A magnetic susceptibility inversion method and system

Abstract

The present invention relates to a magnetic susceptibility inversion method and system, the method comprising: S1, obtaining a spatial domain residual based on observed magnetic field intensity and theoretical magnetic field intensity; S2, expressing the spatial domain residual by two-dimensional discrete Fourier inverse transform based on wave number domain residual; S3, obtaining a wave number domain model perturbation based on the spatial domain residual, and further obtaining a spatial domain model perturbation based on Fourier inverse transform; S4, obtaining a magnetic susceptibility inversion model based on the spatial domain model perturbation. The present invention reduces the required memory space, improves the calculation efficiency, and further improves the inversion efficiency.

Description

Technical Field

[0001] The present invention relates to the field of geophysical technology, and in particular to a magnetic susceptibility inversion method and system. Background Art

[0002] Magnetic survey data has a wide range of applications in the field of geophysical exploration. For example, in mineral exploration, magnetic methods can be used to determine volume parameters; in petroleum exploration, magnetic methods can be used to map underground sedimentary characteristics and defects and to control the sedimentary background of sedimentary basins.

[0003] Inversion of physical parameters, such as calculation of magnetic susceptibility and magnetization intensity, is the main scientific problem in using magnetic field data. In practical applications, the magnetic susceptibility of the target geographical area can be inverted to obtain a magnetic susceptibility model of the target geographical area. The magnetic susceptibility model can reflect the magnetic susceptibility of each geographical location in the target geographical area, and then a geographical location whose magnetic susceptibility meets the preset requirements can be selected as a further research object.

[0004] Among the existing magnetic susceptibility inversion technologies, the generalized inverse iterative inversion optimization method and the damped generalized inverse iterative inversion optimization method are mostly used. However, the existing inversion technologies all have certain disadvantages, including: 1) due to the huge number of subdivision units in the calculation area, a large amount of memory is consumed and the calculation efficiency is low; 2) the measurement points must be regularly distributed, which is not conducive to field construction; 3) the inversion equation group is complex to solve and converges slowly; 4) the parameters cannot be controlled to improve the resolution of the inversion; 5) due to the characteristics of the algorithm itself, it is not conducive to decomposing complex large-scale inversion problems into a finite number of small problems for parallel solution. Summary of the invention

[0005] In view of this, an object of the present invention is to provide a magnetic susceptibility inversion method and system to solve the problems existing in the prior art.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A magnetic susceptibility inversion method, comprising:

[0008] S1, spatial domain residual is obtained based on observed magnetic field intensity and theoretical magnetic field intensity;

[0009] S2, representing the spatial domain residual by a two-dimensional inverse discrete Fourier transform based on the wave number domain residual;

[0010] S3, obtaining a wavenumber domain model disturbance based on the spatial domain residual, and further obtaining a spatial domain model disturbance based on an inverse Fourier transform;

[0011] S4, obtaining a magnetic susceptibility inversion model based on the spatial domain model disturbance.

[0012] Preferably, S3 includes:

[0013] S31, integrating the spatial domain residual based on the shape function to obtain a linear equation system;

[0014] S32, performing regularization processing on the linear equation system to obtain a regularized equation system;

[0015] S33, solving the regularized equation group to obtain the wavenumber domain model disturbance;

[0016] S34, performing inverse Fourier transform on the wavenumber domain model disturbance to obtain the space domain model disturbance.

[0017] Preferably, the S4 includes:

[0018] S41, updating the model vector based on the spatial domain model disturbance to obtain an updated model vector;

[0019] S42, obtaining an average mean square error based on the updated model vector, and judging the average mean square error; when the average mean square error is greater than the error setting value, returning to "S1"; when the average mean square error is less than or equal to the error setting value, executing "S43";

[0020] S43, obtaining a magnetic susceptibility inversion model based on the spatial domain model disturbance.

[0021] Preferably, the shape function is any one of a linear interpolation shape function and a quadratic interpolation shape function.

[0022] The present invention also provides a magnetic susceptibility inversion system, comprising:

[0023] A spatial domain residual module is used to obtain a spatial domain residual based on the observed magnetic field intensity and the theoretical magnetic field intensity;

[0024] A wave number domain residual module, used for representing the spatial domain residual by two-dimensional discrete Fourier inverse transform based on the wave number domain residual;

[0025] A model perturbation module, used to obtain a wavenumber domain model perturbation based on the spatial domain residual, and further obtain a spatial domain model perturbation based on an inverse Fourier transform;

[0026] The magnetic susceptibility inversion module obtains a magnetic susceptibility inversion model based on the spatial domain model disturbance.

[0027] Preferably, the model perturbation module comprises:

[0028] An integration unit, used for integrating the spatial domain residual based on a shape function to obtain a linear equation system;

[0029] A regularization unit, used for performing regularization processing on the linear equation system to obtain a regularized equation system;

[0030] A wavenumber domain model perturbation unit, used for solving the regularized equation group to obtain the wavenumber domain model perturbation;

[0031] The space domain model disturbance unit is used to perform inverse Fourier transform on the wave number domain model disturbance to obtain the space domain model disturbance.

[0032] Preferably, the magnetic susceptibility inversion module comprises:

[0033] A model vector unit, which updates the model vector based on the spatial domain model disturbance to obtain an updated model vector;

[0034] A judgment unit, configured to obtain an average mean square error based on the updated model vector, and to judge the average mean square error; when the average mean square error is greater than the error setting value, return to the spatial domain residual module;

[0035] The magnetic susceptibility inversion unit is used to obtain a magnetic susceptibility inversion model based on the spatial domain model disturbance when the average mean square error is less than or equal to the error setting value.

[0036] Preferably, the shape function is any one of a linear interpolation shape function and a quadratic interpolation shape function.

[0037] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0038] The present invention relates to a magnetic susceptibility inversion method and system, the method comprising: S1, obtaining a spatial domain residual based on observed magnetic field intensity and theoretical magnetic field intensity; S2, expressing the spatial domain residual by two-dimensional discrete Fourier inverse transform based on wave number domain residual; S3, obtaining a wave number domain model perturbation based on the spatial domain residual, and further obtaining a spatial domain model perturbation based on Fourier inverse transform; S4, obtaining a magnetic susceptibility inversion model based on the spatial domain model perturbation. The present invention reduces the required memory space, improves the calculation efficiency, and further improves the inversion efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0040] Figure 1 It is a flow chart of the magnetic susceptibility inversion method of the present invention;

[0041] Figure 2 It is a structural diagram of the magnetic susceptibility inversion system of the present invention;

[0042] Figure 3 This is a diagram showing the magnetic susceptibility inversion effect of the present invention.

[0043] Explanation of symbols: 1-spatial domain residual module, 2-wave number domain residual module, 3-model perturbation module, 4-magnetic susceptibility inversion module. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] The purpose of the present invention is to provide a magnetic susceptibility inversion method and system to reduce the required memory space, improve the calculation efficiency, and further improve the inversion efficiency.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Figure 1 This is a flow chart of the magnetic susceptibility inversion method of the present invention, as shown in Figure 1 As shown, the present invention provides a magnetic susceptibility inversion method, comprising:

[0048] Step S1, obtaining a spatial domain residual based on the observed magnetic field intensity and the theoretical magnetic field intensity.

[0049] Step S2, based on the wave number domain residual, the spatial domain residual is expressed by a two-dimensional discrete Fourier inverse transform; the formula is as follows: in, Then further Simplified

[0050] Where: n∈N, N is the number of layers of the underground medium, ΔE is the spatial domain residual, is the residual in the wave number domain, Mz is the number of units in the z direction in the nth layer of underground medium, x is the x-axis coordinate in the space domain, y is the y-axis coordinate in the space domain, z is the z-axis coordinate in the space domain, k x Wavenumber domain x-axis wavenumber, k y is the y-axis wave number in the wave number domain, is the wavenumber domain Green's function, is the model perturbation in the wavenumber domain, Δhn is the vertical distance from the observation point to the midpoint of the nth layer of underground medium.

[0051] Step S3, obtaining a wavenumber domain model disturbance based on the spatial domain residual, and further obtaining a spatial domain model disturbance based on an inverse Fourier transform; as an optional implementation, step S3 of the present invention includes:

[0052] Step S31, integrating the spatial domain residual based on the shape function to obtain a linear equation system. In this embodiment, the shape function is any one of a linear interpolation shape function and a quadratic interpolation shape function. Specifically:

[0053] Further Where Ne is the number of units in the wavenumber domain, Q is the number of wavenumbers on the x-axis in the wavenumber domain, and P is the number of wavenumbers on the y-axis in the wavenumber domain. Then we can get the linear equation system:

[0054] Among them, ΔE=[ΔE1ΔE2ΔE3...ΔE N ] T , A=[A 1 A 2 A 3 ...... A N ] T , T is the transpose.

[0055] Step S32, regularizing the linear equations to obtain a regularized equation system; specifically, multiplying both sides of the linear equation system by A T , we get the regularized equations as follows:

[0056]

[0057] Step S33, solving the regularized equation group to obtain the wavenumber domain model perturbation. Specifically, one regularized equation group is obtained for each wavenumber, and a total of P×Q regularized equation groups are obtained, and the wavenumber domain model perturbation is obtained by solving the P×Q regularized equation groups.

[0058] Step S34, performing inverse Fourier transform on the wavenumber domain model disturbance to obtain the space domain model disturbance.

[0059] Step S4, obtaining a magnetic susceptibility inversion model based on the spatial domain model disturbance. Specifically, step S4 includes:

[0060] Step S41, updating the model vector based on the spatial domain model disturbance to obtain an updated model vector;

[0061] Step S42, obtaining an average mean square error based on the updated model vector, and judging the average mean square error; when the average mean square error is greater than the error setting value, returning to "step S1"; when the average mean square error is less than or equal to the error setting value, obtaining a magnetic susceptibility inversion model based on the spatial domain model disturbance.

[0062] The specific inversion effect of the present invention is as follows Figure 3 shown.

[0063] Figure 2 The structure diagram of the magnetic susceptibility inversion system of the present invention is shown in FIG. Figure 2 As shown, the present invention provides a magnetic susceptibility inversion system, including: a spatial domain residual module 1, a wave number domain residual module 2, a model perturbation module 3 and a magnetic susceptibility inversion module 4.

[0064] The spatial domain residual module 1 is used to obtain the spatial domain residual based on the observed magnetic field intensity and the theoretical magnetic field intensity.

[0065] The wave number domain residual module 2 is used to represent the spatial domain residual through a two-dimensional discrete Fourier inverse transform based on the wave number domain residual.

[0066] The model perturbation module 3 is used to obtain the wavenumber domain model perturbation based on the spatial domain residual, and further obtain the spatial domain model perturbation based on the inverse Fourier transform.

[0067] The magnetic susceptibility inversion module 4 is used to obtain a magnetic susceptibility inversion model based on the spatial domain model disturbance.

[0068] As an optional implementation, the model perturbation module 3 of the present invention includes: an integration unit, a regularization unit, a wavenumber domain model perturbation unit and a space domain model perturbation unit.

[0069] The integration unit is used to integrate the spatial domain residual based on the shape function to obtain a linear equation system.

[0070] The regularization unit is used to perform regularization processing on the linear equation group to obtain a regularized equation group.

[0071] The wavenumber domain model perturbation unit is used to obtain the wavenumber domain model perturbation by solving the regularized equation group.

[0072] The space domain model disturbance unit is used to perform inverse Fourier transform on the wave number domain model disturbance to obtain the space domain model disturbance.

[0073] As an optional implementation, the magnetic susceptibility inversion module of the present invention includes: a model vector unit, a judgment unit and a susceptibility inversion unit.

[0074] The model vector unit is used to update the model vector based on the spatial domain model disturbance to obtain an updated model vector.

[0075] The judgment unit is used to obtain an average mean square error based on the updated model vector and judge the average mean square error; when the average mean square error is greater than the error setting value, return to the spatial domain residual module 1.

[0076] The magnetic susceptibility inversion unit is used to obtain a magnetic susceptibility inversion model based on the spatial domain model disturbance when the average mean square error is less than or equal to a set error value.

[0077] The beneficial effects of the present invention are as follows:

[0078] 1) The memory space required for inversion will be greatly reduced, and the computational efficiency will be significantly improved;

[0079] 2) It can adapt to the inversion of measuring points at any location, which is conducive to field construction;

[0080] 3) The difficulty of solving the inverse equations is greatly reduced, and the convergence is faster;

[0081] 4) The decay rate of the Green's function can be controlled by changing the wave number, which is beneficial to improving the inversion resolution;

[0082] 5) Since each small problem in the wavenumber domain inversion algorithm is relatively independent, it is very helpful to decompose complex large-scale inversion problems into multiple small problems for parallel solution.

[0083] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0084] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A magnetic susceptibility inversion method, characterized in that: include: S1, spatial domain residual is obtained based on observed magnetic field intensity and theoretical magnetic field intensity; S2, representing the spatial domain residual by a two-dimensional inverse discrete Fourier transform based on the wave number domain residual; S3, obtaining a wavenumber domain model disturbance based on the spatial domain residual, and further obtaining a spatial domain model disturbance based on an inverse Fourier transform; S4, obtaining a magnetic susceptibility inversion model based on the spatial domain model perturbation; The S3 includes: S31, integrating the spatial domain residual based on the shape function to obtain a linear equation system; S32, performing regularization processing on the linear equation system to obtain a regularized equation system; S33, solving the regularized equation group to obtain the wavenumber domain model disturbance; S34, performing inverse Fourier transform on the wavenumber domain model disturbance to obtain the space domain model disturbance.

2. The magnetic susceptibility inversion method according to claim 1, characterized in that: The S4 includes: S41, updating the model vector based on the spatial domain model disturbance to obtain an updated model vector; S42, obtaining an average mean square error based on the updated model vector, and judging the average mean square error; when the average mean square error is greater than the error setting value, returning to "S1"; when the average mean square error is less than or equal to the error setting value, executing "S43"; S43, obtaining a magnetic susceptibility inversion model based on the spatial domain model disturbance.

3. The magnetic susceptibility inversion method according to claim 1, characterized in that: The shape function is any one of a linear interpolation shape function and a quadratic interpolation shape function.

4. A magnetic susceptibility inversion system, characterized in that: include: A spatial domain residual module is used to obtain a spatial domain residual based on the observed magnetic field intensity and the theoretical magnetic field intensity; A wave number domain residual module, used for representing the spatial domain residual by two-dimensional discrete Fourier inverse transform based on the wave number domain residual; A model perturbation module, used to obtain a wavenumber domain model perturbation based on the spatial domain residual, and further obtain a spatial domain model perturbation based on an inverse Fourier transform; A magnetic susceptibility inversion module, which obtains a magnetic susceptibility inversion model based on the spatial domain model disturbance; The model perturbation module includes: An integration unit, used for integrating the spatial domain residual based on a shape function to obtain a linear equation system; A regularization unit, used for performing regularization processing on the linear equation system to obtain a regularized equation system; A wavenumber domain model perturbation unit, used for solving the regularized equation group to obtain the wavenumber domain model perturbation; The space domain model disturbance unit is used to perform inverse Fourier transform on the wave number domain model disturbance to obtain the space domain model disturbance.

5. The magnetic susceptibility inversion system according to claim 4, characterized in that: The magnetic susceptibility inversion module includes: A model vector unit, which updates the model vector based on the spatial domain model disturbance to obtain an updated model vector; A judgment unit, configured to obtain an average mean square error based on the updated model vector, and to judge the average mean square error; when the average mean square error is greater than the error setting value, return to the spatial domain residual module; The magnetic susceptibility inversion unit is used to obtain a magnetic susceptibility inversion model based on the spatial domain model disturbance when the average mean square error is less than or equal to the error setting value.

6. The magnetic susceptibility inversion system according to claim 4, characterized in that: The shape function is any one of a linear interpolation shape function and a quadratic interpolation shape function.

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