A magnetic anomaly polarization method based on equivalent source inversion

Abstract

The present invention discloses a magnetic anomaly pole-localization method based on equivalent source inversion, comprising: uniformly gridding the underground space according to observation data, and constructing an equivalent source space by setting an inversion depth; obtaining a sensitivity matrix for forward and inverse calculations of magnetic survey data according to the observation data and parameters of the equivalent source space; calculating physical parameters of the equivalent source space using a generalized minimum residual method according to the sensitivity matrix and magnetic anomaly data, and constructing an equivalent source model; forward modeling the vertically magnetized geomagnetic field according to the sensitivity matrix and the equivalent source model to obtain a magnetic anomaly pole-localization result. The method reconstructs an inversion calculation framework of the equivalent source model based on the generalized minimum residual method, solves problems such as the difficulty in solving large-scale equation groups in similar inversions, improves the efficiency and accuracy of equivalent field source inversion imaging, can well achieve stable pole-localization under arbitrary geomagnetic inclination conditions, and is suitable for pole-localization processing of magnetic anomalies in regions with low geomagnetic latitudes, especially in the magnetic equatorial region.

Description

Technical Field

[0001] The present application relates to the field of geophysical exploration technology, and in particular to a magnetic anomaly polarization method based on equivalent source inversion. Background Art

[0002] Magnetic data are essential geophysical foundational data for geological surveys and mineral exploration. However, in low-latitude regions, magnetic anomalies are affected by geomagnetic inclination, leading to complex morphologies, particularly near the magnetic equator. This complexity poses significant challenges to the geological interpretation of magnetic data. Polarization processing of magnetic data can effectively reduce or eliminate the effects of oblique magnetization, which is crucial for improving the accuracy and reliability of magnetic data interpretation.

[0003] Methods for depolarizing magnetic anomalies include spatial and frequency domain methods. The frequency domain method is computationally simple and fast, but its accuracy is limited. The spatial domain method offers higher accuracy, but its practical application is limited by the need to solve a large system of equations. Furthermore, when using equivalent source technology for depolarization, the traditional method using magnetic dipoles or dipole elements as equivalent sources may affect the acquisition of low-frequency information due to its limited depth extension, thus reducing the accuracy of the equivalent source inversion method. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a magnetic anomaly pole method based on equivalent source inversion, which achieves stable and accurate pole localization under arbitrary geomagnetic inclination conditions through rapid inversion imaging of the equivalent field source, thereby solving the problems of complex calculation and poor stability in the calculation of magnetic anomaly poles in low latitudes, especially in the magnetic equatorial region.

[0005] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a magnetic anomaly polarization method based on equivalent source inversion, comprising:

[0006] S1. Based on the observation data, the underground space is uniformly gridded and the equivalent source space is constructed by setting the inversion depth;

[0007] S2. Obtain the sensitivity matrix of forward and inversion calculation of magnetic survey data based on observation data and equivalent source space parameters;

[0008] S3. Based on the sensitivity matrix and magnetic anomaly data, the generalized minimum residual method is used to calculate the physical parameters of the equivalent source space and construct an equivalent source model;

[0009] S4. Based on the sensitivity matrix and equivalent source model, the vertical magnetization geomagnetic field is forward modeled to obtain the magnetic anomaly pole result.

[0010] Further: element A in the sensitivity matrix A in S2 i,j The expression is:

[0011]

[0012] k1=cosI0sinD0sinI+sinI0cosIsinD,k2=cosI0cosD0sinI+sinI0cosIcosD,

[0013] k3=cosI0cosD0cosIsinD+cosI0sinD0cosIcosD,

[0014] k4=cosI0cosD0cosIcosD, k5=cosI0sinD0cosIsinD, k6=-sinI0sinI

[0015] Among them, A i,j represents the (i, j)th unit of the sensitivity matrix A, k1, k2, k3, k4, k5 and k6 are all intermediate parameters, r is the distance between the rectangular unit and the observation point; μ0 is the vacuum permeability; I0 and D0 are the inclination and declination of the direction of the geomagnetic field, respectively, and I and D are the inclination and declination of the direction of the total magnetization intensity, respectively; (ξ, η, ζ) are the central coordinates of the volume element of the subdivided unit; ξ1, ξ2, η1, η2, ζ1 and ζ2 are the coordinate positions of the corner points of the underground rectangular unit; (x i ,y i ,z i ) are the coordinates of the observation point.

[0016] Furthermore: S3 includes:

[0017] S31, calculating the initial error r0 according to the sensitivity matrix A and the magnetic anomaly data d in the observation data;

[0018] S32, according to the initial error r0, use the generalized minimum residual method to iterate and obtain the standard orthogonal basis element v j ;

[0019] S33, based on standard orthogonal basis elements v j , by solving the least squares problem, the physical property parameter m of the equivalent source space is obtained;

[0020] S34. Construct an equivalent source model based on the physical property parameter m of the equivalent source space.

[0021] Furthermore: The forward expression of the vertical magnetization geomagnetic field in S4 is:

[0022] dRTP=A·m

[0023] Among them, d RTPTo transform the polar magnetic anomaly, m is the equivalent source model, and the sensitivity matrix A is calculated using the vertical magnetization geomagnetic field with a magnetic inclination of 90° and a magnetic declination of 0°.

[0024] The beneficial effects of the present invention are:

[0025] 1. The generalized minimum residual method is used to solve the equivalent source parameters, which solves the problem of difficulty in solving large-scale equations in similar inversions and improves the efficiency and accuracy of equivalent field source inversion imaging;

[0026] 2. The stability and accuracy of magnetic anomaly polarization based on equivalent source technology are improved by using a uniformly magnetized regular shape to approximate the equivalent source. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flow chart of the magnetic anomaly pole method based on equivalent source inversion.

[0028] Figure 2 Schematic diagram of model magnetic anomaly under horizontal magnetization and vertical magnetization conditions in an embodiment of the present invention.

[0029] Figure 3 Schematic diagram of the magnetic anomaly polarization results and inversion error of the model containing noise in an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0031] like Figure 1 As shown, in one embodiment of the present invention, a magnetic anomaly polarization method based on equivalent source inversion is provided, comprising:

[0032] S1. Based on the observation data, the underground space is uniformly gridded and the equivalent source space is constructed by setting the inversion depth;

[0033] S2. Obtain the sensitivity matrix of forward and inversion calculation of magnetic survey data based on observation data and equivalent source space parameters;

[0034] S3. Based on the sensitivity matrix and magnetic anomaly data, the generalized minimum residual method is used to calculate the physical parameters of the equivalent source space and construct an equivalent source model;

[0035] S4. Based on the sensitivity matrix and equivalent source model, the vertical magnetization geomagnetic field is forward modeled to obtain the magnetic anomaly pole result.

[0036] Specifically, the (i, j)th matrix element A in the sensitivity matrix A is i,j It is determined by the distance between the jth cuboid unit and the i-th observation point, and its A i,j The expression is:

[0037]

[0038] k1=cosI0sinD0sinI+sinI0cosIsinD,k2=cosI0cosD0sinI+sinI0cosIcosD,

[0039] k3=cosI0cosD0cosIsinD+cosI0sinD0cosIcosD,

[0040] k4=cosI0cosD0cosIcosD, k5=cosI0sinD0cosIsinD, k6=-sinI0sinI

[0041] Among them, A i,j represents the (i, j)th unit of the sensitivity matrix A, k1, k2, k3, k4, k5 and k6 are all intermediate parameters, r is the distance between the rectangular unit and the observation point; μ0 is the vacuum permeability; I0 and D0 are the inclination and declination of the direction of the geomagnetic field, respectively, and I and D are the inclination and declination of the direction of the total magnetization intensity, respectively; (ξ, η, ζ) are the central coordinates of the volume element of the subdivided unit; ξ1, ξ2, η1, η2, ζ1 and ζ2 are the coordinate positions of the corner points of the underground rectangular unit; (x i ,y i ,z i ) are the coordinates of the observation point.

[0042] Specifically, S3 includes:

[0043] S31, calculating the initial error r0 according to the sensitivity matrix A and the magnetic anomaly data d in the observation data;

[0044] S32, according to the initial error r0, use the generalized minimum residual method to iterate and obtain the standard orthogonal basis element v j ;

[0045] S33, based on standard orthogonal basis elements v j , by solving the least squares problem, the physical property parameter m of the equivalent source space is obtained;

[0046] S34. Construct an equivalent source model based on the physical property parameter m of the equivalent source space.

[0047] The forward expression of the vertical magnetization geomagnetic field in S4 is:

[0048] dRTP=A·m

[0049] Among them, d RTP To transform the polar magnetic anomaly, m is the equivalent source model, and the sensitivity matrix A is calculated using the vertical magnetization geomagnetic field with a magnetic inclination of 90° and a magnetic declination of 0°.

[0050] Based on the magnetic anomaly polarization method based on equivalent source inversion described in this embodiment, a simulation experiment was conducted, and the simulation parameters were designed as follows: the uniform magnetic body is 3000m long, 3000m wide, and 500m thick, with a magnetization intensity of 1A / M and a center position of (-1500, -1500, 1750)m;

[0051] In this embodiment, the magnetic anomaly under two conditions, horizontal magnetization and vertical magnetization, is simulated and analyzed. The results are as follows: Figure 2 As shown in the figure, and the polarization results of the horizontal magnetization anomaly data containing noise, as shown in the figure Figure 3 shown; combined Figure 2 and Figure 3 As can be seen from the results, the polarization result obtained in this embodiment is not much different from the magnetic anomaly of perpendicular magnetization, and the two are highly consistent in morphology and amplitude, indicating that the present invention has a good application effect. The generalized minimum residual method is used in the equivalent field source inversion to solve the physical parameter model, which solves the problems such as the difficulty in solving large-scale equations in similar inversions. It is a simple and novel physical property inversion method. The amount of calculation is small when performing polarization processing based on this method. By setting a suitable equivalent model space, the offset caused by oblique magnetization can be eliminated, and a stable and accurate polarization result can be obtained. Even under noise interference conditions, a good polarization effect can be obtained, meeting the actual needs of magnetic anomaly polarization in low-latitude areas.

[0052] In summary, the present invention can solve the problems of unstable low-latitude magnetic anomaly polarization calculation and insufficient polarization accuracy in the original polarization method, and improve the stability and accuracy of magnetic anomaly polarization.

[0053] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A magnetic anomaly polarization method based on equivalent source inversion, characterized in that: include: S1. Based on the observation data, the underground space is uniformly gridded and the equivalent source space is constructed by setting the inversion depth; S2. Obtain the sensitivity matrix of forward and inversion calculation of magnetic survey data based on observation data and equivalent source space parameters; S3. Based on the sensitivity matrix and magnetic anomaly data, the generalized minimum residual method is used to calculate the physical parameters of the equivalent source space and construct an equivalent source model; S4. Based on the sensitivity matrix and equivalent source model, the vertical magnetization geomagnetic field is forward modeled to obtain the magnetic anomaly pole result.

2. The magnetic anomaly polarization method based on equivalent source inversion according to claim 1 is characterized in that: The element A in the sensitivity matrix A in S2 i,j The expression is: k1=cosI0sinD0sinI+sinI0cosIsinD,k2=cosI0cosD0sinI+sinI0cosIcosD, k3=cosI0cosD0cosIsinD+cosI0sinD0cosIcosD, k4=cosI0cosD0cosIcosD, k5=cosI0sinD0cosIsinD, k6=-sinI0sinI Among them, A i,j represents the (i, j)th unit of the sensitivity matrix A, k1, k2, k3, k4, k5 and k6 are all intermediate parameters, r is the distance between the rectangular unit and the observation point; μ0 is the vacuum permeability; I0 and D0 are the inclination and declination of the direction of the geomagnetic field, respectively, and I and D are the inclination and declination of the direction of the total magnetization intensity, respectively; (ξ, η, ζ) are the central coordinates of the volume element of the subdivided unit; ξ1, ξ2, η1, η2, ζ1 and ζ2 are the coordinate positions of the corner points of the underground rectangular unit; (x i ,y i ,z i ) are the coordinates of the observation point.

3. The magnetic anomaly polarization method based on equivalent source inversion according to claim 1 is characterized in that S3 include: S31, calculating the initial error r0 according to the sensitivity matrix A and the magnetic anomaly data d in the observation data; S32, according to the initial error r0, use the generalized minimum residual method to iterate and obtain the standard orthogonal basis element v j ; S33, based on standard orthogonal basis elements v j , by solving the least squares problem, the physical property parameter m of the equivalent source space is obtained; S34. Construct an equivalent source model based on the physical property parameter m of the equivalent source space.

4. The magnetic anomaly polarization method based on equivalent source inversion according to claim 1 is characterized in that: The forward expression of the vertical magnetization geomagnetic field in S4 is: d RTP =A·m Among them, d RTP To transform the polar magnetic anomaly, m is the equivalent source model, and the sensitivity matrix A is calculated using the vertical magnetization geomagnetic field with a magnetic inclination of 90° and a magnetic declination of 0°.

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