A high-precision magnetization vector inversion method

Abstract

The present invention relates to the field of magnetic vector inversion, and specifically to a high-precision magnetization intensity vector inversion method, comprising the following steps: converting magnetic anomalies into normalized magnetic source intensity that is weakly sensitive to magnetization direction; performing seamless partitioning based on data features according to the normalized magnetic source intensity data; subjecting the three components of the magnetization intensity and the magnetization intensity obtained by NSS inversion to Gramian constraints, thereby obtaining an objective function for magnetization intensity vector inversion based on the data feature partition-normalized magnetic source intensity constraints; and performing magnetization vector inversion using the objective function to obtain magnetization intensity and magnetization direction distribution. In actual calculations, the present invention performs seamless partitioning based on the normalized magnetic source intensity data features for magnetic anomalies under complex remanent magnetization conditions, performs physical property correlation constraint inversion on the three components of the magnetization intensity and the normalized magnetic source intensity data inversion results of each subdomain, and obtains high-precision magnetization vector inversion results.

Description

Technical Field

[0001] The invention relates to the field of magnetic vector inversion, in particular to a high-precision magnetization intensity vector inversion method. Background Art

[0002] Magnetization vector inversion takes into account the effects of remanence and demagnetization, allowing direct retrieval of the subsurface magnetic structure and magnetization direction distribution. Currently, two methods are commonly used for magnetization vector inversion: direct inversion of the three orthogonal components of the magnetization vector (MMM); and direct inversion of magnetization, dip, and declination (MID).

[0003] The MID inversion method requires estimating the magnetization direction before inversion. Given an initial model, there are many methods for estimating the magnetization direction, but conventional methods are more suitable for simple, isolated anomalies. The MMM inversion method can obtain reliable results without any prior information. However, compared to magnetic scalar inversion, the MMM inversion method requires the simultaneous inversion of the three components of the magnetization intensity, which increases the solution parameters and makes the inversion process unstable. Moreover, during the inversion process, the three components of the magnetization intensity (Mx, My, and Mz) are independently modeled according to their own characteristics, and the obtained inversion results are often unrealistic. To address this issue, Gramian constraints can be introduced during the magnetic vector inversion process. The total magnetization intensity obtained by magnetic vector inversion is used to constrain the three components of the magnetization intensity, thereby obtaining stable results. This method is called self-constrained inversion of the magnetization intensity vector. However, this method is not suitable for magnetic data under complex remanent magnetization conditions.

[0004] In reality, underground conditions are extremely complex, with varying magnetization directions occurring within the same study area. Therefore, researchers have partitioned the study area to ensure that inversion results are more realistic. For Gramian-constrained magnetic vector inversion, researchers partition the study area and then perform constrained inversion on each subdomain to obtain more accurate magnetization intensity and direction. However, current partitioning methods cannot be combined to obtain subdomains, resulting in distorted results in uncoupled regions. Summary of the Invention

[0005] The current conventional method for inverting the magnetization vector introduces Gramian constraints during the inversion of the three-component magnetization. During the inversion process, the three components of the magnetization are Gramian-constrained together with the calculated total magnetization to obtain a stable solution. This method can also be called self-constrained inversion of the magnetization vector. However, for magnetic anomalies (different magnetization directions) under complex underground remanent magnetic conditions, the inversion error of the three-component magnetization vector is large, and the use of self-constrained results cannot obtain an accurate magnetization vector distribution. For partitioned magnetic vector inversion based on Gramian constraints, the study area is partitioned and constrained inversion is performed on each subdomain to obtain more accurate magnetization and magnetization directions. However, the subdomains obtained by the current partitioning method cannot be combined, and the results in the uncoupled area are distorted.

[0006] The high-precision magnetization intensity vector inversion method proposed in this invention, based on data feature partitioning and normalized magnetic source intensity constraints, can obtain accurate underground magnetization intensity and magnetization direction distribution, improving the accuracy of the inversion results. The invention provides the following technical solutions:

[0007] A high-precision magnetization intensity vector inversion method comprises the following steps:

[0008] The first step is to convert the magnetic anomaly into a normalized magnetic source intensity that is weakly sensitive to the magnetization direction;

[0009] The second step is to perform seamless partitioning based on data features according to the normalized magnetic source intensity data;

[0010] In the third step, the three components of the magnetization intensity and the magnetization intensity obtained by NSS inversion are subjected to partition Gramian constraints to obtain the objective function of magnetization intensity vector inversion based on data feature partitioning-normalized magnetic source intensity constraints. The magnetization vector inversion is performed using the objective function of magnetization intensity vector inversion based on data feature partitioning-normalized magnetic source intensity constraints to obtain the magnetization intensity and magnetization direction distribution.

[0011] As a further solution of the present invention: the expression of normalized magnetic source intensity is as follows: , C m =10 -7 H / m, m is the magnetic moment of the dipole, and r is the distance between the field source and the observation point.

[0012] As a further solution of the present invention, performing seamless partitioning based on data features according to normalized magnetic source intensity data includes the following steps:

[0013] The number of extreme points of the search normalized magnetic source intensity data is the number of subdomains;

[0014] Search around each extreme point, and the initial boundary of the subdomain is where the amplitude is less than half of the extreme point or the amplitude begins to increase;

[0015] The initial area S of each subdomain and the distance R between the unpartitioned point and the extreme point of a subdomain are used as the reference basis for the subdomain. According to the ratio of the control area to the distance To assign the point to the corresponding subdomain, search again until the subdomain boundaries coincide, which is the subdomain boundary.

[0016] As a further solution of the present invention: the objective function of the magnetization intensity vector inversion based on the data feature partition-normalized magnetic source intensity constraint is:

[0017] ,

[0018] The kernel function matrix representing the three components of magnetization intensity, are the three components of magnetization intensity, Represents the north component M x , East component M y and the vertical component M z， is the magnetic anomaly data, is the kernel function matrix of the normalized magnetic source intensity, M N The magnetization intensity is obtained by inverting NSS, where NSS is the normalized magnetic source intensity data, N is the number of sub-regions, and W is the m is the model weighting function, is the dot product of the vector group, is the physical property vector in the i-th subdomain, is the regularization parameter, are the Gramian matrix parameters, is the calculated total magnetization intensity, is the three components of magnetization intensity M M and the magnetization M obtained by inverting NSS N The partitioned Gramian matrix of is the total magnetization M and the magnetization M obtained by inverting NSS N The partitioned Gramian matrix of .

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] In actual calculations, this method seamlessly partitions magnetic anomalies under complex remanent magnetization conditions based on the characteristics of normalized magnetic source intensity data. Physical property correlation-constrained inversion is performed on the three components of the magnetization intensity and the normalized magnetic source intensity data inversion results for each subdomain, yielding highly accurate magnetization vector inversion results. This method addresses the shortcomings of existing methods and, through simulation experiments, demonstrates that it can improve the accuracy of inversion results compared to previous methods under complex remanent magnetization conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Flowchart of a high-precision magnetization intensity vector inversion method in an embodiment of the present invention.

[0022] Figure 2 The following are examples of magnetic anomalies and partitioning effects of two cubes in an embodiment of the present invention. (a) is a 3D view and magnetic anomaly map; (b) is the partitioning result based on data and the seamless partitioning result based on data features.

[0023] Figure 3 The following is an example of the inversion of two cubic magnetic anomalies in the embodiment of the present invention. (a) is the north component M of the self-constrained inversion result of the magnetic vector. x ; (b) is the east component M of the self-constrained inversion result of the magnetic vector y ; (c) is the vertical component M of the self-constrained inversion result of the magnetic vector z (d) is the total magnetization intensity M of the self-constrained inversion result of the magnetic vector; (e) is the north component M of the magnetic vector inversion result of the algorithm of the present invention x ; (f) is the east component M of the magnetic vector inversion result of the algorithm of the present invention y ; (g) is the vertical component M of the magnetic vector inversion result of the algorithm of the present invention z ; (h) is the total magnetization intensity M of the magnetic vector inversion result of the algorithm of the present invention. DETAILED DESCRIPTION

[0024] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0025] 1. Self-constrained inversion of magnetization vector:

[0026] The self-constrained inversion method of the magnetization intensity vector is to add the Gramian constraint to the magnetization intensity vector inversion. Then the objective function of the self-constrained inversion of the magnetization intensity vector can be expressed as:

[0027] . is the magnetic anomaly data, are the three components of magnetization intensity, is the kernel function matrix of the three components of magnetization intensity, Represents the north component M x , East component M y and the vertical component M z， is the regularization parameter, W m is the model weight matrix, is the calculated total magnetization intensity, is the Gramian matrix parameter, is the three components of magnetization intensity M M The Gramian matrix between the components and the total magnetization M is used to strengthen the linear correlation between each component and the total magnetization to obtain a stable solution.

[0028] 2. Magnetization vector inversion based on normalized magnetic source intensity constraint:

[0029] The expression of normalized magnetic source intensity is as follows:

[0030] .

[0031] Where C m =10 -7 H / m, m is the magnetic moment of the dipole, and r is the distance between the field source and the observation point. It can be seen that NSS is inversely proportional to the distance, proportional to the magnetic moment, has nothing to do with the magnetization direction, and has a good correspondence with the underground field source. The underground magnetic structure distribution can be obtained by inverting NSS. Therefore, the present invention constrains the three components of the magnetization intensity by the normalized magnetic source intensity inversion result, thereby obtaining a reliable inversion result. The Gramian matrix is ​​added to the inversion objective function so that the three components of the magnetization intensity and the normalized magnetic source intensity inversion result are linearly correlated during the inversion iteration process. The objective function of the magnetic vector inversion based on the normalized magnetic source intensity constraint is as follows:

[0032] .

[0033] Where, The kernel function matrix representing the three components of magnetization intensity, are the three components of magnetization intensity, Represents the north component M x , East component M y and the vertical component M z， It is magnetic anomaly data. is the kernel function matrix of the normalized magnetic source intensity, MN The magnetization intensity is obtained by inverting NSS, where NSS is the normalized magnetic source intensity data. m is the model weighting function, is the regularization parameter, are the Gramian matrix parameters, is the calculated total magnetization. is the three components of magnetization intensity M M and the magnetization M obtained by inverting NSS N Gramian matrix, strengthening the three components of magnetization intensity M M The magnetization M obtained by inverting NSS N The magnetization vector inversion is performed based on the linear correlation between them. is the total magnetization M and the magnetization M obtained by inverting NSS N The Gramian matrix of .

[0034] 3. Magnetization intensity vector inversion based on data feature partitioning and normalized magnetic source intensity constraints:

[0035] In practice, magnetic bodies with different magnetization directions often exist underground, so it is necessary to perform zoning inversion. To reduce residual magnetic interference, this paper uses normalized magnetic source intensity data and proposes an adaptive seamless zoning method based on the geometric characteristics of the normalized magnetic source intensity data. The zoning steps are as follows:

[0036] 1) Search for the number of extreme points of the normalized magnetic source intensity data, which is the number of subdomains.

[0037] 2) Search around each extreme point. The initial boundary of the subdomain is where the amplitude is less than half of the extreme point or the amplitude begins to increase.

[0038] 3) Take the initial area S of each subdomain and the distance R between the unpartitioned point and the extreme point of a subdomain as the reference basis of the subdomain, and control the ratio of area to distance. To assign the point to the corresponding subdomain, search again until the subdomain boundaries coincide, which is the subdomain boundary.

[0039] After the above adaptive seamless partitioning, the study area is divided into N sub-regions with different magnetization directions. Then, the three components of the magnetization intensity of each sub-domain and the magnetization intensity M obtained by inverting NSS are calculated. N Perform physical property correlation constrained inversion. The objective function of the magnetization intensity vector inversion based on data feature partitioning and normalized magnetic source intensity constraints is as follows:

[0040] .

[0041] Where, The kernel function matrix representing the three components of magnetization intensity, are the three components of magnetization intensity, Represents the north component M x , East component M y and the vertical component M z， is the magnetic anomaly data, is the kernel function matrix of the normalized magnetic source intensity, M N The magnetization intensity is obtained by inverting NSS, where NSS is the normalized magnetic source intensity data, N is the number of sub-regions, and W is the m is the model weighting function. is the dot product of the vector group, is the regularization parameter, are the Gramian matrix parameters, is the calculated total magnetization intensity, is the three components of magnetization intensity M M and the magnetization M obtained by inverting NSS N The partitioned Gramian matrix of is the total magnetization M and the magnetization M obtained by inverting NSS N The partitioned Gramian matrix of . is the physical property vector in the i-th subdomain, which can be expressed as:

[0042] .

[0043] Among them, i represents the subdomain number, and Represents the physical properties of the entire area, Represents the physical properties of the i-th subdomain.

[0044] The magnetization vector inversion is performed using the objective function of the magnetization vector inversion under the constraint of data feature partitioning and normalized magnetic source intensity, which can improve the accuracy of the inversion results and obtain the true underground magnetization intensity distribution and magnetization direction.

[0045] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0046] See Figure 1-Figure 3 , the magnetization intensity vector inversion of two underground cubes is calculated by the method of the present invention, Figure 2 (a) is the cube distribution and magnetic anomaly results, Figure 2 (a) shows the three-dimensional positions of two cubes with their centers at (900, 1000, -650) m and (2000, 1000, -800) m, as well as the magnetic anomalies. Table 1 shows the actual physical parameters of the model.

[0047] Table 1 Physical parameters of the model

[0048]

[0049] As can be seen in Table 1, the magnetization intensity of the two cubes is 5 A / m, and the inclination and declination of the Earth's magnetic field are I0 = 60° and D0 = 10°. Cube 1 has a magnetization inclination of I1 = -20° and a declination of D1 = 10°, while cube 2 has a magnetization inclination of I2 = 40° and a declination of D2 = -20°. Figure 2 (b) is the normalized magnetic source intensity and the results of two partitioning methods. Figure 2 The black box in the middle represents the model location, and the red circle delineates the data-based partitioning range. Self-constrained inversion of the magnetization intensity vector is performed based on the partitioning results delineated by the red circle. The white lines delineate the seamless partitioning range based on data features. This is the partitioning result obtained by the partitioning method of the present invention. Compared with previous partitioning results, the sub-regions generated by the partitioning method of the present invention can process the entire area.

[0050] Figure 3 is the inversion result of the method of the present invention and the self-constrained inversion method of the magnetic vector, Figure 3 The black box in the middle indicates the model position, and the black arrow indicates the magnetization direction. Figure 3 (a) ~ Figure 3 (c) shows the M obtained by the self-constrained inversion method of the magnetic vector x 、M y 、M z The three-dimensional result of the component is a slice diagram at y=1000m. Among them, the north component M x The position of cube 1 cannot be displayed, and the result at cube 2 diverges, which deviates greatly from the true value. The east component My and the vertical component Mz can reflect the positions of the two cubes, but the result at cube 1 is closer to that at cube 2, and the result is distorted in the non-coupling area. For the total magnetization intensity M obtained by the above three-component combination, see Figure 3 (d) The results diverge and the true position of the model cannot be obtained. Its accuracy is 59.4%. Figure 3 (e)~ Figure 3 (h) shows the M obtained by the method of the present invention x 、M y 、M z The three-dimensional results of the component and total magnetization intensity are sliced ​​at y=1000m. Figure 3 Results show that the proposed method can accurately obtain the positions and boundaries of the two cubes. The obtained three-component data is closer to the actual physical parameters of the model, and the inversion results are more convergent and smooth. The proposed method has an accuracy of 71.4%, which greatly improves the accuracy of the inversion results.

[0051] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A high-precision magnetization intensity vector inversion method, characterized in that: The following steps are involved: The first step is to convert the magnetic anomaly into a normalized magnetic source intensity that is weakly sensitive to the magnetization direction; The second step is to perform seamless partitioning based on data features according to the normalized magnetic source intensity data; In the third step, the three components of the magnetization intensity and the magnetization intensity obtained by NSS inversion are subjected to Gramian constraints in the partitions to obtain the objective function of the magnetization intensity vector inversion under the constraint of data feature partition-normalized magnetic source intensity. The magnetization vector inversion is performed using the objective function of the magnetization intensity vector inversion under the constraint of data feature partition-normalized magnetic source intensity to obtain the magnetization intensity and magnetization direction distribution. The objective function of the magnetization vector inversion under the constraint of data feature partition-normalized magnetic source intensity is: ， The kernel function matrix representing the three components of magnetization intensity, are the three components of magnetization intensity, Represents the north component M x , East component M y and the vertical component M z， is the magnetic anomaly data, is the kernel function matrix of the normalized magnetic source intensity, M N The magnetization intensity is obtained by inverting NSS, where NSS is the normalized magnetic source intensity data, N is the number of sub-regions, and W is the m is the model weighting function, is the dot product of the vector group, is the physical property vector in the i-th subdomain, is the regularization parameter, are the Gramian matrix parameters, is the calculated total magnetization intensity, is the three components of magnetization intensity M M and the magnetization M obtained by inverting NSS N The partitioned Gramian matrix of is the total magnetization M and the magnetization M obtained by inverting NSS N The partitioned Gramian matrix of .

2. The high-precision magnetization intensity vector inversion method according to claim 1, characterized in that: The expression of the normalized magnetic source intensity is as follows: , C m =10 -7 H / m, m is the magnetic moment of the dipole, and r is the distance between the field source and the observation point.

3. The high-precision magnetization intensity vector inversion method according to claim 1, characterized in that: The seamless partitioning based on data features according to the normalized magnetic source intensity data comprises the following steps: The number of extreme points of the search normalized magnetic source intensity data is the number of subdomains; Search around each extreme point, and the initial boundary of the subdomain is where the amplitude is less than half of the extreme point or the amplitude begins to increase; The initial area S of each subdomain and the distance R between the unpartitioned point and the extreme point of a subdomain are used as the reference basis for the subdomain. According to the ratio of the control area to the distance To assign the point to the corresponding subdomain, search again until the subdomain boundaries coincide, which is the subdomain boundary.

Images