Magnetic source target positioning method

Abstract

The invention discloses a magnetic source target positioning method, which belongs to the technical field of geophysical exploration, is used for positioning a magnetic source target, and comprises the following steps: collecting and preprocessing plane grid magnetic anomaly data, constructing a simplified Euler deconvolution model under the constraint of derivative features, segmenting observation data by using a local sliding window, and resolving to generate an Euler solution point cloud. The method comprises the following steps: converting a selection problem of an equivalent scale factor into a one-dimensional global optimization problem, adaptively searching an optimal solution through a Bayesian optimization method, identifying a magnetic source high-probability solution point and a noise solution point by using a density-based spatial clustering method, introducing a density penalty term to strengthen a high-probability solution constraint, and constructing a final positioning target function. And outputting the optimal position solution of the magnetic source. According to the method, a traditional Euler deconvolution model is simplified, noise interference is effectively suppressed, the stability and robustness of the inversion process are improved, uncertainty caused by manual parameter selection is avoided, and the positioning precision is improved.

Description

Technical Field

[0001] This invention discloses a method for locating magnetic source targets, belonging to the field of geophysical exploration technology. Background Technology

[0002] Magnetic anomalies are localized distortions of the Earth's magnetic field caused by ferromagnetic objects. They possess strong cross-medium detection capabilities, high positioning accuracy, stealth, and high detection efficiency, making them widely used for locating ferromagnetic targets. Existing magnetic source localization methods mainly include analytical localization methods based on magnetic dipole models, target tracking algorithms based on filtering and state estimation, and direct localization algorithms based on geometry and analysis. Among these, direct localization algorithms based on geometry and analysis derive analytical solutions for target position parameters by utilizing the inherent mathematical properties of the magnetic field or magnetic gradient, offering advantages such as high computational efficiency and clear structure. The Euler deconvolution inversion algorithm, as a typical representative of this method, is widely used due to its significant advantages, as it does not require specific geological model assumptions.

[0003] To further improve positioning accuracy, some studies have proposed an improved algorithm based on the integral form of the Euler equation, combined with a specially designed multi-coil sensor. Using the linear solution as the initial value for nonlinear least-squares optimization, high-precision positioning of magnetic source targets is achieved. Furthermore, the improved tilted Euler inversion method enhances the robustness of the solution by avoiding computational singularities and reducing instability factors during the inversion process. In recent years, with the integration of multiple disciplines, Euler deconvolution combined with deep learning target detection models has achieved high-precision identification and detection of typical magnetic sources such as underwater unexploded ordnance. Other research, based on the second-order magnetic gradient tensor system, has achieved high-precision single-point positioning of magnetic source targets without prior background magnetic field information by fusing Euler deconvolution with invariant constraints in the magnetic gradient tensor space. Furthermore, by combining automatic Euler deconvolution initialization with neural network-assisted Kalman filtering, high-precision robust tracking and positioning of the position, velocity, and magnetic moment of moving magnetic sources has been achieved without requiring noise statistical priors or relying on manual initial values. Despite the significant progress made by the above methods, problems still exist in complex real-world environments, such as reliance on empirical selection of the equivalent scaling factor, scattered solution results, and insufficient multi-target resolution. There is an urgent need to develop more adaptive, robust, and automated magnetic source target localization technology. Summary of the Invention

[0004] The purpose of this invention is to provide a magnetic source target localization method to solve the problems in the prior art, such as model parameters relying on human experience, high subjectivity and low efficiency, divergent inversion solution results, poor stability and weak anti-interference ability.

[0005] A method for locating a magnetic source target, comprising: S1. Collect planar grid magnetic anomaly data and perform preprocessing. Preprocessing includes local weighted regression smoothing based on the magnetic anomaly data, calculating the first derivative of the preprocessed magnetic anomaly data to extract the preliminary magnetic anomaly boundary, calculating the second derivative of the preprocessed magnetic anomaly data to extract the zero intersection point constrained preliminary magnetic anomaly boundary, and using the constrained preliminary magnetic anomaly boundary as the initial search range of the Euler deconvolution algorithm. S2. Randomly set the initial position of the magnetic source target within the initial search range, construct a simplified Euler deconvolution model, introduce an equivalent scaling factor to characterize the model parameters, and construct a preliminary positioning objective function by minimizing the sum of squared residuals. S3. Set up a local sliding window, segment the observation data based on the local sliding window, invert candidate solutions for the magnetic source target position in the local sliding window based on the preliminary positioning objective function, summarize all candidate solutions of the local sliding window to construct the Euler solution point cloud, transform the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, construct the observation objective function based on the covariance trace of the solution point cloud, introduce Bayesian optimization to solve the observation objective function, and obtain the optimal equivalent scaling factor. S4. Use density-based spatial clustering to identify high-density solution points and noise points of the magnetic source, introduce a density penalty term, construct the final positioning objective function based on the optimal equivalent scaling factor, density penalty term and preliminary positioning objective function, and output the optimal magnetic source target position estimate through the final positioning objective function.

[0006] S1 includes S1.1, collecting planar grid magnetic anomaly data and performing preprocessing, including neighborhood weighted regression smoothing based on the magnetic anomaly data; S1 includes S1.2, calculating the first derivative of the preprocessed magnetic anomaly data and taking its absolute value, using the peak-finding function to identify the location of the maximum value, and estimating the preliminary magnetic anomaly boundary; S1 includes S1.3, calculating the second derivative of the preprocessed magnetic anomaly data, determining the zero intersection point based on the sign change, and using the zero intersection point to constrain the preliminary magnetic anomaly boundary; S1 includes S1.4, which uses the constrained initial magnetic anomaly boundary as the initial search range for the Euler deconvolution algorithm.

[0007] S2 includes, S2.1, setting the coordinates of the observation point within the initial search range as... The initial position of the magnetic source target is The model parameters are incorporated into the equivalent scaling factor. The model parameters include the background field. and construction index Construct a simplified Euler deconvolution model: ; ; In the formula, The sign of the partial derivative. for Gradient of direction, for Gradient of direction, As an equivalent scaling factor, This represents the preprocessed magnetic anomaly value.

[0008] S2 includes S2.2, for any observation point : ; In the formula, For the index of observation points, For the first The residuals at each observation point In the first At each observation point exist gradient in direction, In the first At each observation point exist gradient in direction, In the first Preprocessed magnetic anomaly values ​​at each observation point; S2 includes S2.3, constructing a preliminary localization objective function by minimizing the sum of squared residuals: ; In the formula, The number of observation points. .

[0009] S3 includes, S3.1, setting a partial sliding window. The size is The observation data is divided into indivual Each The initial application of the objective function to invert candidate solutions for the magnetic source target location is as follows: ; In the formula, For the index of a local sliding window, , for Candidate solutions obtained from inversion. For a given Under the conditions, The magnetic source target inside Coordinate estimates For a given Under the conditions, The magnetic source target inside Coordinate estimates; Summarize all candidate solutions to form an Euler solution point cloud. : ; In the formula, It is a two-dimensional real number space.

[0010] S3 includes S3.2, which transforms the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, and uses the covariance trace to characterize the overall dispersion of the solution point cloud. And construct a Gaussian process proxy model: ; ; In the formula, For covariance trace, The function on the left side of the sign follows the probability distribution on the right side of the sign. It is a mean function. Let covariance function be used. It is a Gaussian process.

[0011] S3 includes S3.3, constructing the acquisition function: ; In the formula, In order to improve, This is the current optimal observation value. For the posterior probability density, for The possible values ​​of ; Choose to Reaching the maximum value As an evaluation point for the next iteration : ; In the formula, To find the independent variable that maximizes the expected improvement function; like ,renew Recalculate Iterate until The improvement amount is less than Output makes Minimum optimal equivalent scaling factor .

[0012] S4 includes, S4.1, evaluating the clustering relationships of the Eulerian solution point cloud using a density-based spatial clustering method, including setting a point density threshold. and region radius threshold ,by With the center as the center, Construct the solution set region with radius . ; like The number of candidate solutions contained within is greater than or equal to ,definition For high-density solution sets, clustering is performed to preserve the high-density solution sets. like The number of candidate solutions contained within is less than ,definition To identify isolated points, these isolated points are removed as noise points.

[0013] S4 includes S4.2, which uses a density penalty term to improve clustering performance: ; In the formula, For density penalty terms, For Let be the set of all candidate solutions within the solution set region centered at the circle. for The set of all candidate solutions in the cluster to which it belongs. This is the intersection symbol.

[0014] S4 includes S4.3, based on , Construct the final localization objective function from the initial localization objective function. : ; In the formula, For regularization parameters; Solve using the least squares method Obtain the optimal magnetic source target position estimate .

[0015] Compared with existing technologies, this invention has the following advantages: By introducing derivative analysis to constrain the initial position selection of the model, this invention effectively avoids the divergence and discretization problems of solutions, ensuring the accuracy of the initial position selection. Based on this, the traditional Euler deconvolution model is simplified by reducing the dimensionality and complexity of unknown parameters, and the background field and depth, which are difficult to estimate stably, are uniformly absorbed into the equivalent scaling factor. This transforms the physically rigorous inversion model into a geometric positioning model centered on planar position determination. This simplification effectively suppresses parameter coupling and noise interference, improving the stability and robustness of the inversion process. Furthermore, the Bayesian optimization method is used to adaptively determine the equivalent scaling factor, avoiding the uncertainty caused by manual parameter selection and further improving positioning accuracy. In multi-target positioning, the algorithm constructs a density penalty term, transforming the noisy multi-magnetic-source positioning problem into a clustering and screening problem of planar geometric space solutions. Utilizing the difference between the spatial clustering of real magnetic source solutions and the random discretization of noise pseudo-solutions, the density of the solutions is used as a reliability metric. This allows for accurate identification of real targets and effective elimination of noise interference within a unified model framework, significantly enhancing the accuracy and robustness of multi-target positioning. This invention simplifies the calculation process, improves positioning efficiency, and exhibits good adaptability and scalability under complex background fields and large-scale data conditions, comprehensively improving the accuracy and reliability of magnetic anomaly source positioning. Attached Figure Description

[0016] Figure 1 This is a detailed flowchart of the present invention; Figure 2 The results are localization results of the Euler deconvolution method under simulated noisy conditions and a single magnetic source. Figure 3 The results are localization results of the density clustering-based Euler deconvolution method under simulated noisy conditions and a single magnetic source. Figure 4 The results are the localization results of the method of the present invention under simulated noisy conditions and a single magnetic source. Figure 5 The results are localization results of the Euler deconvolution method under simulated noisy conditions and multiple magnetic sources. Figure 6 The results are localization results of the density clustering-based Euler deconvolution method under simulated noisy conditions and multiple magnetic sources. Figure 7 The results are the localization results of the method of this invention under simulated noisy and multi-magnetic-source conditions. Figure 8 The results are the localization results of the Euler deconvolution method under measured multi-magnetic-source conditions. Figure 9 The results are localization results of the Euler deconvolution method based on density clustering under measured multi-magnetic-source conditions. Figure 10 The results are the localization results of the method of this invention under actual measurement with multiple magnetic sources. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0018] A method for locating a magnetic source target, comprising: S1. Collect planar grid magnetic anomaly data and perform preprocessing. Preprocessing includes local weighted regression smoothing based on the magnetic anomaly data, calculating the first derivative of the preprocessed magnetic anomaly data to extract the preliminary magnetic anomaly boundary, calculating the second derivative of the preprocessed magnetic anomaly data to extract the zero intersection point constrained preliminary magnetic anomaly boundary, and using the constrained preliminary magnetic anomaly boundary as the initial search range of the Euler deconvolution algorithm. S2. Randomly set the initial position of the magnetic source target within the initial search range, construct a simplified Euler deconvolution model, introduce an equivalent scaling factor to characterize the model parameters, and construct a preliminary positioning objective function by minimizing the sum of squared residuals. S3. Set up a local sliding window, segment the observation data based on the local sliding window, invert candidate solutions for the magnetic source target position in the local sliding window based on the preliminary positioning objective function, summarize all candidate solutions of the local sliding window to construct the Euler solution point cloud, transform the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, construct the observation objective function based on the covariance trace of the solution point cloud, introduce Bayesian optimization to solve the observation objective function, and obtain the optimal equivalent scaling factor. S4. Use density-based spatial clustering to identify high-density solution points and noise points of the magnetic source, introduce a density penalty term, construct the final positioning objective function based on the optimal equivalent scaling factor, density penalty term and preliminary positioning objective function, and output the optimal magnetic source target position estimate through the final positioning objective function.

[0019] S1 includes S1.1, collecting planar grid magnetic anomaly data and performing preprocessing, including neighborhood weighted regression smoothing based on the magnetic anomaly data; S1 includes S1.2, calculating the first derivative of the preprocessed magnetic anomaly data and taking its absolute value, using the peak-finding function to identify the location of the maximum value, and estimating the preliminary magnetic anomaly boundary; S1 includes S1.3, calculating the second derivative of the preprocessed magnetic anomaly data, determining the zero intersection point based on the sign change, and using the zero intersection point to constrain the preliminary magnetic anomaly boundary; S1 includes S1.4, which uses the constrained initial magnetic anomaly boundary as the initial search range for the Euler deconvolution algorithm.

[0020] S2 includes, S2.1, setting the coordinates of the observation point within the initial search range as... The initial position of the magnetic source target is The model parameters are incorporated into the equivalent scaling factor. The model parameters include the background field. and construction index Construct a simplified Euler deconvolution model: ; ; In the formula, The sign of the partial derivative. for Gradient of direction, for Gradient of direction, As an equivalent scaling factor, This represents the preprocessed magnetic anomaly value.

[0021] S2 includes S2.2, for any observation point : ; In the formula, For the index of observation points, For the first The residuals at each observation point In the first At each observation point exist gradient in direction, In the first At each observation point exist gradient in direction, In the first Preprocessed magnetic anomaly values ​​at each observation point; S2 includes S2.3, constructing a preliminary localization objective function by minimizing the sum of squared residuals: ; In the formula, The number of observation points. .

[0022] S3 includes, S3.1, setting a partial sliding window. The size is The observation data is divided into indivual Each The initial application of the objective function to invert candidate solutions for the magnetic source target location is as follows: ; In the formula, For the index of a local sliding window, , for Candidate solutions obtained from inversion. For a given Under the conditions, The magnetic source target inside Coordinate estimates For a given Under the conditions, The magnetic source target inside Coordinate estimates; Summarize all candidate solutions to form an Euler solution point cloud. : ; In the formula, It is a two-dimensional real number space.

[0023] S3 includes S3.2, which transforms the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, and uses the covariance trace to characterize the overall dispersion of the solution point cloud. And construct a Gaussian process proxy model: ; ; In the formula, For covariance trace, The function on the left side of the sign follows the probability distribution on the right side of the sign. It is a mean function. Let covariance function be used. It is a Gaussian process.

[0024] S3 includes S3.3, constructing the acquisition function: ; In the formula, In order to improve, This is the current optimal observation value. For the posterior probability density, for The possible values ​​of ; Choose to Reaching the maximum value As an evaluation point for the next iteration : ; In the formula, To find the independent variable that maximizes the expected improvement function; like ,renew Recalculate Iterate until The improvement amount is less than Output makes Minimum optimal equivalent scaling factor .

[0025] S4 includes, S4.1, evaluating the clustering relationships of the Eulerian solution point cloud using a density-based spatial clustering method, including setting a point density threshold. and region radius threshold ,by With the center as the center, Construct the solution set region with radius . ; like The number of candidate solutions contained within is greater than or equal to ,definition For high-density solution sets, clustering is performed to preserve the high-density solution sets. like The number of candidate solutions contained within is less than ,definition To identify isolated points, these isolated points are removed as noise points.

[0026] S4 includes S4.2, which uses a density penalty term to improve clustering performance: ; In the formula, For density penalty terms, For Let be the set of all candidate solutions within the solution set region centered at the circle. for The set of all candidate solutions in the cluster to which it belongs. This is the intersection symbol.

[0027] S4 includes S4.3, based on , Construct the final localization objective function from the initial localization objective function. : ; In the formula, For regularization parameters; Solve using the least squares method Obtain the optimal magnetic source target position estimate .

[0028] The process of this invention is as follows Figure 1As shown, the first step involves initial positional constraints on the raw magnetic anomaly data, including calculating the first and second derivatives to identify anomaly boundaries, generating initial intervals based on the anomaly boundaries, and simplifying the model using the Euler deconvolution inversion model. Specifically, this includes performing neighborhood-weighted regression smoothing on the raw magnetic anomaly data. The neighborhood-weighted regression smoothing process involves, for each survey line data... , This represents the total number of measurement points on the current survey line. For any point to be smoothed, use the index of the measurement point on the current measurement line. Select the closest Each point is used as a neighborhood subset. Calculate the neighborhood radius ; ; In the formula, for The first in Neighboring points, for index, ; right Calculate normalized distance : ; calculate weight : ; right Smoothed estimate at To make an estimate, assume that it follows a first-order multinomial distribution in the neighborhood: ; In the formula, and These are local regression coefficients; Solving by minimizing the weighted sum of squared residuals. and : ; for The original value at that location, when At that time, the smoothed estimate of that point is obtained. : ; In the formula, These are the optimal regression coefficients; Calculate the first derivative of the preprocessed magnetic anomaly data and take its absolute value; then use a peak-finding function to identify the neighborhood. The location of the inner maximum is used to estimate the initial magnetic anomaly boundary. Then, the second derivative of the preprocessed magnetic anomaly data is calculated, and the zero intersection point is determined based on the sign change. The zero intersection point is used to constrain the initial magnetic anomaly boundary, and the initial magnetic anomaly boundary is used as the initial search range of the Euler deconvolution algorithm.

[0029] The second step utilizes Bayesian optimization. This includes constructing the objective function for the observed values, updating the posterior distribution using a cyclic Gaussian process surrogate model, and expecting to improve the next... The process involves three steps: evaluation, convergence, and solution selection. The Bayesian optimization results are then filtered based on a density penalty term, including density-based spatial clustering and calculation of the density penalty term to identify density clusters and noise points. Finally, the objective function is minimized to obtain the target location.

[0030] The principle behind using the Euler deconvolution inversion model to locate magnetic sources includes: if the function... satisfy: ; In the formula, Scaling factor for The homogeneous order; So Satisfy the following partial differential equations: ; ; ; ; In the formula, For grid points Take the value at that location. for Grid points in the direction, for Grid points in the direction, for Grid points in the direction, The difference; In the geophysical field, Treating it as a coordinate function, for a single magnetic source anomaly field, let the position of the magnetic source be... We can obtain: ; Assuming the magnetic anomaly data contains One observation point, Under the condition of single magnetic source localization, in order to simplify the calculation process, the position of the single magnetic source is estimated by the global least squares method based on the Euler deconvolution equation. The linear equation system is expressed as follows: ; ; ; ; In the formula, For the observation matrix, Let be the parameter vector to be determined. It is a data vector; Then the optimal solution for: ; In the formula, This is the transpose symbol.

[0031] The pseudocode for the method of this invention is as follows: Input planar grid magnetic anomaly data; perform local weighted smoothing on the magnetic anomaly data to suppress high-frequency noise and maintain the continuity of the anomaly morphology; calculate the first derivative of the data to extract candidate positions of the anomaly boundary; calculate the zero intersection points of the second derivative of the data to constrain the geometric boundary and eliminate pseudo-boundaries caused by noise or background fluctuations; identify the anomaly boundary positions as the spatial interval where the magnetic source exists, and use them as the constraint range for the initial position of the Euler deconvolution; randomly set the initial position of the target within the constraint range to construct a simplified Euler deconvolution model and an equivalent scaling factor. And initially locate the objective function; divide the observation data into A local sliding window The target position of each local window is solved, and the Eulerian solution point cloud is obtained by summing the results. An objective function based on the observations is constructed, and Bayesian optimization is introduced to adaptively seek the optimal value. Density-based spatial clustering methods identify high-density clusters and noise points; a density penalty term based on the proportion of noise points is introduced, utilizing optimal... The final target location function is constructed by combining the density penalty term and the preliminary location objective function; the optimal magnetic source location solution is output.

[0032] This invention first utilizes the first and second derivative features of magnetic anomaly data to provide a reliable initial search region for magnetic source inversion. Then, it simplifies the Euler deconvolution inversion model by incorporating the difficult-to-estimate background field and depth parameters into an equivalent scaling factor, reducing the dimensionality and complexity of unknown parameters and improving inversion stability. Bayesian optimization is then used to adaptively determine the equivalent scaling factor. Finally, a density penalty term is introduced to further screen the Euler solution point cloud, effectively suppressing discrete misinterpretation points. The performance of the method of this invention is then evaluated.

[0033] First, the effectiveness of the proposed method is verified based on simulation data. (Settings) , , Set magnetic declination to 0 and magnetic tilt to 90° (magnetic poles), and directly generate the simulation using COMSOL software. Data in a planar coordinate system (unit: meters). In the simulation data, from... Figure 2 , Figure 3 and Figure 4 It is known that under noisy conditions and with only a single magnetic source, the traditional Eulerian deconvolution method has a large positioning error, making it difficult to effectively identify the target. Introducing a density-clustered Eulerian deconvolution method significantly improves target positioning accuracy. Based on this, the method of this invention further improves positioning accuracy and stability. (See figure...) The magnetic field strength is expressed in nanotesla (NTL). The positioning results are shown in Table 1. Table 1. Simulation results of localization under noisy conditions and single magnetic source. .

[0034] Depend on Figure 5 , Figure 6 and Figure 7 As can be seen, under noisy conditions and with multiple magnetic sources, the traditional Euler deconvolution method also exhibits a large positioning error and limited target recognition capability. The Euler deconvolution method that introduces density clustering can effectively improve the positioning results, while the method of this invention shows better positioning accuracy and robustness in multi-target scenarios. The positioning results are shown in Table 2. Table 2. Simulation results of localization under noisy conditions and multiple magnetic sources. .

[0035] Subsequently, performance evaluation was further conducted based on the measured data. The measurement area was a beach with a magnetic declination of -7°29' and a magnetic inclination of 53°44'. A [database / structure] was constructed within the measurement area. A Cartesian coordinate system was established, with the starting point of the survey line as the origin, north as the horizontal axis, and east as the vertical axis. The origin coordinates were set as (0,0), and the ending point coordinates as (20,20), with units in meters. After setting up the survey line, two hollow iron cylinders were selected as magnetic sources within the survey area and buried 0.5 meters below the sand. Experiments were conducted, and magnetic data were acquired using a cesium atomic magnetometer. To eliminate the influence of the tilted magnetization of the geomagnetic field, the collected raw magnetic anomaly data was first polarized to improve the subsequent positioning effect. The positioning performance of the method of this invention was evaluated by comparing and analyzing the distance of the positioning point relative to the center of the magnetic source (the center of the red area) in the polarized data. Figure 8 , Figure 9 and Figure 10The results show that, under multiple magnetic source conditions, the positioning points of the traditional Euler deconvolution method deviate significantly. The method after introducing density clustering significantly improves the positioning accuracy, making the positioning points closer to the actual positions of the magnetic sources. The method of this invention further optimizes the positioning effect, with the positioning points closest to the center region of the magnetic sources. This verifies the effectiveness and superiority of this method in multi-magnetic source positioning scenarios. The positioning results are shown in Table 3. Table 3. Measured positioning results under multiple magnetic sources .

[0036] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating a magnetic source target, characterized in that, include: S1. Collect planar grid magnetic anomaly data and perform preprocessing. Preprocessing includes local weighted regression smoothing based on the magnetic anomaly data, calculating the first derivative of the preprocessed magnetic anomaly data to extract the preliminary magnetic anomaly boundary, calculating the second derivative of the preprocessed magnetic anomaly data to extract the zero intersection point constrained preliminary magnetic anomaly boundary, and using the constrained preliminary magnetic anomaly boundary as the initial search range of the Euler deconvolution algorithm. S2. Randomly set the initial position of the magnetic source target within the initial search range, construct a simplified Euler deconvolution model, introduce an equivalent scaling factor to characterize the model parameters, and construct a preliminary positioning objective function by minimizing the sum of squared residuals. S3. Set up a local sliding window, segment the observation data based on the local sliding window, invert candidate solutions for the magnetic source target position in the local sliding window based on the preliminary positioning objective function, summarize all candidate solutions of the local sliding window to construct the Euler solution point cloud, transform the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, construct the observation objective function based on the covariance trace of the solution point cloud, introduce Bayesian optimization to solve the observation objective function, and obtain the optimal equivalent scaling factor. S4. Use density-based spatial clustering to identify high-density solution points and noise points of the magnetic source, introduce a density penalty term, construct the final positioning objective function based on the optimal equivalent scaling factor, density penalty term and preliminary positioning objective function, and output the optimal magnetic source target position estimate through the final positioning objective function.

2. The magnetic source target localization method according to claim 1, characterized in that, S1 includes S1.1, collecting planar grid magnetic anomaly data and performing preprocessing, including neighborhood weighted regression smoothing based on the magnetic anomaly data; S1 includes S1.2, calculating the first derivative of the preprocessed magnetic anomaly data and taking its absolute value, using the peak-finding function to identify the location of the maximum value, and estimating the preliminary magnetic anomaly boundary; S1 includes S1.3, calculating the second derivative of the preprocessed magnetic anomaly data, determining the zero intersection point based on the sign change, and using the zero intersection point to constrain the preliminary magnetic anomaly boundary; S1 includes S1.4, which uses the constrained initial magnetic anomaly boundary as the initial search range for the Euler deconvolution algorithm.

3. The magnetic source target localization method according to claim 2, characterized in that, S2 includes, S2.1, setting the coordinates of the observation point within the initial search range as... The initial position of the magnetic source target is The model parameters are incorporated into the equivalent scaling factor. The model parameters include the background field. and construction index Construct a simplified Euler deconvolution model: ； ； In the formula, The sign of the partial derivative. for Gradient of direction, for Gradient of direction, As an equivalent scaling factor, This represents the preprocessed magnetic anomaly value.

4. The magnetic source target localization method according to claim 3, characterized in that, S2 includes S2.2, for any observation point : ； In the formula, For the index of observation points, For the first The residuals at each observation point In the first At each observation point exist gradient in direction, In the first At each observation point exist gradient in direction, In the first Preprocessed magnetic anomaly values ​​at each observation point; S2 includes S2.3, constructing a preliminary localization objective function by minimizing the sum of squared residuals: ； In the formula, The number of observation points. .

5. The magnetic source target localization method according to claim 4, characterized in that, S3 includes, S3.1, setting a partial sliding window. The size is The observation data is divided into indivual Each The initial application of the objective function to invert candidate solutions for the magnetic source target location is as follows: ； In the formula, For the index of a local sliding window, , for Candidate solutions obtained from inversion. For a given Under the conditions, The magnetic source target inside Coordinate estimates For a given Under the conditions, The magnetic source target inside Coordinate estimates; Summarize all candidate solutions to form an Euler solution point cloud. : ； In the formula, It is a two-dimensional real number space.

6. The magnetic source target localization method according to claim 5, characterized in that, S3 includes S3.2, which transforms the problem of selecting the equivalent scaling factor into a one-dimensional global optimization problem, and uses the covariance trace to characterize the overall dispersion of the solution point cloud. And construct a Gaussian process proxy model: ； ； In the formula, For covariance trace, The function on the left side of the sign follows the probability distribution on the right side of the sign. It is a mean function. Let covariance function be used. It is a Gaussian process.

7. The magnetic source target localization method according to claim 6, characterized in that, S3 includes S3.3, constructing the acquisition function: ； In the formula, In order to improve, This is the current optimal observation value. For the posterior probability density, for The possible values ​​of ; Choose to Reaching the maximum value As an evaluation point for the next iteration : ； In the formula, To find the independent variable that maximizes the expected improvement function; like ,renew Recalculate Iterate until The improvement amount is less than Output makes Minimum optimal equivalent scaling factor .

8. The magnetic source target localization method according to claim 7, characterized in that, S4 includes, S4.1, evaluating the clustering relationships of the Eulerian solution point cloud using a density-based spatial clustering method, including setting a point density threshold. and region radius threshold ,by With the center as the center, Construct the solution set region with radius . ; like The number of candidate solutions contained within is greater than or equal to ,definition For high-density solution sets, clustering is performed to preserve the high-density solution sets. like The number of candidate solutions contained within is less than ,definition To identify isolated points, these isolated points are removed as noise points.

9. A method for locating a magnetic source target according to claim 8, characterized in that, S4 includes S4.2, which uses a density penalty term to improve clustering performance: ； In the formula, For density penalty terms, For Let be the set of all candidate solutions within the solution set region centered at the circle. for The set of all candidate solutions in the cluster to which it belongs. This is the intersection symbol.

10. A method for locating a magnetic source target according to claim 9, characterized in that, S4 includes S4.3, based on , Construct the final localization objective function from the initial localization objective function. : ； In the formula, For regularization parameters; Solve using the least squares method Obtain the optimal magnetic source target position estimate .

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