Magnetic positioning method for underground ferromagnetic pipeline based on adaptive euler inversion and geometric constraint

Abstract

A magnetic positioning method for underground magnetic pipelines based on adaptive Euler inversion and geometric constraints includes: initially determining the principal axis direction of the underground magnetic pipeline and, while maintaining a constant sampling height, collecting three-component magnetic field data and position coordinates of multiple sampling points along the main survey line; performing adaptive SI selection and cross-sectional joint inversion on the measurement window of the main survey line to obtain the optimal SI value; and inverting the pipeline burial depth based on the optimal SI value to generate the pipeline trajectory. This invention, without relying on any idealized model assumptions, can quantitatively evaluate the degree of aggregation of inversion solutions under different SI candidate values, adaptively selecting the optimal SI value for the current measurement window, thereby effectively overcoming the model mismatch problem caused by the finite length and complex magnetization characteristics of the pipeline. Under the constraint of a known pipeline axis, this invention simplifies the three-dimensional inversion problem into a two-dimensional cross-sectional positioning problem, achieving high-precision, ambiguity-free solution for pipeline location with only a single main survey line.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration and non-destructive testing technology for underground infrastructure, specifically involving a magnetic positioning method for underground ferromagnetic pipelines based on adaptive Euler inversion and geometric constraints. Background Technology

[0002] Underground magnetic pipelines are a crucial component of national critical infrastructure. Accurate location of these pipelines is essential for preventing damage during third-party construction, ensuring public safety, and facilitating maintenance and upgrades. Magnetic Anomaly Detection (MAD) technology, due to its non-contact nature, ease of operation, low cost, and sensitivity to ferromagnetic targets, has become one of the mainstream methods for detecting underground metal pipelines. In MAD data interpretation, Euler Deconvolution is a widely adopted automated method for locating potential field sources. The core idea of ​​this method stems from a class of homogeneous partial differential equations satisfied by potential fields (such as gravitational and magnetic fields)—that is, the concrete manifestation of Euler's homogeneous function theorem in geophysical fields. Because this method requires no initial model, has high computational efficiency, and can automatically output source locations, it has become the preferred tool for rapid interpretation of MAD data. However, its accuracy is highly dependent on the structure index. The correct selection of the Structural Index (SI) can lead to a large number of scattered solutions for ductile linear targets (such as pipelines), affecting the accurate location of underground magnetic pipelines.

[0003] In MAD practice, underground magnetic pipelines are usually approximated as linear magnetization sources, therefore theoretically, a more suitable approach is to use... =1. However, real pipelines have finite lengths, may be curved, non-uniformly magnetized, or affected by nearby disturbances, causing their effective SI to deviate from the ideal value. Therefore, although the Euler inversion is theoretically attractive, its practical application to finite-length, approximately linear underground magnetic pipelines faces two fundamental challenges: 1. Structural index SI mismatch problem: Theoretically, an infinitely long horizontal current source corresponds to... =1, while the isolated magnetic dipole corresponds to =2 or 3. Actual buried pipelines are neither infinitely long nor point sources; their effective SI is affected by various factors such as length, burial depth, curvature, residual magnetism distribution, and surrounding interference. Typically, the SI is between 1 and 2 and is unknown. If a fixed SI is forcibly adopted (e.g....), =1 or =2), which will introduce significant systematic errors. For example, when the pipeline is short or buried at a great depth, using =1 will severely underestimate the depth; while using A value of 2 might overestimate the depth or lead to unraveling.

[0004] 2. Dimensionality and accuracy issues in single-line inversion: In practical engineering, to improve efficiency, only a single one-dimensional survey line is laid out along the inferred pipeline route. In this case, traditional three-dimensional Eulerian inversion suffers from unstable and ambiguous solutions because the number of unknown parameters (lateral offset, burial depth, background field, etc.) exceeds the number of effective equations.

[0005] In summary, existing technologies have not yet effectively solved the coordination problem between SI adaptive selection and single-line 3D positioning. Therefore, an innovative technical solution is urgently needed to fundamentally improve the inversion accuracy and reliability of extended pipeline targets while ensuring exploration efficiency. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention aims to provide a magnetic positioning method for underground magnetic pipelines based on adaptive Euler inversion and geometric constraints. Through an adaptive SI selection mechanism, without relying on any idealized model assumptions, it can quantitatively evaluate the clustering degree of inversion solutions under different SI candidate values ​​and adaptively select the optimal SI value for the current measurement window, thereby effectively overcoming the model mismatch problem caused by the finite length and complex magnetization characteristics of the pipeline. Furthermore, under the constraint of the known pipeline axis, the present invention cleverly transforms the complex three-dimensional magnetic source inversion problem into a series of positioning problems within a two-dimensional cross-section perpendicular to the pipeline. Further, by jointly utilizing three-component magnetic field data to construct an overdetermined equation system, the well-posedness of the inversion problem is significantly enhanced, greatly improving positioning accuracy and noise suppression capabilities.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A magnetic location method for underground subway magnetic pipelines based on adaptive Euler inversion and geometric constraints includes the following steps: Step 1: Use two non-parallel orthogonal survey lines to initially determine the main axis direction of the underground magnetic pipeline, and lay out the main survey lines; Step 2: Collect three-component magnetic field data from multiple sampling points along the main survey line. and its position coordinates Furthermore, the sampling points are set to be fixed only along the Z-axis direction, and their Z-axis coordinates satisfy... , It is a constant; Step 3: Based on the collected three-component magnetic field data The optimal structural index is obtained by adaptively selecting the SI (Search Indices) and performing joint cross-sectional inversion on the measurement window of the main survey line. ; Step 4: Based on the optimal structure index The burial depth of underground magnetic pipelines is determined by inversion, and the pipeline trajectory is generated.

[0008] The preliminary determination of the main axis direction of the underground magnetic pipeline is as follows: Two non-parallel orthogonal one-dimensional ground survey lines are laid out in the area to be measured. Component magnetic field intensity data or total magnetic field intensity data are continuously collected along the two ground survey lines. The peak positions of magnetic anomalies on the two ground survey lines, i.e., the points of maximum gradient or maximum amplitude, are identified by the preprocessed component magnetic field intensity data or total magnetic field intensity data, and denoted as... and ;connect and The direction angle of the straight line obtained from the two points is then determined as the estimated value of the principal axis direction of the underground magnetic pipeline. ,along The main survey line is laid out in the direction.

[0009] The preprocessing of the component magnetic field strength data or the total magnetic field strength data is as follows: remove non-sampling point values ​​and outliers from the component magnetic field strength data or the total magnetic field strength data. Outliers are data with a deviation greater than one order of magnitude.

[0010] The process of adaptive SI selection and cross-sectional joint inversion is as follows: Step 3.1: Align the Z-axis with the main axis of the underground magnetic pipeline, and establish geometric constraints by assuming that the Z-axis extends in a straight line within the sliding window; Step 3.2: Construct the Euler-similarity equation for the cross section under geometric constraints; Step 3.3: Let the number of sampling points contained in the current measurement window be... An overdetermined linear system was constructed based on the Euler-Zion equation for the cross-section, and the three-component magnetic field data within the current measurement window were analyzed. By performing a joint inversion of the cross sections, an estimate of the magnetic source location is obtained. ; Step 3.4: For the main test line Three-component magnetic field data at each sampling point Define the candidate set of the structural index SI Set step size ; Step 3.5: Based on the estimated location of the magnetic source Candidate set of structural index SI Cluster stability assessment was performed to obtain the optimal structure index. .

[0011] Based on the sampling points within the current measurement window Three-component magnetic field data The Euler-Simulated equation for the XY cross section for each magnetic field component Independently established: in, The structural index SI, These are the center coordinates of the underground magnetic pipeline.

[0012] Three-component magnetic field data within the current measurement window The cross-sectional joint inversion is as follows: according to The overdetermined linear system is constructed from the three-component magnetic field data collected at each sampling point, and the expression is as follows: in, To sample points within the current measurement window The magnetic field scalar values ​​were collected at the location; the least squares method was used to solve the overdetermined linear system to obtain an estimate of the magnetic source location. .

[0013] The process of cluster stability assessment is as follows: Based on the estimated location of the magnetic source Calculate the centroid of the magnetic source location: Calculate the average Euclidean distance between the centroids as a clustering metric: Select the candidate value that minimizes the clustering metric as the optimal structure index: in, This is the candidate set for the structural index SI.

[0014] According to the optimal structure index The process of reversing the burial depth of underground magnetic pipelines is as follows: Step 4.1: Sliding window inversion; The optimal structure index Substituting into the Euler-Sigmier equation within the XY cross section, for The three-component magnetic field data contained in each sampling point are inverted to obtain the corresponding magnetic field data under the current measurement window. of One inversion point Subsequently, the measurement window is moved along the main survey line in steps smaller than the window width. Slide forward, and after the slide ends, any sampling point on the main test line have One corresponding inversion point; Step 4.2: Single-point optimal inversion position fitting; For any sampling point on the main test line of Least square fitting is performed on the inversion points to obtain the center coordinates. The center coordinates That is, the coordinates of the optimal inversion point corresponding to the sampling point; the center coordinates The solution formula is as follows: Step 4.3: Trajectory Generation; Calculate the corresponding pipeline burial depth based on the optimal inversion point coordinates of each sampling point: All sampling points Connect them to form the pipeline centerline and generate the pipeline trajectory.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention cleverly reduces the complex three-dimensional inversion problem to a two-dimensional pipeline axial cross-section location problem by introducing the pipeline's principal axis direction, initially determined by two simple orthogonal survey lines, as a key geometric constraint. Within this cross-section, the Euler-Sigma equation is constructed and solved, reducing the number of unknown parameters and computational load. This fundamentally eliminates the coupling ambiguity between lateral offset and burial depth, thus achieving high-precision, ambiguity-free pipeline location calculation with only a single principal survey line, perfectly meeting the core requirement of MAD's "rapid survey."

[0016] 2. This invention, through an adaptive SI selection mechanism, can quantitatively evaluate the degree of aggregation of inversion solutions under different SI candidate values ​​without relying on any idealized model assumptions. It adaptively selects the optimal SI value (N) for the current measurement window, achieving accurate matching of the equivalent magnetization model of underground magnetic pipelines and solving the systematic error introduced by improper SI selection in traditional methods.

[0017] 3. This invention achieves unambiguous and high-precision calculation of the three-dimensional spatial position of pipelines by cross-sectional joint inversion based on geometric constraints, requiring only a single main survey line, which greatly improves the efficiency of field exploration.

[0018] In summary, compared with existing technologies, this invention, by initially determining the principal axis direction of the underground magnetic pipeline, uses this axis as a key geometric prior constraint, which is seamlessly embedded into the precise depth inversion. This design fundamentally breaks the coupling ambiguity between lateral offset and burial depth in traditional single-line inversion, ensuring the uniqueness and physical rationality of the final positioning result. The magnetic positioning method for underground magnetic pipelines proposed in this invention has extremely strong versatility and robustness, does not depend on prior parameters such as the specific dimensions and magnetization intensity of the pipeline, and is suitable for complex urban underground environments. Attached Figure Description

[0019] Figure 1This is a flowchart of the magnetic positioning method for underground magnetic pipelines according to the present invention.

[0020] Figure 2 This is a schematic diagram of the layout of any three survey lines in this invention.

[0021] Figure 3 The component magnetic field strength and total magnetic field strength data are acquired using fluxgate sensors for Line 1 and Line 2.

[0022] Figure 4 These are photos of the actual detection and testing site.

[0023] Figure 5 The inversion results are shown in the comparison chart when the pipeline is buried at a depth of 0.75 m.

[0024] Figure 6 The inversion results are shown in the comparison chart when the pipeline is buried at a depth of 1.50 m. Detailed Implementation

[0025] To enable those skilled in the art to clearly understand and implement the present invention, the present invention will be further described in detail below with reference to a specific field verification example.

[0026] like Figure 1 As shown, the magnetic location method for underground subway magnetic pipelines based on adaptive Euler inversion and geometric constraints specifically includes the following steps: Step 1: Use two non-parallel orthogonal survey lines to initially determine the main axis direction of the underground magnetic pipeline, and lay out the main survey lines; like Figure 2 As shown, two mutually orthogonal (or non-parallel) one-dimensional ground survey lines, denoted as Line 1 and Line 2, are laid out in the area to be measured. High-precision fluxgate sensors are used to continuously collect component magnetic field strength data or total magnetic field strength (TMI) data along Line 1 and Line 2, such as... Figure 3 As shown; the collected component magnetic field strength data or TMI data are preprocessed, that is, non-sampling point values ​​(null values) and outliers are removed from the component magnetic field strength data or TMI data. Data with a deviation greater than one order of magnitude are defined as outliers, and the peak positions of magnetic anomalies on Line 1 and Line 2 are identified, that is, the maximum gradient (component magnetic field strength) or the maximum amplitude point (TMI), denoted as... and ;connect and The direction angle of the straight line obtained from the two points is then determined as the estimated value of the principal axis direction of the underground magnetic pipeline. ,along A third survey line, Line 3, is laid out to serve as the main survey line for subsequent precise positioning; the estimated value of the main axis direction of the underground magnetic pipeline. The calculation formula is: like Figure 4 As shown, in this embodiment, a 6-meter-long, 150-m outer diameter abandoned steel pipe is horizontally buried 0.75m underground, with its designed orientation being 35° east of north. Line 1 (east-west) and Line 2 (north-south) are laid out above the pipe. Neither line is directly above the pipe to simulate the situation where the precise location is unknown during actual surveys. A Bartington Mag-03 high-precision fluxgate magnetometer is used to continuously collect TMI data along Line 1 and Line 2 at a height of 0.1m above the ground. It was calculated to be 34.8°.

[0027] Step 2: Use a fluxgate sensor to collect three-component magnetic field data at multiple sampling points along the main measurement line Line 3. and its position coordinates And keeping the height of the fluxgate sensor constant, that is, setting the sampling points on the main measurement line to be fixed only along the Z-axis direction, and their Z-axis coordinates satisfying , The values ​​are constants, but the X and Y axes can vary; in this embodiment, 1000 stable magnetic data points were collected.

[0028] Step 3: Based on adaptive Euler inversion and geometric constraints, adaptive SI selection and cross-sectional joint inversion are performed on the measurement window on the main measurement line Line 3 to obtain the optimal structural index. ; For the measurement window (width) on the main measurement line Line 3 Perform the following sub-steps: Step 3.1: Establish geometric constraints; Based on the direction of the main axis of the underground magnetic pipeline determined in step 1 A new coordinate system is established, aligning the Z-axis with the pipeline axis, and geometric constraints are established by assuming that the Z-axis extends linearly within the sliding window. Under these geometric constraints, the magnetic field remains unchanged in the Z-direction. The location problem is simplified to solving for the center coordinates of a series of underground magnetic pipelines within the XY cross section.

[0029] Step 3.2: Construct the Euler-similarity equation for the cross section under geometric constraints; Based on each sampling point within the current measurement window Three-component magnetic field data Based on translation invariance, the Euler-Sigmoid equations within the XY cross section are valid for each magnetic field component. Independently established: in, The structure index (SI) is a dimensionless parameter. The center coordinates of the underground magnetic pipeline; Step 3.3: Let the number of sampling points contained in the current measurement window be... An overdetermined linear system was constructed based on the Euler-Zion equation for the cross-section, and the three-component magnetic field data within the current measurement window were analyzed. Perform cross-sectional joint inversion; In this example, Take 10; according to The overdetermined linear system is constructed from the three-component magnetic field data collected at each sampling point, and the expression is as follows: in, To sample points within the current measurement window The magnetic field scalar values ​​(unit: nanotesla, nT) were collected at the location; the system was solved using the least squares method to obtain an estimate of the magnetic source location. ; Step 3.4, targeting the main test line Line 3 Three-component magnetic field data at each sampling point Define a physically reasonable candidate set of structural indices (SI). Set step size ; In this embodiment, the SI candidate set Step length It is 0.1; Step 3.5: Cluster stability assessment; Based on the estimated location of the magnetic source Calculate the centroid of the magnetic source location: Calculate the average Euclidean distance between the centroids as a clustering metric: Select the candidate value that minimizes the clustering metric as the optimal structure index: Step 4: Based on the optimal structure index The complete burial depth of underground magnetic pipelines is determined by inversion, and the pipeline trajectory is generated. Step 4.1: Sliding window inversion; The optimal structure index Substituting into the Euler-Sigmier equation within the XY cross section, for The three-component magnetic field data contained in each sampling point are inverted to obtain the corresponding magnetic field data under the current measurement window. of One inversion point .

[0030] Subsequently, the measurement window is moved along the main measurement line Line 3 in steps smaller than the window width. Slide forward and repeat steps 3.2 to 4.1 of the inversion process. Since the window is sliding, assume any sampling point on the main survey line Line 3... During the sliding process It is covered by several different windows, each with an optimal structure index. Therefore, each window contributes a representative inversion point to that sampling point, and after the sliding ends, that sampling point will have... Each corresponding inversion point .

[0031] In this example, the top 10 optimal structure indices (SI) are: 1.7345, 1.8531, 1.9015, 1.6151, 1.6264, 1.8784, 1.8871, 1.9044, 2.1123, and 2.2015; step size... Set to 1.

[0032] Step 4.2: Single-point optimal inversion position fitting; To obtain any sampling point on the main test line Line 3 The unique and optimal pipeline center location estimate is obtained by least-squares fitting to the K inversion points of the sampled point. Specifically, the following optimization problem is solved: Its analytical solution is the arithmetic mean of these K inversion points, i.e., the center coordinates; these center coordinates That is, the sampling point The corresponding optimal inversion point coordinates.

[0033] Step 4.3: Trajectory Generation; Based on each sampling point Find the optimal inversion point coordinates and calculate the corresponding pipeline burial depth: All sampling points Connecting them forms a continuous, smooth pipeline centerline, generating the final pipeline trajectory, such as... Figure 5 As shown.

[0034] To further verify the effectiveness and accuracy of the invented method, the inversion positioning of the pipeline at a burial depth of 1.50 m was also verified based on the 0.75 m depth. The results are as follows: Figure 6 As shown.

[0035] Figure 5 and Figure 6 The figures show a comparison of pipeline burial depth results obtained by the proposed "adaptive SI" method with two traditional fixed SI methods (N=1, N=2) under two working conditions: actual burial depths of 0.75 m and 1.51 m. In the figures, the horizontal dashed line represents the actual burial depth, and the independent measurement results of each method are displayed as curves. As can be seen from the figures, under the two working conditions of actual burial depths of 0.75 m and 1.51 m, the pipeline burial depth obtained by the proposed "adaptive SI" method is closer to the actual burial depth, indicating that the proposed "adaptive SI" method has higher magnetic positioning accuracy for underground magnetic pipelines.

[0036] To quantitatively evaluate the performance of each method, five key indicators were calculated and summarized in Tables 1 and 2. These indicators are: Mean: the average value of the measurement results; Bias: the absolute value of the difference between the mean and the true value, reflecting systematic error; Std: reflecting the dispersion of the measurement results, i.e., stability; MAD (mean absolute deviation): the average of the absolute values ​​of the deviations of all measured values ​​from the true value, comprehensively reflecting accuracy; and RMSE (root mean square error): the most commonly used indicator to comprehensively measure accuracy and stability. The unit for all five key indicators is meters (m).

[0037] Table 1. Comparison of performance indicators of various methods at a true burial depth of 0.75 m Table 2 Comparison of performance indicators of various methods at an actual burial depth of 1.51 m As can be seen from Tables 1 and 2, the present invention has the following advantages: 1. Significantly Improved Accuracy: At both burial depths, the "Adaptive SI" method of this invention comprehensively and significantly outperforms the traditional fixed SI method in all three core accuracy indicators: Bias, MAD, and RMSE. In particular, at a burial depth of 1.50m, its RMSE is only 0.0446 m, while the RMSE of the N=1 and N=2 methods are as high as 0.3092 m and 0.1645 m, respectively.

[0038] 2. Excellent stability: As can be seen from the Std index, the results of the "adaptive SI" method have small dispersion, indicating that it has excellent repeatability and robustness and is not significantly affected by random noise or small environmental changes.

[0039] 3. Strong applicability: Whether it is a shallow burial (0.75m) or deep burial (1.50m) scenario, the present invention can automatically find the optimal SI value, overcoming the inherent defects of the fixed SI method that requires human experience judgment and has unstable results.

[0040] In summary, this invention successfully solves two core challenges in the magnetic positioning of underground magnetic pipelines by combining adaptive SI selection with cross-sectional inversion under geometric constraints, providing a reliable technical solution for the efficient and accurate detection of urban underground pipe networks.

Claims

1. A magnetic positioning method for underground subway magnetic pipelines based on adaptive Euler inversion and geometric constraints, characterized in that, Includes the following steps: Step 1: Use two non-parallel orthogonal survey lines to initially determine the main axis direction of the underground magnetic pipeline, and lay out the main survey lines; Step 2: Collect three-component magnetic field data from multiple sampling points along the main survey line. and its position coordinates Furthermore, the sampling points are set to be fixed only along the Z-axis direction, and their Z-axis coordinates satisfy... , It is a constant; Step 3: Based on the collected three-component magnetic field data The optimal structural index is obtained by adaptively selecting the SI (Search Indices) and performing joint cross-sectional inversion on the measurement window of the main survey line. ; Step 4: Based on the optimal structure index The burial depth of underground magnetic pipelines is determined by inversion, and the pipeline trajectory is generated.

2. The magnetic positioning method for underground magnetic pipelines according to claim 1, characterized in that, The preliminary determination of the main axis direction of the underground magnetic pipeline is as follows: Two non-parallel orthogonal one-dimensional ground survey lines are laid out in the area to be measured. Component magnetic field intensity data or total magnetic field intensity data are continuously collected along the two ground survey lines. The peak positions of magnetic anomalies on the two ground survey lines, i.e., the points of maximum gradient or maximum amplitude, are identified by the preprocessed component magnetic field intensity data or total magnetic field intensity data, and denoted as... and ;connect and The direction angle of the straight line obtained from the two points is then determined as the estimated value of the principal axis direction of the underground magnetic pipeline. ,along The main survey line is laid out in the direction.

3. The magnetic positioning method for underground magnetic pipelines according to claim 2, characterized in that, The preprocessing of the component magnetic field strength data or the total magnetic field strength data is as follows: remove non-sampling point values ​​and outliers from the component magnetic field strength data or the total magnetic field strength data. Outliers are data with a deviation greater than one order of magnitude.

4. The magnetic positioning method for underground magnetic pipelines according to claim 1, characterized in that, The process of adaptive SI selection and cross-sectional joint inversion is as follows: Step 3.1: Align the Z-axis with the main axis of the underground magnetic pipeline, and establish geometric constraints by assuming that the Z-axis extends in a straight line within the sliding window; Step 3.2: Construct the Euler-similarity equation for the cross section under geometric constraints; Step 3.3: Let the number of sampling points contained in the current measurement window be... An overdetermined linear system was constructed based on the Euler-Zion equation for the cross-section, and the three-component magnetic field data within the current measurement window were analyzed. By performing a joint inversion of the cross sections, an estimate of the magnetic source location is obtained. ; Step 3.4: For the main test line Three-component magnetic field data at each sampling point Define the candidate set of the structural index SI Set step size ; Step 3.5: Based on the estimated location of the magnetic source Candidate set of structural index SI Cluster stability assessment was performed to obtain the optimal structure index. .

5. The magnetic positioning method for underground magnetic pipelines according to claim 4, characterized in that, Based on the sampling points within the current measurement window Three-component magnetic field data The Euler-Simulated equation for the XY cross section for each magnetic field component Independently established: in, The structural index SI, These are the center coordinates of the underground magnetic pipeline.

6. The magnetic positioning method for underground magnetic pipelines according to claim 4, characterized in that, Three-component magnetic field data within the current measurement window The cross-sectional joint inversion is as follows: according to The overdetermined linear system is constructed from the three-component magnetic field data collected at each sampling point, and the expression is as follows: in, To sample points within the current measurement window The magnetic field scalar values ​​were collected at the location; the least squares method was used to solve the overdetermined linear system to obtain an estimate of the magnetic source location. .

7. The magnetic positioning method for underground magnetic pipelines according to claim 4, characterized in that, The process of cluster stability assessment is as follows: Based on the estimated location of the magnetic source Calculate the centroid of the magnetic source location: Calculate the average Euclidean distance between the centroids as a clustering metric: Select the candidate value that minimizes the clustering metric as the optimal structure index: in, This is the candidate set for the structural index SI.

8. The magnetic positioning method for underground magnetic pipelines according to claim 1, characterized in that, According to the optimal structure index The process of reversing the burial depth of underground magnetic pipelines is as follows: Step 4.1: Sliding window inversion; The optimal structure index Substituting into the Euler-Sigmier equation within the XY cross section, for The three-component magnetic field data contained in each sampling point are inverted to obtain the corresponding magnetic field data under the current measurement window. of One inversion point ; Subsequently, the measurement window is moved along the main survey line in steps smaller than the window width. Slide forward, and after the slide ends, any sampling point on the main test line have One corresponding inversion point; Step 4.2: Single-point optimal inversion position fitting; For any sampling point on the main test line of Least square fitting is performed on the inversion points to obtain the center coordinates. The center coordinates That is, the coordinates of the optimal inversion point corresponding to the sampling point; the center coordinates The solution formula is as follows: Step 4.3: Trajectory Generation; Calculate the corresponding pipeline burial depth based on the optimal inversion point coordinates of each sampling point: All sampling points Connect them to form the pipeline centerline and generate the pipeline trajectory.

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