阅读说明：本技术 一种自反馈类正则化反演方法 (Self-feedback regularization inversion method ) 是由 陈杭 任利兵 王旭龙 刘利 柳建新 魏登武 雷文太 杨刚强 郭荣文 于 2021-07-19 设计创作，主要内容包括：本发明提供了一种自反馈类正则化反演方法,步骤S1：将平面磁异常数据进行化极并成图；步骤S2：根据化极后的磁异常平面图进行圈定,并对圈定数据进行插值；步骤S3：寻找极大值的平面位置,将此平面位置作为反演的初始位置；步骤S4：开始反演迭代过程,首先给初始模型赋值,然后对模型参数进行迭代更新,同时计算拟合差；迭代完毕后,得到输出反演的结果；步骤S5：得到反演模型参数以及吻合度；吻合度满足要求,则输出结果；吻合度不满足,则返回步骤S2,重新圈定数据,直到输出吻合度满足要求为止。本发明的新方法有效避免观测数据中噪声的影响,使反演过程更加稳健,更容易跳出局部极值,得出的反演结果更加接近实际位置。(The invention provides a self-feedback regularization inversion method, comprising the following steps of S1: polarizing and mapping the plane magnetic anomaly data; step S2: delineating according to the magnetic anomaly plan after polarization, and interpolating delineation data; step S3: searching a plane position of the maximum value, and taking the plane position as an initial position of inversion; step S4: starting an inversion iteration process, firstly assigning values to an initial model, then carrying out iteration updating on model parameters, and simultaneously calculating a fitting difference; after iteration is finished, obtaining an output inversion result; step S5: obtaining inversion model parameters and goodness of fit; if the goodness of fit meets the requirements, outputting a result; if the goodness of fit is not satisfied, the process returns to step S2 to define the data again until the output goodness of fit satisfies the requirement. The new method of the invention effectively avoids the influence of noise in the observed data, makes the inversion process more stable, makes it easier to jump out local extreme values, and makes the obtained inversion result more approximate to the actual position.)

1. A self-feedback regularization inversion method is characterized by comprising the following steps:

step S1: polarizing the collected plane magnetic anomaly data and mapping;

step S2: delineating according to the magnetic anomaly plan after polarization, and interpolating delineation data;

step S3: searching a plane position of a maximum value in the polarized and interpolated data, and taking the plane position as an initial position of inversion;

step S4: starting an inversion iteration process, firstly assigning values to an initial model, then carrying out iteration updating on model parameters, and simultaneously calculating a fitting difference; after iteration is finished, obtaining an output inversion result;

step S5: finishing inversion iteration to obtain inversion model parameters and goodness of fit; if the goodness of fit meets the requirements, outputting a result; if the goodness of fit is not satisfied, the process returns to step S2 to re-define the data until the output goodness of fit satisfies the requirement.

2. The self-feedback regularization inversion method according to claim 1, wherein in the step S4, model parameters are iteratively updated by using equations (1) and (2):

wherein m is^(k)、m^(k+1)Models for the kth and k +1 iterations, respectively; j. the design is a square_kA Jacobian matrix of the kth iteration, namely a partial derivative matrix of forward model data to an inversion model; r is_kFitting difference at the k iteration;denotes J_kThe transposed matrix of (2); i is an identity matrix; lambda [ alpha ]_kThe adjustment factor for the k-th iteration is referred to as the regularization factor for correspondence with the conventional hyper-parametric inversion.

3. The self-feedback regularization inversion method according to claim 2, wherein in dipole inversion, the selected inversion target function is as follows (3):

wherein m is a model of the dipole to be inverted; phi_d(m) is the two-norm of the fitting difference between the forward model data and the observed data, i.e.:

wherein, F [ m ]]Is a model forward data vector;the ith data of the forward modeling data vector; d^obsIs an observation data vector;the ith data which is an observation data vector; w_dRepresented is a diagonal matrix of observation errors, oa_iIs the data of the ith row and the ith column of the diagonal matrix of the observation errors, and N represents the total amount of the observation data;

and (3) continuously modifying and iterating the model parameters according to the formula (1) and the formula (2) until the set iteration times are finished.

4. The self-feedback regularization inversion method according to claim 3, wherein the forward model data is obtained by dipole forward, specifically, a magnetic total field is obtained by equation (5):

ΔT＝H_axL₀+H_ayM₀+Z_aN₀ (5)，

wherein L is₀＝cosI₀cosA₀，M₀＝cosI₀sinA₀，N₀＝sinI₀；I₀Is the declination of the earth's magnetic field, A₀Is the magnetic inclination of the earth magnetic field, Δ T is the total magnetic field, H_ax、H_ayAnd Z_aThe magnitude on the x, y and z components of the magnetic field, respectively.

5. The self-feedback regularization-based inversion method according to claim 4, wherein H_ax、H_ayAnd Z_aThe calculation method of (c) is as follows:

let the magnetic declination of total magnetization be I, the magnetic dip angle be A, and the center of the magnetic dipole be O (x)₀，y₀B), the coordinates of the observation point are (x, y, z), and the magnetization intensity is M; and (3) calculating an expression of each component of the magnetic field by using a Poisson equation:

wherein M is_x、M_y、M_zRespectively representing the x, y and z directional components of the magnetization, where M_x＝McosIcosA，M_y＝McosIsinA，M_z＝MsinI；u₀Is the magnetic permeability; g is the universal gravitation constant; σ is the object density; pi is the circumference ratio; v_xx，V_yx，V_zx，V_xy，V_yy，V_zy，V_xz，V_yz，V_zzRespectively, the second partial derivatives of the gravitational potential in the corresponding direction;

the gravitational potential V is calculated by equation (7):

wherein v is the volume of the object, and r is the distance from the center of the object to the observation point;

the formula for each component of the magnetic field is directly obtained by substituting the second-order partial derivative of the attraction site into formula (6) for the erasure site, where m is Mv, α is cosIcosA, β is cosIsinA, and γ is sinI, according to the definition of magnetic moment m:

6. the self-feedback regularization inversion method according to claim 1, wherein in step S4, the assignment to the initial model includes 6 parameters, which are x, y and z position parameters, two angle parameters of magnetization dip angle and declination angle, and magnetic dipole polar distance.

7. The self-feedback regularization inversion method according to claim 6, wherein the initial values of x and y are the positions of the maximum values of the data after polar interpolation in step S3, and the initial value of the model depth z is assigned according to actual conditions.

8. The self-feedback regularization inversion method according to claim 1, wherein in step S5, goodness of fit is calculated according to equation (9):

where mean represents the average.

9. The self-feedback regularization inversion method according to claim 8, wherein in step S5, the requirement is satisfied when the goodness of fit is greater than 0.9.

Technical Field

The invention relates to the technical field of magnetic prospecting, in particular to a self-feedback regularization inversion method.

Background

Magnetic prospecting plays an important role in mineral exploration, geological exploration, deep structure and underground metal exploration. The magnetic dipole can be generally used for describing magnetic anomaly characteristics of various objects, and therefore, the inversion of the position of the magnetic dipole has important practical application significance.

In the magnetic dipole inversion, because magnetic measurement interference is often relatively strong, the inversion is easily influenced by noise to become unstable, and the inversion easily falls into a local extreme value. Meanwhile, due to the existence of noise, a plurality of models can be fitted to observed data. If the fitting difference between the observation data and the forward response data is only used as an optimization target in the inversion, the noise of the observation data can have a great influence on the inversion process in the inversion process. In the inversion process, if the fitting difference between the forward model data and the observation data is continuously reduced, the inversion result is often unreliable when the magnetic interference is strong. Therefore, how to improve the problem in dipole inversion and reduce the influence of errors in observed data on an inversion result has great significance in dipole inversion application.

In the latest robust gaussian newton method inversion, the model parameters are updated iteratively, generally using the following formula:

wherein m is^(k)，m^(k+1)Model parameters for the kth and k +1 iterations, respectively, J_kThe Jacobian matrix for the kth iteration, i.e. the partial derivative matrix of the forward model data on the inverse model, r_kAs the fitting difference at the kth iteration,denotes J_kThe transposed matrix of (2).

This Gaussian Newton method requires J_kThe matrix array is full-rank, and meanwhile, the optimization process is only related to fitting difference and is easily influenced by data noise; meanwhile, the method has the problems that the method is easy to fall into a local minimum value and overfitting the data.

In view of the above, there is a need for a self-feedback regularization inversion method to solve the problems in the prior art.

Disclosure of Invention

The invention aims to provide a self-feedback regularization inversion method, which aims to solve the problems that the existing inversion method is easily influenced by data noise, is easily trapped into a local minimum value and is overfitting data, and the specific technical scheme is as follows:

a self-feedback regularization inversion method comprises the following steps:

step S1: polarizing the collected plane magnetic anomaly data and mapping;

step S2: delineating according to the magnetic anomaly plan after polarization, and interpolating delineation data;

step S3: searching a plane position of a maximum value in the polarized and interpolated data, and taking the plane position as an initial position of inversion;

step S4: starting an inversion iteration process, firstly assigning values to an initial model, then carrying out iteration updating on model parameters, and simultaneously calculating a fitting difference; after iteration is finished, obtaining an output inversion result;

step S5: finishing inversion iteration to obtain inversion model parameters and goodness of fit; if the goodness of fit meets the requirements, outputting a result; if the goodness of fit is not satisfied, the process returns to step S2 to re-define the data until the output goodness of fit satisfies the requirement.

Preferably, in the above technical solution, in the step S4, the model parameters are iteratively updated by using the following equations (1) and (2):

wherein m is^(k)、m^(k+1)Models for the kth and k +1 iterations, respectively; j. the design is a square_kA Jacobian matrix of the kth iteration, namely a partial derivative matrix of forward model data to an inversion model; r is_kFitting difference at the k iteration;denotes J_kThe transposed matrix of (2); i is an identity matrix; lambda [ alpha ]_kThe adjustment factor for the k-th iteration is referred to as the regularization factor for correspondence with the conventional hyper-parametric inversion.

Preferably, in the dipole inversion, the selected inversion target function is as follows:

wherein m is a model of the dipole to be inverted; phi_d(m) is the two-norm of the fitting difference between the forward model data and the observed data, i.e.:

wherein, F [ m ]]Is a model forward data vector;the ith data of the forward modeling data vector; d^obsIs an observation data vector;the ith data which is an observation data vector; w_dRepresentative is a diagonal matrix of observation errors,is the data of the ith row and the ith column of the diagonal matrix of the observation errors, and N represents the total amount of the observation data;

and (3) continuously modifying and iterating the model parameters according to the formula (1) and the formula (2) until the set iteration times are finished.

Preferably, in the above technical solution, the forward model data is obtained by dipole forward, specifically, the magnetic total field is obtained by formula (5):

ΔT＝H_axL₀+H_ayM₀+Z_aN₀ (5)，

wherein L is₀＝cosI₀cosA₀，M₀＝cosI₀sinA₀，N₀＝sinI₀；I₀Is the declination of the earth's magnetic field, A₀Is the magnetic inclination of the earth magnetic field, Δ T is the total magnetic field, H_ax、H_ayAnd Z_aThe magnitude on the x, y and z components of the magnetic field, respectively.

Preferred in the above technical solution, wherein H_ax、H_ayAnd Z_aThe calculation method of (c) is as follows:

let the magnetic declination of total magnetization be I, the magnetic dip angle be A, and the center of the magnetic dipole be O (x)₀，y₀B), the coordinates of the observation point are (x, y, z), and the magnetization intensity is M; and (3) calculating an expression of each component of the magnetic field by using a Poisson equation:

wherein M is_x、M_y、M_zRespectively representing the x, y and z directional components of the magnetization, where M_x＝McosIcosA，M_y＝McosIsinA，M_z＝MsinI；u₀Is the magnetic permeability; g is the universal gravitation constant; σ is the object density; pi is the circumference ratio; v_xx，V_yx，V_zx，V_xy，V_yy，V_zy，V_xz，V_yz，V_zzRespectively, the second partial derivatives of the gravitational potential in the corresponding direction;

the gravitational potential V is calculated by equation (7):

wherein v is the volume of the object, and r is the distance from the center of the object to the observation point;

the formula for each component of the magnetic field is directly obtained by substituting the second-order partial derivative of the attraction site into formula (6) for the erasure site, where m is Mv, α is cosIcosA, β is cosIsinA, and γ is sinI, according to the definition of magnetic moment m:

preferably, in the above technical solution, the assignment to the initial model includes 6 parameters, which are x, y, and z position parameters, two angle parameters of a magnetization dip angle and a declination angle, and a magnetic dipole polar distance.

Preferably, in the above technical solution, the initial values of x and y adopt the position of the maximum value of the data after polar interpolation in step S3, and the initial value of the model depth z is assigned according to the actual situation.

Preferably, in the above technical solution, in step S5, the goodness of fit is calculated according to equation (9):

where mean represents the average.

In the above technical solution, it is preferable that, in step S5, the goodness of fit is greater than 0.9, which satisfies the requirement.

The technical scheme of the invention has the following beneficial effects:

the invention provides a self-feedback regularization inversion method, provides a self-feedback technology based on the change of parameters, and solves the problem that the parameter updating is greatly influenced by data noise and becomes unstable during inversion. The new inversion method adds a regularization-like term in the iterative process of inversion, the weight of the regularization-like term is changed in a self-feedback manner based on the change of the parameter, namely, the regularization factor is determined according to the change of the parameter, so that a more accurate inversion result can be obtained. Compared with the traditional method, the new method can more effectively avoid the influence of noise in the observed data, and simultaneously enables the inversion process to be more stable, so that local extremum values can be more easily jumped out, and the obtained inversion result is closer to the actual position.

The invention changes the traditional three-position parameter (namely x, y and z) inversion into a new six-parameter inversion, so that the actual data can be better fitted, and the residual magnetization intensity is also included in the inversion; the inversion with 6 parameters obviously conforms to the actual situation, and a more accurate inversion result can be obtained. Meanwhile, the method adopts the steps of manually delineating the anomaly and determining the initial central position of the magnetic dipole anomaly body through the polarization, so that the inverted initial model is close to the real position, and the inversion is faster in convergence and more accurate.

In addition, the invention is beneficial to improving the data information amount in inversion by interpolating the measured data, thereby improving the inversion precision. In addition, goodness of fit calculation is added, and the reliability of the inversion can be known through goodness of fit, so that whether the position of the inversion is accurate or not can be judged.

In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:

FIG. 1 is a flow chart of a self-feedback regularization inversion method of the present invention;

FIG. 2 is a schematic diagram of the magnetic field generated by a magnetic dipole;

FIG. 3a is a schematic diagram of the original magnetic anomaly data before polarization (white crosses represent the true horizontal center position of the anomaly);

FIG. 3b is a schematic of magnetic anomaly data after poling (white boxes represent artificially delineated regions):

FIG. 4 is a comparison of the inversion algorithm of the present invention with the international latest robust Gaussian Newton inversion location parameter x;

FIG. 5 is a comparison of the inversion algorithm of the present invention with the international latest robust Gaussian Newton inversion position parameter y;

FIG. 6 is a comparison of the inversion algorithm of the present invention with the international latest robust Gaussian Newton inversion position parameter z;

FIG. 7 is a comparison of the inversion algorithm of the present invention and the latest international steady Gaussian Newton inversion fitting difference;

FIG. 8a is the result of data synthesis of anomaly at (2m, 5m) position with oblique magnetization and Gaussian white noise addition;

FIG. 8b is the result of data synthesis of anomaly at (5m, 5m) position with oblique magnetization adding Gaussian white noise;

FIG. 8c is the result of data synthesis of anomalous body at (5m, 2m) position skewed magnetization with Gaussian white noise addition;

FIG. 8d is the result of data synthesis of anomaly at (2m, 2m) position with oblique magnetization adding Gaussian white noise;

FIG. 9a shows the measured data of the oblique magnetization at the (4.0m, 3.01m) position of the abnormal body;

FIG. 9b shows the measured data of the oblique magnetization at the (3.56m, 3.5m) position of the abnormal body;

FIG. 9c shows the measured data of the oblique magnetization at the (3.96m, 3.75m) position of the abnormal body;

FIG. 9d shows the measured data of the oblique magnetization of the anomaly at the (2.56m, 3.7m) position with another dipole interference.

Detailed Description

In order that the invention may be more fully understood, a more particular description of the invention will now be rendered by reference to specific embodiments thereof that are illustrated in the appended drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

Example 1:

referring to fig. 1, a self-feedback regularization inversion method is characterized by comprising the following steps:

as shown in fig. 3a and 3b, step S1: polarizing the collected plane magnetic anomaly data and mapping; the polarization can eliminate the influence of oblique magnetization and simplify the magnetic field form. Therefore, the magnetic anomaly map after polarization is equivalent to underground magnetic anomaly projection, and subsequent manual delineation of magnetic anomalies can be easily realized.

Preferably, the frequency domain polarization technology is adopted in the embodiment, the form of the polarized data is simpler, and meanwhile, the extreme value of the data basically covers the real position of the underground abnormal body, so that the data can be easily manually defined according to the polarized magnetic abnormal image for inversion.

Step S2: manually delineating according to the magnetic anomaly plan after polarization, and interpolating delineation data; in this embodiment, a kriging interpolation method is preferably adopted, the number of data is increased by interpolation, and the interpolated data is used as the data of subsequent inversion;

step S3: finding a plane position of a maximum value in the data after polarization and interpolation, and taking the plane position as an initial position of inversion (namely regularization-like inversion);

step S4: starting an inversion iteration process, firstly assigning values to an initial model, then carrying out iteration updating on model parameters, and simultaneously calculating a fitting difference; after iteration is finished, obtaining an output inversion result;

preferably, in step S4, the initial model is assigned with 6 parameters, namely x, y and z position parameters, two angle parameters of the magnetization dip angle and the declination angle, and the magnetic dipole polar distance. The initial values of x and y are the positions of the maximum values of the data after polar interpolation in step S3, the initial value of the model depth z is assigned according to the actual situation, and preferably the initial value of the model depth z is assigned to 1m, because in the practical application of the magnetic dipole, the buried depth of the abnormal body is usually 0.5 to 2m, the initial value is set to 1m, which facilitates iterative convergence.

Step S5: finishing inversion iteration to obtain inversion model parameters and goodness of fit; if the goodness of fit meets the requirements, outputting a result; if the goodness of fit is not satisfied, returning to the step S2, and manually delineating the data again until the output goodness of fit satisfies the requirement. Preferably, the goodness of fit is greater than 0.9.

The above is the processing flow of the self-feedback regularization-based inversion method in this embodiment, and then the inversion (i.e. regularization-based inversion) process in step S4 in this embodiment is described in detail.

In step S4 in this embodiment, the model parameters are iteratively updated by using equations (1) and (2):

wherein m is^(k)、m^(k+1)Models for the kth and k +1 iterations, respectively; j. the design is a square_kA Jacobian matrix of the kth iteration, namely a partial derivative matrix of forward model data to an inversion model; r is_kFitting difference at the k iteration;denotes J_kThe transposed matrix of (2); i is an identity matrix; lambda [ alpha ]_kThe adjustment factor for the kth iteration is called a regularization factor for corresponding to the traditional hyper-parametric inversion; as can be seen from equation (2), the adjustment factor is the sum of the absolute values of the last model update amount.

In the dipole inversion, the selected inversion target function is as follows:

wherein m is a model of the dipole to be inverted; phi_d(m) is the two-norm of the fitting difference between the forward model data and the observed data, i.e.:

wherein, F [ m ]]Is a model forward data vector; d_i ^predThe ith data of the forward modeling data vector; d^obsIs an observation data vector;the ith data which is an observation data vector; w_dIs represented by the observationA diagonal matrix of the error is formed,is the data of the ith row and the ith column of the diagonal matrix of the observation errors, and N represents the total amount of the observation data;

in the inversion process, the error between the observation data and the forward model data, namely the fitting difference, is required to be minimized; the process needs to continuously modify and iterate the model parameters through the formula (1) and the formula (2) until the set iteration times are finished; iteration times can be set by a person in the field according to actual conditions, the requirement that the value of m obtained by the current and later two inversions is basically unchanged can be met, and the inversion can be considered to be converged at the moment.

Further, as known in the art, in the magnetic dipole inversion problem, the forward problem of the magnetic dipole is firstly solved, and the magnetic field generated by the magnetic dipole is correctly simulated to ensure the accuracy of the inversion, so that the forward evolution will be described in detail below.

In this embodiment, forward model data is obtained by dipole forward, specifically, a total magnetic field is obtained by formula (5):

ΔT＝H_axL₀+H_ayM₀+Z_aN₀ (5)，

wherein L is₀＝cosI₀cosA₀，M₀＝cosI₀sinA₀，N₀＝sinI₀；I₀Is the declination of the earth's magnetic field, A₀Is the magnetic inclination of the earth magnetic field, Δ T is the total magnetic field, H_ax、H_ayAnd Z_aThe magnitude on the x, y and z components of the magnetic field, respectively.

For an object with magnetism on the earth, if the object is spherical or ellipsoid-like in shape (as shown in fig. 2), the magnetic field generated by the object is equivalent to the magnetic field generated by a magnetic dipole. The magnetic field of the magnetic dipole can be derived from the Poisson's equation, specifically, H in equation (5)_ax、H_ayAnd Z_aCan be calculated as follows:

as shown in FIG. 2The x and y coordinate systems are shown as being north and east, and the z axis is vertically downward; let the magnetic declination of total magnetization be I, the magnetic dip angle be A, and the center of magnetic dipole R be O (x)₀，y₀B), the coordinate of the observation point P is (x, y, z), and the magnetization intensity is M; and (3) calculating an expression of each component of the magnetic field by using a Poisson equation:

wherein M is_x、M_y、M_zRespectively representing the x, y and z directional components of the magnetization, where M_x＝McosIcosA，M_y＝McosIsinA，M_z＝MsinI；u₀Is the magnetic permeability; g is the universal gravitation constant; σ is the object density; pi is the circumference ratio; v_xx，V_yx，V_zx，V_xy，V_yy，V_zy，V_xz，V_yz，V_zzRespectively, the second partial derivatives of the gravitational potential V in the corresponding directions, such as: v_xyIt means that the x-direction partial derivative is first calculated for V and then the y-direction partial derivative is calculated,

the gravitational potential V is calculated by equation (7):

wherein v is the volume of the object, and r is the distance from the center of the object to the observation point;

from the definition of magnetic moment m, let α ═ cosIcosA, β ═ cosIsinA, and γ ═ sinI, the second order partial derivative of the attraction site is substituted into formula (6) for the erasure site, and the formula for each component of the magnetic field can be directly obtained:

in this embodiment, preferably, in step S5, the goodness of fit is calculated according to equation (9):

where mean represents the average.

Furthermore, in order to test the effectiveness of the method of the embodiment, verification is performed by measuring data in theoretical data and data in an abnormal body in a certain place.

In theoretical data, the data is closer to the real situation by adding white gaussian noise to the data. Meanwhile, the method of the embodiment is compared with the newly published robust inversion of the gauss-newton method, as shown in fig. 4, fig. 5, fig. 6 and fig. 7. In comparison, it can be seen that the method of the present embodiment converges quickly and to the true position parameter. The international latest published steady gauss-newton method inversion is slow in convergence, and meanwhile, the inversion cannot converge to a real position parameter. In addition, although the international latest robust gauss-newton method can converge to a lower fitting difference, the international latest robust gauss-newton method falls into a local minimum value, overfitts data, fits noise and is poor in searching capability. The algorithm of the present embodiment converges well to the true position without overfitting the data, thus fitting the noise as well.

Fig. 8 a-8 d are the simulation data of the anomalous body, the magnetic anomaly generated under the oblique magnetization, and the white gaussian noise is added. From the results, it can be seen that in the theoretical synthetic data, the new algorithm of the present embodiment can be very accurate to invert the true position of the anomaly no matter which orientation the anomaly is in.

In addition, the present embodiment also performs a test by actually measuring the abnormal body data. In the actual measurement data, three groups of actual measurement data in fig. 9a, 9b and 9c are not provided with an interference body, and the actual measurement data in fig. 9d is artificially added with a magnetic dipole interference, so that the inversion difficulty is greatly increased. However, from the results, the new inversion algorithm and the flow of the embodiment can still accurately invert the real position of the abnormal body on the measured data. Therefore, the novel method of the embodiment can effectively invert the real positions of the dipoles in various practical situations.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.