r is the distance between the density volume element and the observation point P. Figure 6 Take the tetrahedron as an example. The derivation finally obtains the tetrahedron external gravitational potential V and gravitational potential gradient and its gradient tensor The analytical formula is:

[0077] where r f 、r e are the vector from point P to a face ABC of the tetrahedron and the vector from point P to an edge CA of the tetrahedron, respectively. f 、E e are the tensor products of faces and edges, ω f , L e are two coefficients determined by the relative positions of point P and the surface and edge. where r i 、r j 、r k are the vectors from point P to vertices C, A, and B, and their magnitudes are r i 、r j 、r k , d ij is the length of side CA; n f is the external normal vector of face ABC; n1 and n2 are the two external normal vectors of edge CA, located on face ABC and face ACD respectively; n 1f 、n 2f are the external normal vectors of n1 and n2 on the surface ABC and surface ACD respectively. According to the Poisson formula between gravitational potential and magnetic potential, Where U is the magnetic potential, M Q is the magnetization intensity, and the derivative is:

[0078] Combining formulas There is a tetrahedral magnetic component B x , B y , B z The analytical expression of the tetrahedron magnetic response calculation in spherical coordinates is obtained by coordinate transformation, and finally the formula T ABC-AB'C' =T OABC -T OAB'C'Calculate the magnetic response of the spherical triangular prism unit, perform high-precision magnetic response calculations through spherical triangulation and fine grid units (spherical triangular prisms), and derive the analytical expression of the tetrahedron magnetic response to comprehensively analyze the magnetic response components of the underground geological body in different directions (B x , B y , B z ) obtains a comprehensive magnetic response analysis and obtains an efficient calculation method by using the Poisson formula between the gravitational potential and the magnetic potential and combining it with the expression of the gradient tensor.

[0079] In a preferred embodiment of the present invention, according to the tetrahedron magnetic response calculation analytical expression, a recursive hierarchical spherical triangulation magnetic modulus data physical property inversion equation is constructed to obtain an analytical calculation formula for the magnetic modulus data response under spherical triangulation, including:

[0080] The analytical expression is calculated based on the tetrahedron magnetic response, through The analytical calculation formula of the magnetic modulus data response under spherical triangulation is obtained, where T a Represents magnetic anomaly vector data T a The modulus, B x , B y , B z The magnetic component data can be calculated by the analytical expression of the tetrahedron magnetic response calculation;

[0081] In the embodiment of the present invention, the tetrahedron magnetic response calculation analytical expression can be used to accurately simulate and analyze the underground magnetic field distribution, thereby obtaining accurate magnetic modulus data response. By calculating the modulus of the magnetic anomaly vector data (T a ) and magnetic component data (B x , B y , B z ), can provide a deeper understanding of the characteristics and distribution of the underground magnetic field.

[0082] In a preferred embodiment of the present invention, the magnetic modulus data is obtained by an analytical calculation formula of the magnetic modulus data response under spherical triangulation, and a linear relationship between the magnetic modulus data and the effective magnetic susceptibility is constructed to obtain the overall objective function of the physical property inversion of the magnetic modulus data, including:

[0083] The magnetic modulus data is obtained through the analytical calculation formula of the magnetic modulus data response under spherical triangulation;

[0084] The effective magnetic susceptibility is obtained by X=μ0M / T0, where M is the effective magnetization intensity, T0 is the geomagnetic field intensity, and μ0 is the vacuum permeability;

[0085] By constructing a linear relationship between magnetic modulus data and effective magnetic susceptibility obs=F(m), where dobs is the data vector constructed from the magnetic modulus data, and F(m) represents the nonlinear forward operator;

[0086] According to the linear relationship, The total objective function of the inversion of the physical properties of magnetic modulus data is obtained, where W d is the data weighting matrix, W m is the model weight matrix, m apr is the initial model vector, and λ is used to balance the data fitting term φ d With the regularization term φ m The regularization parameter W m Multiply three diagonal matrices: W m =W·W e Z, where W is a diagonal weight matrix; W e is the diagonal focusing constraint matrix considering the volume, which is used to generate non-smooth, focused inversion results; Z is the depth weighting matrix related to the radial depth in spherical coordinates, which is used to improve the resolution of the inversion results in radial depth. apr Can be constructed from prior information, and is set to m when there is no prior information apr =0.001.

[0087] In the embodiment of the present invention, the effective magnetic susceptibility is obtained by X=μ0M / T0, where M is the effective magnetization intensity, T0 is the geomagnetic field intensity, and μ0 is the vacuum permeability. The underground space is discretized into a large number of grid units, and the effective magnetic susceptibility in each grid unit constructs a model parameter vector m , at this time, B x =G x m, B y =G y m, B z =G z m, where G x , G y , G z are the forward kernel matrices corresponding to the magnetic components. According to the above content, there is a nonlinear relationship between the magnetic modulus data and the effective magnetic susceptibility. obs =F(m), and Tikhonov regularization is used to establish the overall objective function of the physical property inversion of magnetic modulus data. By constructing a linear relationship between magnetic modulus data and effective magnetic susceptibility, the magnetic modulus data can be accurately interpreted. The construction of the overall objective function makes the physical property inversion problem of magnetic modulus data more stable and reliable. By converting the problem into a linear relationship, efficient linear algebra methods can be used to solve it, providing support for complex geological modeling.

[0088] In a preferred embodiment of the present invention, the total objective function of the inversion of the physical properties of the magnetic modulus data is iterated to obtain an iterative solution of the inversion equation of the physical properties of the magnetic modulus data under the recursive hierarchical spherical triangulation, including:

[0089] The total objective function of the inversion of the physical properties of the magnetic modulus data is linearized. When k iterations are performed, let m apr k =m k-1 , F(m) is linearized by Taylor series approximation, F(m k )≈F(m k-1 )+J k (m k -m k-1 ), where J k is the Jacobian matrix at the kth iteration,

[0090] pass The iterative solution form is: k =m k-1 +Δm k ,

[0091] In the embodiment of the present invention, the formula Linearization is performed. At the kth iteration, m apr k =m k-1 , F(m) is linearized by Taylor series approximation, F(m k )≈F(m k-1 )+J k (m k -m k-1 ), where J k is the Jacobian matrix at the kth iteration, pass The iterative solution form is: k =m k-1 +Δm k , The true solution can be gradually approached through iterative solution. Each iteration will be corrected according to the previous result to improve the inversion accuracy. The convergence judgment in the iterative process is provided. Among them, F(m) represents the nonlinear forward operator of magnetic modulus data, T a is the modulus data, B x , B y , B z are magnetic component data in different directions, W a is the data weighting matrix, Wn is the model weight matrix, m apr is the initial model vector, λ is the regularization parameter, k is the current iteration number, m is the model vector to be calculated, k-1 is the previous iteration number, G x is the kernel matrix corresponding to the x component, G y is the kernel matrix corresponding to the y component, J k is the Jacobian matrix of the kth iteration, d as is the data vector, m qr is the reference model vector, Δm k is the k-th iteration model disturbance term, T is the transposition symbol, φ a is the data fitting term, φ m is the model constraint, is the k-1th iteration prediction data, G z , is the data weighted diagonal matrix, is the model weighted diagonal matrix, m k-1 is the k-1th model disturbance term.

[0092] like Figure 2 As shown, an embodiment of the present invention further provides a physical property inversion device 20 for large-area aeromagnetic modulus data, comprising:

[0093] The acquisition module 21 is used to perform irregular subdivision of the underground space to obtain a recursive hierarchical subdivision schematic diagram; construct a multi-resolution grid structure through the recursive hierarchical subdivision schematic diagram to obtain a grid unit schematic diagram under spherical triangulation; derive an analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data according to the grid unit schematic diagram under the spherical triangulation to obtain an analytical expression for calculating the tetrahedral magnetic response, and obtain the magnetic response of the spherical triangular prism unit;

[0094] The processing module 22 is used to calculate the analytical expression of the tetrahedral magnetic response and construct the inversion equation of the physical property of the magnetic modulus data under the recursive hierarchical spherical triangulation to obtain the analytical calculation formula of the magnetic modulus data response under the spherical triangulation; obtain the magnetic modulus data through the analytical calculation formula of the magnetic modulus data response under the spherical triangulation, and construct the linear relationship between the magnetic modulus data and the effective magnetic susceptibility to obtain the total objective function of the inversion of the physical property of the magnetic modulus data; iterate the total objective function of the inversion of the physical property of the magnetic modulus data to obtain the iterative solution of the inversion equation of the physical property of the magnetic modulus data under the recursive hierarchical spherical triangulation.

[0095] It should be noted that the device is a device corresponding to the above method, and all implementation methods in the above method embodiment are applicable to this embodiment and can achieve the same technical effect.

[0096] The embodiment of the present invention further provides a computing device, comprising: a processor, a memory storing a computer program, wherein when the computer program is executed by the processor, the method described above is executed. All implementations in the above method embodiment are applicable to this embodiment and can achieve the same technical effect.

[0097] The embodiment of the present invention also provides a computer-readable storage medium storing instructions, which, when executed on a computer, enable the computer to execute the method described above. All implementations in the above method embodiment are applicable to this embodiment and can achieve the same technical effect.

[0098] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0099] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0100] In the embodiments provided by the present invention, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0101] 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 on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0102] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0103] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, ROM, RAM, magnetic disks, or optical disks.

[0104] In addition, it should be noted that in the apparatus and method of the present invention, it is obvious that each component or each step can be decomposed and / or recombined. These decompositions and / or recombinations should be regarded as equivalent schemes of the present invention. Moreover, the steps of performing the above-mentioned series of processing can naturally be performed in chronological order according to the order of description, but it is not necessary to perform them in chronological order, and some steps can be performed in parallel or independently of each other. For those of ordinary skill in the art, it is understood that all or any steps or components of the method and apparatus of the present invention can be implemented in any computing device (including processors, storage media, etc.) or a network of computing devices in hardware, firmware, software or a combination thereof, which can be achieved by those of ordinary skill in the art using their basic programming skills after reading the description of the present invention.

[0105] Therefore, the purpose of the present invention can also be achieved by running a program or a group of programs on any computing device. The computing device can be a well-known general device. Therefore, the purpose of the present invention can also be achieved by simply providing a program product containing a program code that implements the method or device. That is to say, such a program product also constitutes the present invention, and the storage medium storing such a program product also constitutes the present invention. Obviously, the storage medium can be any well-known storage medium or any storage medium developed in the future. It should also be pointed out that in the device and method of the present invention, it is obvious that each component or each step can be decomposed and / or recombined. These decompositions and / or recombinations should be regarded as equivalent schemes of the present invention. In addition, the steps of performing the above-mentioned series of processing can naturally be performed in chronological order according to the order of description, but it is not necessary to perform them in chronological order. Some steps can be performed in parallel or independently of each other.

[0106] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for inverting physical properties of large-area aeromagnetic modulus data, characterized in that: The method comprises: The underground space is irregularly divided to obtain a recursive hierarchical subdivision schematic diagram; By recursively dividing the schematic diagram into subdivisions, a multi-resolution grid structure is constructed to obtain a schematic diagram of grid units under spherical triangulation; According to the schematic diagram of the grid unit under the spherical triangulation, the analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data is derived to obtain the analytical expression for calculating the tetrahedral magnetic response, and the magnetic response of the spherical triangular prism unit is obtained; According to the analytical expression of tetrahedral magnetic response calculation, the inversion equation of magnetic modulus data under recursive hierarchical spherical triangulation is constructed to obtain the analytical calculation formula of magnetic modulus data response under spherical triangulation; The magnetic modulus data is obtained through the analytical calculation formula of the magnetic modulus data response under spherical triangulation, and the linear relationship between the magnetic modulus data and the effective magnetic susceptibility is constructed to obtain the overall objective function of the physical property inversion of the magnetic modulus data; By iterating the total objective function of the inversion of the physical properties of the magnetic modulus data, the iterative solution of the inversion equation of the physical properties of the magnetic modulus data under the recursive hierarchical spherical triangulation is obtained; The underground space is irregularly divided to obtain a recursive hierarchical subdivision schematic diagram, including: The irregular subdivision of underground space is carried out by adopting the recursive hierarchical spherical triangulation method; Place the icosahedron in spherical coordinates, with the north and south poles corresponding to a vertex of the icosahedron respectively, align one edge of the icosahedron with the meridian, and align it with the prime meridian to obtain an aligned icosahedron; The 20 basic equilateral triangles of the aligned regular icosahedron are taken as the 0th level, and the midpoints of each side of the equilateral triangle of the previous level are connected to form 4 equilateral triangles of the next level, and recursive hierarchical subdivision is performed to obtain a recursive hierarchical subdivision schematic diagram; Through the recursive hierarchical subdivision schematic diagram, a multi-resolution grid structure is constructed to obtain a grid unit schematic diagram under spherical triangulation, including: Through the recursive hierarchical subdivision diagram, the geocentric radius of the small triangle facet vertices on the sphere, ground, and interface is mapped to the sphere, ground, and interface, and a primary resolution grid structure is constructed at the same level of subdivision; Based on the primary resolution grid structure, the region is recursively and hierarchically subdivided to construct a multi-resolution grid structure, and a schematic diagram of the grid unit under spherical triangulation is obtained.

2. The method for inverting physical properties of large-area aeromagnetic modulus data according to claim 1, characterized in that: According to the schematic diagram of the grid unit under the spherical triangulation, the analytical formula for calculating the modulus response of the recursive hierarchical spherical aeromagnetic data is derived to obtain the analytical expression for calculating the tetrahedral magnetic response, and the magnetic response of the spherical triangular prism unit is obtained, including: According to the schematic diagram of the grid unit under spherical triangulation, the grid unit is a spherical triangular prism with triangular surface elements on the upper and lower surfaces, and through T ABC-AB′C′ =T OABC -T OAB′C′ Get the magnetic response of the grid unit; where: T OABC -T OAB′C′ is the difference between the magnetic responses of two tetrahedrons with the same center, T ABC-AB′C′ is the magnetic response of the grid cell; In Cartesian coordinates, with point O as the origin, the Z axis pointing vertically upward, an object with a volume of v and uniform density, passes through The gravitational potential of the observation point P in the external space is calculated, where G is the gravitational constant, ρ is the density, and r is the distance between the density volume element and the observation point P; Through Derivation is performed to obtain the external gravitational potential V and gravitational potential gradient of the tetrahedron and its gradient tensor The analytical formula of where r f 、r e are the vector from point P to a face ABC of the tetrahedron and the vector from point P to an edge CA of the tetrahedron, respectively. f 、E e are the tensor products of faces and edges, ω f , L e are two coefficients determined by the relative positions of point P and the surface and edge. where r i 、r j 、r k are the vectors from point P to vertices C, A, and B respectively; n f is the external normal vector of face ABC; n1 and n2 are the two external normal vectors of edge CA, located on face ABC and face ACD respectively; n 1f 、n 2f are the external normal vectors of n1 and n2 on the surface ABC and surface ACD respectively; According to the Poisson formula between gravitational potential and magnetic potential, we can get And combined with the gradient tensor The expression gives the tetrahedral magnetic component B x , B y , B z The analytical expression of the tetrahedron magnetic response calculation in spherical coordinates is obtained by coordinate transformation to obtain the magnetic response of the spherical triangular prism unit.

3. The method for inverting physical properties of large-area aeromagnetic modulus data according to claim 2, characterized in that: According to the analytical expression of tetrahedral magnetic response calculation, the inversion equation of the physical property of magnetic modulus data under recursive hierarchical spherical triangulation is constructed to obtain the analytical calculation formula of magnetic modulus data response under spherical triangulation, including: The analytical expression is calculated based on the tetrahedron magnetic response, through The analytical calculation formula of the magnetic modulus data response under spherical triangulation is obtained, where T a Represents magnetic anomaly vector data T a The modulus, B x , B y , B z The magnetic component data can be calculated by the analytical expression of tetrahedron magnetic response.

4. The method for inverting physical properties of large-area aeromagnetic modulus data according to claim 3, characterized in that: The magnetic modulus data is obtained through the analytical calculation formula of the magnetic modulus data response under spherical triangulation, and the linear relationship between the magnetic modulus data and the effective magnetic susceptibility is constructed to obtain the overall objective function of the physical property inversion of the magnetic modulus data, including: The magnetic modulus data is obtained by the analytical calculation formula of the magnetic modulus data response under spherical triangulation; The effective magnetic susceptibility is obtained by X=μ0M / T0, where M is the effective magnetization intensity, T0 is the geomagnetic field intensity, and μ0 is the vacuum permeability; By constructing a linear relationship between magnetic modulus data and effective magnetic susceptibility obs =F(m), where dobs is the data vector constructed from the magnetic modulus data, and F(m) represents the nonlinear forward operator; According to the linear relationship, The total objective function of the inversion of the physical properties of magnetic modulus data is obtained, where W d is the data weighting matrix, W m is the model weight matrix, m apr is the initial model vector, and λ is used to balance the data fitting term φ d With the regularization term φ m The regularization parameter, W m Multiply three diagonal matrices: W m =W·W e Z, where W is a diagonal weight matrix; W e is the diagonal focusing constraint matrix of the volume; Z is the depth weighting matrix related to the radial depth in spherical coordinates, m apr =0.

001.

5. The method for inverting physical properties of large-area aeromagnetic modulus data according to claim 4, characterized in that: By iterating the total objective function of the inversion of the physical properties of the magnetic modulus data, the iterative solution of the inversion equation of the physical properties of the magnetic modulus data under the recursive hierarchical spherical triangulation is obtained, including: The total objective function of the inversion of the physical properties of the magnetic modulus data is linearized. When k iterations are performed, let m apr k =m k-1 , F(m) is linearized by Taylor series approximation, F(m k )≈F(m k-1 )+J k (m k -m k-1 ), where J k is the Jacobian matrix at the kth iteration, pass The iterative solution form is: m k =m k-1 +Δm k , Where F(m) represents the nonlinear forward operator of magnetic modulus data, T a is the modulus data, B x , B y , B z are magnetic component data in different directions, W a is the data weighting matrix, W n is the model weight matrix, m apr is the initial model vector, λ is the regularization parameter, k is the current iteration number, m is the model vector to be calculated, k-1 is the previous iteration number, G x is the kernel matrix corresponding to the x component, G y is the kernel matrix corresponding to the y component, J k is the Jacobian matrix of the kth iteration, d as is the data vector, m qr is the reference model vector, Δm k is the k-th iteration model disturbance term, T is the transposition symbol, φ a is the data fitting term, φ m is the model constraint, is the k-1th iteration prediction data, G z , is the data weighted diagonal matrix, is the model weighted diagonal matrix, m k-1 is the k-1th model disturbance term.

6. A physical property inversion device for large-area aeromagnetic modulus data, characterized in that: include: An acquisition module is used to perform irregular subdivision of the underground space to obtain a recursive hierarchical subdivision schematic diagram; Through the recursive hierarchical subdivision schematic diagram, a multi-resolution grid structure is constructed to obtain a grid unit schematic diagram under spherical triangulation; according to the grid unit schematic diagram under spherical triangulation, an analytical formula for calculating the modulus response of recursive hierarchical spherical aeromagnetic data is derived to obtain an analytical expression for calculating the tetrahedral magnetic response, and the magnetic response of the spherical triangular prism unit is obtained; wherein, the underground space is irregularly subdivided to obtain a recursive hierarchical subdivision schematic diagram, including: The irregular subdivision of underground space is carried out by adopting the recursive hierarchical spherical triangulation method; Place the icosahedron in spherical coordinates, with the north and south poles corresponding to a vertex of the icosahedron respectively, align one edge of the icosahedron with the meridian, and align it with the prime meridian to obtain an aligned icosahedron; The 20 basic equilateral triangles of the aligned regular icosahedron are taken as the 0th level, and the midpoints of each side of the equilateral triangle of the previous level are connected to form 4 equilateral triangles of the next level, and recursive hierarchical subdivision is performed to obtain a recursive hierarchical subdivision schematic diagram; Through the recursive hierarchical subdivision schematic diagram, a multi-resolution grid structure is constructed to obtain a grid unit schematic diagram under spherical triangulation, including: Through the recursive hierarchical subdivision diagram, the geocentric radius of the small triangle facet vertices on the sphere, ground, and interface is mapped to the sphere, ground, and interface, and a primary resolution grid structure is constructed at the same level of subdivision; According to the primary resolution grid structure, the region is recursively subdivided at a deeper level to construct a multi-resolution grid structure, and a schematic diagram of the grid unit under the spherical triangulation is obtained; The processing module is used to calculate the analytical expression of the tetrahedron magnetic response and construct the inversion equation of the physical property of the magnetic modulus data under the recursive hierarchical spherical triangulation to obtain the analytical calculation formula of the magnetic modulus data response under the spherical triangulation; obtain the magnetic modulus data through the analytical calculation formula of the magnetic modulus data response under the spherical triangulation, and construct the linear relationship between the magnetic modulus data and the effective magnetic susceptibility to obtain the total objective function of the inversion of the physical property of the magnetic modulus data; iterate the total objective function of the inversion of the physical property of the magnetic modulus data to obtain the iterative solution of the inversion equation of the physical property of the magnetic modulus data under the recursive hierarchical spherical triangulation.

7. A computing device, characterized in that include: one or more processors; A storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors implement the method as claimed in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a program, which implements the method according to any one of claims 1 to 5 when executed by a processor.

Images