A method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes

Abstract

This invention provides a method for precise location of underground metal pipelines based on borehole magnetic gradient inversion, belonging to the field of underground pipeline detection technology. The method includes: treating the underground pipeline as an infinitely long horizontal cylinder, establishing a unified forward modeling physical model including the horizontal distance between the pipeline center and the borehole, and the burial depth of the pipeline center; then, standardizing the forward modeling response model for the measured difference method, deriving a gradient-standardized forward modeling expression that establishes a unique correspondence between the shape of the borehole magnetic gradient curve and the relative spatial relationship; subsequently, constructing an objective function with static weights, and using a multi-starting-point strategy to solve the constrained optimization problem; finally, updating the model parameters through iterative calculation to obtain the optimal solution. This invention solves the problem of horizontal location calculation using the borehole magnetic gradient method, achieving simultaneous and accurate calculation of the horizontal position and burial depth of underground metal pipelines.

Description

Technical Field

[0001] This invention relates to the field of underground pipeline detection technology, and in particular to a method for precise location of underground metal pipelines based on inversion of magnetic gradient in boreholes. Background Technology

[0002] In underground metal pipeline detection, the borehole magnetic gradient method effectively identifies magnetic anomalies caused by ferromagnetic pipelines by measuring changes in the vertical component of the magnetic field in underground boreholes. This method boasts extremely high resolution in depth detection and is considered a reliable method for determining the depth of deeply buried pipelines. Currently, the mainstream method for obtaining borehole magnetic gradient data in engineering practice is the measured difference method, which involves simultaneously measuring the magnetic field using two sensors spaced at a fixed distance and using the difference as the gradient value in that direction. This method naturally suppresses common environmental noise such as diurnal variations and exhibits high data stability.

[0003] However, existing borehole magnetic gradient methods primarily address the issue of high-precision depth detection, but they have significant limitations in determining the horizontal position, i.e., the distance between the borehole and the pipeline. Current measured difference methods lack rigorous physical models and quantitative inversion techniques, and the determination of horizontal position largely relies on empirical interpretations of anomalous curve morphologies, resulting in insufficient horizontal positioning accuracy and difficulty in generating complete spatial positioning results. Although there is some research on computational gradient methods, they require extremely high data accuracy and are not suitable for mainstream measured difference equipment. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a method for accurately locating underground metal pipelines based on magnetic gradient inversion in boreholes. This invention solves the problem that existing measured difference methods lack rigorous physical models and quantitative inversion methods, which leads to the inability to accurately determine the horizontal position of underground metal pipelines.

[0005] To achieve the above objectives, the present invention provides the following solution: A method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes includes: Treating underground pipelines as infinitely long horizontal cylinders, a unified forward modeling physical model is established based on the vertical magnetic component formula of the borehole magnetic gradient method, which includes two core unknowns: the horizontal distance between the pipeline center and the borehole and the burial depth of the pipeline center. Based on the measured difference method, the parameter of the distance between the upper and lower sensors is introduced, and the parameters of the unified forward modeling physical model are merged to derive the gradient-normalized forward modeling expression of the vertical magnetic component in the well. The gradient-normalized forward modeling expression establishes a unique correspondence between the shape of the magnetic gradient curve in the well and the relative spatial relationship between the observation point and the pipeline center. Based on the residual between the observed values ​​from the well measuring points and the calculated values ​​obtained using the gradient-normalized forward modeling expression, an objective function containing static weights is constructed. A multi-starting-point strategy is adopted to solve the constrained optimization problem of the objective function. By iteratively updating the model parameters, the optimal model parameters, including the horizontal distance between the pipeline center and the borehole and the burial depth of the pipeline center, are obtained to achieve precise positioning of underground metal pipelines.

[0006] The present invention discloses the following technical effects: This invention provides a method for precise positioning of underground metal pipelines based on borehole magnetic gradient inversion. By establishing a unified objective function that includes the horizontal distance between the pipeline center and the borehole, and solving it using a constrained optimization algorithm, this invention effectively fills the theoretical gap in horizontal positioning of the measured difference method, solves the problem that traditional methods cannot quantify and determine the horizontal distance between the borehole and the pipeline, and realizes the synchronous and accurate calculation of the horizontal position and burial depth of underground metal pipelines, significantly improving the integrity and accuracy of spatial positioning. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 A flowchart of a method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the spatial physical model of a horizontal metal pipeline provided in an embodiment of the present invention; Figure 3 The flowchart of the inversion calculation provided in the embodiment of the present invention. Detailed Implementation

[0009] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0010] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0011] like Figure 1As shown, this invention provides a method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes, comprising: Step 100: Treat the underground pipeline as an infinitely long horizontal cylinder, and based on the formula of the vertical magnetic component of the borehole magnetic gradient method, establish a unified forward modeling physical model that includes the two core unknowns: the horizontal distance between the pipeline center and the borehole and the burial depth of the pipeline center. Step 200: Based on the measured difference method, the parameter of the distance between the upper and lower sensors is introduced, and the parameters of the unified forward modeling physical model are merged to derive the gradient-normalized forward modeling expression of the vertical magnetic component in the well. The gradient-normalized forward modeling expression establishes a unique correspondence between the shape of the magnetic gradient curve in the well and the relative spatial relationship between the observation point and the pipeline center. Step 300: Based on the residual between the observed values ​​of the well measuring points and the calculated values ​​obtained using the gradient-normalized forward modeling expression, construct an objective function containing static weights; Step 400: Use a multi-starting-point strategy to solve the constrained optimization problem of the objective function. By iteratively updating the model parameters, obtain the optimal model parameters that include the horizontal distance between the pipeline center and the borehole and the burial depth of the pipeline center, so as to achieve accurate positioning of underground metal pipelines.

[0012] Furthermore, the inputs to the unified forward modeling physical model include: magnetic moment and local magnetization tilt angle, and the variables include: the depth of each probe point in the well.

[0013] Specifically, such as Figure 2 As shown, the vertical component of the magnetic field of the underground magnetic tube That is, the basic formula of the magnetic gradient method in the hole: Establish a unified system of surface and underground models.

[0014] ; The underground pipeline can be considered as an infinitely long horizontal cylinder. In the model established based on the fundamental formula of the borehole magnetic gradient method, there are only two core unknowns: the horizontal distance between the pipeline centerline and the borehole. δx and center burial depth h .

[0015] Orifice position B、 Pipeline Center x Can be used directly δx The alternative does not require separate participation in the inversion solution. When δx After the inversion solution is obtained, the pipeline center can be determined using the known borehole locations. x .

[0016] Magnetic moment and local magnetization tilt i Treated as a known constant. The depth of each probe point in the well is... zBased on this, a unified vertical magnetic component for horizontal metal pipelines is established. Forward physical model: ; Where the proportionality coefficient A Incorporating the pipeline's effective magnetic moment and other physical properties, the effective magnetization tilt angle i The local magnetic field characteristics can be used as the input of known geomagnetic parameters.

[0017] Furthermore, based on the forward modeling system, the formula for obtaining the magnetic gradient response in the hole using the measured difference method in current engineering practice is as follows: ; The distance between the upper and lower sensors is d The parameters are merged to obtain the vertical magnetic components in the well. gradient Standardized forward expression: ; In the formula, the proportionality coefficient A Incorporating the pipeline's effective magnetic moment and other physical properties, the effective magnetization tilt angle i As known geomagnetic parameters are input z The depth of each measuring point in the well. h For pipeline burial depth, d The distance between the two sensors, δx For horizontal positioning. This expression shows that all the morphological characteristics of the magnetic gradient curve in the well are determined by the relative spatial relationship between the observation point and the pipeline center. δx,zh The only decision.

[0018] Construct the objective function: ; in, This represents the observed value at the i-th measuring point in the well. Static weights are assigned based on the quality of data at each point (such as signal-to-noise ratio).

[0019] Furthermore, such as Figure 3 As shown, the multi-starting-point strategy includes: Multiple starting points are generated based on the initial estimated parameters to form a starting point matrix, which contains at least four starting points. The constrained optimization problem is solved independently for each starting point in the starting point matrix to obtain the corresponding local optimum. Compare the cost function values ​​corresponding to all the local optima, and select the solution with the smallest cost function value as the global optimum.

[0020] Specifically, the L2 norm squared of the standardized residuals is used as the cost function: ; Where σ MAD The standardization factor for the median absolute deviation of the observed data is used as a static weight.

[0021] Establish a constrained optimization problem: The physical constraints of the parameters are ; The boundary values ​​are determined based on physical rationality and initial estimates.

[0022] More specifically, a multi-starting-point strategy is employed to solve the optimization problem in parallel, thereby obtaining the optimal model parameters. ; Uncertainty in calculating parameters based on the Jacobian matrix at the optimal solution ; in, , n -3 represents the degrees of freedom.

[0023] Based on initial estimated parameters Generate multiple starting points to form a starting point matrix. where m≥4; For each starting point Solve constrained optimization problems independently to obtain local optima. ; Choose the solution with the lowest cost as the global optimal solution: ,in .

[0024] Furthermore, it also includes: The covariance matrix of the parameters is calculated based on the Jacobian matrix at the optimal model parameters; Calculate the standard error of the parameters based on the covariance matrix, and determine the confidence interval of the parameters; The coefficient of determination is calculated as an index of goodness of fit.

[0025] Specifically, in the k-th iteration, the linear system is solved: ; in, It is the residual vector; Update model parameters: , The step size.

[0026] Uncertainty assessment: Calculate the standard error of the parameters: ; Determine the 95% confidence interval: ; Calculate the goodness-of-fit index: coefficient of determination .

[0027] Specifically, the inversion method's specific process is as follows: I. Initialization Phase: 1. Data loading: Read the observation data ΔZ_obs; 2. Initial parameter estimation: Use fast estimation methods such as peak method to obtain initial parameters; 3. Set boundary constraints: Define physically reasonable upper and lower bounds for the parameters; 4. Configure optimizer: Choose an optimization algorithm (least squares method, conjugate gradient method, Newton's method, etc.); Set the gradient calculation method (central difference, analytical method, automatic differentiation, etc.); Set convergence tolerance (typically 1e) -8 ~1e -10 ); Configure iterative process monitoring; II. Optimize the iterative loop: 5. Forward modeling: Calculate the theoretical response based on the current parameters. Z_calc=f(params); 6. Residual calculation: Calculate the difference r between the theoretical value and the observed value. Z_calc- Z_obs; 7. Weight assignment: Assign robust weights w_i based on the residual distribution; 8. Cost function calculation: Calculate the weighted least squares cost. =½∑w_i·r_i 2 ; 9. Gradient Calculation: Calculate the gradient of the cost function with respect to the parameters. = / params; 10. Parameter Update: Update parameters along the gradient descent direction: params_new = params - α ; 11. Boundary check: Ensure that the updated parameters meet the physical constraints; 12. Convergence check: Check the gradient norm Is it less than the preset tolerance ε? If convergence is not achieved, return to step 5 and continue iterating; If convergence is achieved, proceed to subsequent processing; III. Post-processing and analysis: 13. Output optimal parameters: Save the optimization results as params_opt; 14. Uncertainty Analysis: Numerical calculation of the Hessian matrix H= 2 / params 2 ; Estimated parameter covariance matrix C=H -1 ; Calculate the standard deviation of the parameter σ = [diag(C)] -1 / 2 ; 15. Visualization and Saving: Generate result charts and save the data.

[0028] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0029] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for accurate positioning of underground metallic pipelines based on inversion of magnetic gradients in boreholes, characterized in that, include: Treating underground pipelines as infinitely long horizontal cylinders, a unified forward modeling physical model is established based on the vertical magnetic component formula of the borehole magnetic gradient method, which includes two core unknowns: the horizontal distance between the pipeline center and the borehole and the burial depth of the pipeline center. Based on the measured difference method, the parameter of the distance between the upper and lower sensors is introduced to perform parameter merging processing on the unified forward modeling physical model, and the gradient-normalized forward modeling expression of the vertical magnetic component in the well is derived. The gradient-normalized forward modeling expression establishes a unique correspondence between the shape of the magnetic gradient curve in the well and the relative spatial relationship between the observation point and the pipeline center. Based on the residual between the observed values ​​from the well measuring points and the calculated values ​​obtained using the gradient-normalized forward modeling expression, an objective function containing static weights is constructed. A multi-starting-point strategy is adopted to solve the constrained optimization problem of the objective function. By iteratively updating the model parameters, the optimal model parameters, including the horizontal distance between the pipeline center and the borehole and the burial depth of the pipeline center, are obtained to achieve accurate positioning of underground metal pipelines. The gradient normalization forward modeling expression is: ； in, A This is the proportionality coefficient. i For effective magnetization tilt angle, z The depth of each measuring point in the well. h For pipeline burial depth, d The distance between the two sensors, δx For horizontal positioning.

2. The method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes according to claim 1, characterized in that, The inputs to the unified forward modeling physics model include: magnetic moment and local magnetization tilt angle, and the variables include: the depth of each probe point in the well.

3. The method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes according to claim 1, characterized in that, The expression for the objective function is: ； in, This represents the observed value at the i-th measuring point in the well. Static weights are assigned based on the quality of data at each point.

4. The method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes according to claim 1, characterized in that, The multi-starting-point strategy includes: Multiple starting points are generated based on the initial estimated parameters to form a starting point matrix, which contains at least four starting points. The constrained optimization problem is solved independently for each starting point in the starting point matrix to obtain the corresponding local optimum. Compare the cost function values ​​corresponding to all the local optima, and select the solution with the smallest cost function value as the global optimum.

5. The method for precise location of underground metal pipelines based on magnetic gradient inversion in boreholes according to claim 1, characterized in that, Also includes: The covariance matrix of the parameters is calculated based on the Jacobian matrix at the optimal model parameters; Calculate the standard error of the parameters based on the covariance matrix, and determine the confidence interval of the parameters; The coefficient of determination is calculated as an index of goodness of fit.

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