A combined advanced detection method based on borehole transient electromagnetics and DC resistivity

Abstract

This invention discloses a joint advanced detection method based on borehole transient electromagnetics and DC resistivity. Advanced boreholes are deployed along the tunneling direction at the tunnel face to collect and invert transient electromagnetic data, obtaining the borehole transient electromagnetic inversion results. Based on the inversion results and corresponding estimation methods, Gaussian variation models in three principal axis directions are calculated and extended to arbitrary directions. Subsequently, the Gaussian variation models in arbitrary directions are substituted into the covariance calculation formula to calculate the covariance value between any two grid cells in the desired detection area, and assembled into a covariance constraint matrix. Finally, this matrix is ​​introduced as a regularization term into the inversion objective function of DC resistivity advanced detection, achieving covariance-constrained DC resistivity inversion, thereby significantly improving the inversion stability and inversion imaging accuracy of DC resistivity advanced detection. This method is suitable for advanced detection scenarios such as tunnel faces or underground coal mine tunneling.

Description

Technical Field

[0001] This invention belongs to the field of geological exploration technology, specifically a combined advanced detection method based on borehole transient electromagnetics and DC resistivity. Background Technology

[0002] In tunnel excavation, prior assessment of the geological conditions ahead is crucial. The area ahead may contain various water-bearing types, such as fault fracture zones with water-bearing potential, collapse columns with water-bearing potential, goaf water accumulation, and karst water-rich areas. Common methods for investigating adverse geological factors include drilling and geophysical exploration. While drilling offers high precision, it is costly, time-consuming, and has a limited detection range. Furthermore, because it requires drilling multiple boreholes, these boreholes can easily become channels for hidden water-bearing bodies to enter the tunnel, causing secondary accidents. Therefore, drilling alone cannot meet actual production needs. Currently, borehole transient electromagnetic methods have been developed, which can detect a certain area around the borehole, but the detection range is still relatively limited. Geophysical exploration, on the other hand, is widely used in water exploration due to its low cost, large detection range, and speed. Although there are many types of geophysical methods, such as seismic reflection wave method and DC resistivity method, they are subject to the sensitivity of each method itself, the limitation of tunnel excavation space, and external influences such as metal anchor support. Although these methods have a large detection range, their detection accuracy is low. In particular, the DC resistivity method will have multiple solutions after inversion (i.e., the inversion result is not unique).

[0003] Joint inversion has long been a novel approach in geophysical inversion. Its principle involves using different types of geophysical parameters to jointly constrain the inversion, aiming to improve the reliability and accuracy of the results. Currently, various types of joint inversion exist, such as seismic-transient electromagnetic (TEM) joint inversion, TEM-electrical joint inversion, and seismic-electrical joint inversion. These joint methods primarily involve using two different geophysical methods to probe the same area, then superimposing the inversion results to ultimately delineate the anomaly region. While this approach improves detection accuracy compared to single-method probing, because it essentially combines two geophysical approaches, its detection accuracy remains relatively low, and it may also suffer from multiple solutions.

[0004] Therefore, the research direction of this invention is to provide a new joint advanced detection method that can effectively improve the accuracy of advanced detection while maintaining the scope of geophysical exploration. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a joint advanced detection method based on borehole transient electromagnetics and DC resistivity. The inversion results of borehole transient electromagnetics are extracted as structural priors and used to constrain the inversion results of the DC resistivity method, thereby effectively improving the accuracy of advanced detection while maintaining the geophysical detection range.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a combined advanced detection method based on borehole transient electromagnetics and DC resistivity, comprising the following steps:

[0007] Step 1: Lay out advance boreholes: Establish a coordinate system with the tunnel axis as the x-axis, the tunnel top and bottom slabs as the y-axis, and the tunnel top and bottom slabs as the z-axis. Construct advance boreholes along the x-axis at the center of the tunnel face.

[0008] Step 2, transient electromagnetic detection in borehole: Detection points are set at different locations in the pre-drilled borehole, and transient electromagnetic detection equipment is placed in the borehole. Transient electromagnetic detection is performed at each detection point to obtain the transient electromagnetic observation data of all detection points in the entire pre-drilled borehole.

[0009] Step 3: Transient Electromagnetic Inversion: For the transient electromagnetic observation data of each detection point obtained in Step 2, radial inversion is performed on the transient electromagnetic observation data of each detection point to obtain a set of circular discrete points. ;gather The resistivity profile is mapped to a resistivity model with the depth of the detection point as the cross section and the borehole axis as the center, thereby obtaining the resistivity profile distribution of all detection points.

[0010] Step 4: Calculate the effective range and Gaussian variation model of the borehole transient electromagnetic x-axis: Extract the resistivity profile distribution of each detection point (which is itself a set of discrete points). Extract the resistivity values ​​with the same y and z coordinates from the resistivity profile distribution of each detection point into a discrete curve along the x-axis, thus obtaining several discrete curves along the x-axis. Superimpose all the curves and calculate the average value. Specifically, calculate the average value of the resistivity profile distribution of each detection point (i.e., if there are n resistivity values ​​on the resistivity profile distribution of a detection point, add these resistivity values ​​and divide by the number n to obtain the average resistivity of that detection point). Use the average values ​​obtained above to represent the resistivity distribution of each detection point within a certain range of the borehole radial direction, thus obtaining a uniquely determined curve x(k), where the value of k is the x-axis coordinate of each detection point. Calculate the experimental half-variation based on this curve x(k), then use the Gaussian variation model for fitting and parameter estimation, and finally obtain the effective range and Gaussian variation model of the borehole transient electromagnetic x-axis.

[0011] Step 5: DC resistivity method advance detection: Deploy a DC resistivity method observation system to conduct advance detection in front of the tunnel and obtain DC resistivity data of the required detection area.

[0012] Step Six: Calculate the effective range and Gaussian variation model of the borehole transient electromagnetic y and z axes: The DC resistivity data from Step Five is inverted using smoothing constraints to obtain the DC resistivity advance detection inversion results under smoothing constraints. Then, the effective range of the DC resistivity under smoothing constraints is calculated according to the method in Step Four. Combined with the effective range of the borehole transient electromagnetic y and z axes in Step Four, the effective range and Gaussian variation model of the borehole transient electromagnetic y and z axes are calculated.

[0013] Step 7: Calculate the effective range and Gaussian variation model of the borehole transient electromagnetic in any direction: Based on the effective range and Gaussian variation models of the borehole transient electromagnetic x-axis, y-axis and z-axis obtained in Steps 4 and 6, calculate the effective range and Gaussian variation model in any direction.

[0014] Step 8: Construct the covariance constraint matrix: Discretize the required detection area into three dimensions using the inversion grid, and calculate the covariance value of any two grid cells using the Gaussian variation model in any direction, thereby constructing the covariance constraint matrix.

[0015] Step 9: DC resistivity advance detection inversion with covariance constraints: The DC resistivity detection data is inverted using the covariance constraint matrix, and the geological conditions of the required detection area are obtained based on the inversion results and the borehole transient electromagnetic inversion results.

[0016] Furthermore, after the drilling is completed, the borehole coordinates, elevation, axial orientation and depth markings are recorded, and the borehole inclination is checked and the borehole is cleaned (with clean water circulation) to ensure that the medium inside the borehole is stable and the passage is unobstructed.

[0017] Furthermore, the specific formula for the radial inversion in step three is as follows:

[0018] (1)

[0019] in, This is the weighting matrix for borehole transient electromagnetic observation data; The transient electromagnetic data of the borehole is the observation data (induced voltage decay curve) at the i-th detection point, where i ranges from 1 to N; For drilling transient electromagnetic positive simulation operator; A predictive resistivity model for transient electromagnetics during borehole drilling; For the model constraint term regularization factor of borehole transient electromagnetics; The model smoothing constraint weighting matrix for transient electromagnetics in borehole drilling can be constructed using zero-order, first-order, and second-order derivative operators.

[0020] Furthermore, the formula for calculating the experimental half-variation in step four is as follows:

[0021] (2)

[0022] Where N(h) is the number of selected lag distances; to ensure calculation accuracy, the largest lag distance needs to have more than 5 calculation samples, that is, at least 5 groups. It can be calculated; otherwise, the amount of data is too small, and the credibility will decrease.

[0023] The specific formula for the Gaussian variation model function is as follows:

[0024] (3)

[0025] in, This represents the variance of all discrete points in the borehole transient electromagnetic inversion result; For the effective travel distance in the x-axis direction of the transient electromagnetic drilling, targeting The values ​​are optimized using least squares to find an optimal value. The value minimizes the residual between the Gaussian variation model curve and the previously calculated experimental semivariogram; the optimal value is... Substituting the value back into formula (3), we obtain the Gaussian variation model of the borehole transient electromagnetic x-axis direction.

[0026] Furthermore, the objective function for inversion using smoothness constraints in step six is:

[0027] (4)

[0028] in, The model smoothing constraint weighting matrix for DC resistivity can be constructed using zero-order, first-order, and second-order derivative operators.

[0029] Let the effective path lengths of the x-axis, y-axis, and z-axis under DC resistivity smoothing constraints be respectively , , The effective travel distance of the transient electromagnetic drilling in the x-axis direction is The effective travel distance in the y and z axes of the transient electromagnetic borehole drilling is calculated using the following formula. , :

[0030] (5)

[0031] (6)

[0032] Next, the calculated , Substituting into formula (3), we obtain the Gaussian variation model of the transient electromagnetic y and z axes of the borehole.

[0033] Furthermore, step seven specifically includes:

[0034] Define the angle between any direction and the plane containing the x and y axes as The angle between this arbitrary direction and the positive x-axis direction on the plane containing the x and y axes is... Then the effective range in any direction The calculation formula is:

[0035] (7)

[0036] The effective distance in any direction will be calculated. Substituting into formula (3), we obtain the Gaussian variation model in any direction.

[0037] Furthermore, in step eight, the covariance value of any two grid cells is calculated using the following formula:

[0038] (8)

[0039] Where C(h) is the covariance function value. Once the direction is determined, this function value is only related to the lag distance h. Therefore, in the same direction, two grid cells with the same lag distance h have the same covariance value.

[0040] Assume there are a total of [number] grid cells. There are , and the corresponding covariance matrix to be constructed has dimensions of . This matrix is ​​a symmetric matrix, where the value of any i-th row and j-th column is... Let represent the covariance value between the i-th and j-th grid cells. Then, the formula for the covariance constraint matrix is:

[0041] (9).

[0042] Furthermore, in step nine, the covariance matrix is ​​used to invert the DC resistivity detection data, and its objective function is:

[0043] (10)

[0044] in, This is the data weighting matrix for the DC resistivity method; Potential difference data acquired using the DC resistivity method; This is the positive analog operator for the DC resistivity method; This is the predicted resistivity model in the DC resistivity method; This is the regularization factor for the covariance constraint term in the DC resistivity method; This is the covariance constraint matrix.

[0045] Compared with existing technologies, this invention involves deploying advance boreholes along the tunneling direction at the working face to collect and invert transient electromagnetic data from the boreholes, obtaining circular resistivity profiles of the borehole transient electromagnetic data at each detection point. Based on the inversion results of the borehole transient electromagnetic data and corresponding estimation methods, Gaussian variation models in three principal axis directions are calculated and extended to arbitrary directions. Subsequently, the Gaussian variation models in arbitrary directions are substituted into the covariance calculation formula to calculate the covariance value between any two grid cells in the desired detection area, and assembled into a covariance constraint matrix. Finally, this matrix is ​​introduced as a regularization term into the inversion objective function of DC resistivity advance detection to achieve covariance-constrained DC resistivity inversion. Because borehole transient electromagnetic inversion is highly sensitive to low-resistivity bodies near the wellbore (within a certain radial range of the borehole) and has high resolution along the borehole direction, its coverage is also limited. DC resistivity method has a wider coverage, but is affected by the non-uniqueness of inversion. This invention uses the structured prior (covariance) of borehole transient electromagnetic inversion information to constrain the DC resistivity method inversion, that is, using the high resolution near the wellbore to guide a large-scale inversion, so that the two different methods complement each other, which can significantly improve the inversion stability and inversion imaging accuracy of DC resistivity inversion. Ultimately, this invention can be applied to scenarios such as tunnel face or underground coal mine excavation inversion, to accurately identify water-rich fractured zones, hidden faults, karst caves and other adverse geological anomalies that may exist in the surrounding rock ahead. Attached Figure Description

[0046] Figure 1 This is an overall flowchart of the present invention;

[0047] Figure 2 This is a schematic diagram of the layout of the borehole transient electromagnetic detection in this invention;

[0048] Figure 3 This is a schematic diagram of the layout for DC resistivity detection in this invention.

[0049] Figure 4 This is a schematic diagram illustrating the calculation of the effective distance in any direction in this invention. Detailed Implementation

[0050] The present invention will be further described below.

[0051] like Figure 1 As shown, the present invention includes the following steps:

[0052] Step 1: Lay out advance boreholes: Establish a coordinate system with the tunnel axis as the x-axis, the axis parallel to the tunnel top and bottom slabs as the y-axis, and the axis perpendicular to the tunnel top and bottom slabs as the z-axis, such as... Figure 2As shown, advance drilling is carried out along the x-axis at the center of the tunnel face; the hole direction should be as consistent with the axis as possible and the deviation should be as small as possible; the hole diameter needs to meet the requirements of the transient electromagnetic probe and cable laying; non-metallic sleeves should be used in the required detection area to avoid metal components entering the measurement depth range and affecting the detection effect; after drilling, the borehole coordinates, elevation, axial orientation and depth mark are recorded, and the basic borehole inclination is checked and the hole is cleaned (clean water circulation) to ensure the stability of the medium inside the hole and the unobstructed passage.

[0053] Step 2, Transient Electromagnetic Detection in Borehole: Based on the pre-drilling depth, multiple detection points are set at equal intervals in the borehole. The transient electromagnetic detection equipment is placed in the borehole, and transient electromagnetic detection is performed at each detection point to obtain the transient electromagnetic observation data of all detection points in the entire pre-drilling borehole.

[0054] Step 3, Transient Electromagnetic Inversion: For the transient electromagnetic observation data of each detection point obtained in Step 2, radial inversion is performed on the transient electromagnetic observation data of each detection point. The specific formula is as follows:

[0055] (1)

[0056] in, This is the weighting matrix for borehole transient electromagnetic observation data; The transient electromagnetic data of the borehole is the observation data (induced voltage decay curve) at the i-th detection point, where i ranges from 1 to N; For drilling transient electromagnetic positive simulation operator; A predictive resistivity model for transient electromagnetics during borehole drilling; For the model constraint term regularization factor of borehole transient electromagnetics; The smoothing constraint weighting matrix for the transient electromagnetic model of borehole drilling can be constructed using zero-order, first-order, and second-order derivative operators. The set of circular discrete points is obtained through the above formula. ;gather The resistivity profile is mapped to a resistivity model with the depth of the detection point as the cross section and the borehole axis as the center, thereby obtaining the resistivity profile distribution of all detection points.

[0057] Step 4: Calculate the effective range and Gaussian variation model along the x-axis of the borehole transient electromagnetic path: Extract the resistivity profile distribution at each detection point (which is itself a set of discrete points). Extract the resistivity values ​​with the same y and z coordinates from the resistivity profile distribution at each detection point into a discrete curve along the x-axis, thus obtaining several discrete curves along the x-axis. Calculate the average value by superimposing all the corresponding curves. Specifically: calculate the average value of the resistivity profile distribution at each detection point (i.e., if there are n resistivity values ​​on the resistivity profile distribution at a detection point, then average these resistivity values). Adding and then dividing by the number n yields the average resistivity of the detection point. These average values ​​are used to represent the resistivity distribution of each detection point within a certain radial range of the borehole, thus obtaining a unique curve x(k), where k is the x-axis coordinate of each detection point. Since there are N detection points for the borehole transient electromagnetic test, the x(k) curve is a set of N discrete points. This curve characterizes the overall trend of the resistivity of the surrounding rock ahead of the tunnel along the x-axis. The experimental half-variation is calculated based on this curve x(k), using the following formula:

[0058] (2)

[0059] Where N(h) is the number of selected lag distances; to ensure calculation accuracy, the largest lag distance needs to have more than 5 calculation samples, that is, at least 5 groups. It can be calculated; otherwise, the amount of data is too small, and the credibility will decrease. Finally, an experimental half-variation curve that monotonically increases with h is obtained.

[0060] Next, a Gaussian variation model is used for fitting and parameter estimation. The specific formula is as follows:

[0061] (3)

[0062] in, This represents the variance of all discrete points in the borehole transient electromagnetic inversion result; For the effective travel distance in the x-axis direction of the transient electromagnetic drilling, targeting The values ​​are optimized using least squares to find an optimal value. The value minimizes the residual between the Gaussian variation model curve and the previously calculated experimental semivariogram; the optimal value is... Substituting the value back into formula (3), we obtain the Gaussian variation model of the borehole transient electromagnetic x-axis direction.

[0063] Step 5: DC Resistivity Method Advanced Detection: Deploy the DC resistivity method observation system as follows Figure 3As shown, this embodiment uses a fixed-point source triode method for deployment. Specifically, the positive power supply electrode A is fixed at the tunnel face, and the negative return electrode B is deployed at a relatively far distance behind the tunnel and kept fixed. The precise coordinates of A and B are recorded, and A and B remain fixed in subsequent remeasurements. Measurement electrodes M and N are arranged on the line connecting A and B, and different combinations of measurement electrodes M and N are switched to achieve full coverage in front of the tunnel face. The coordinates of measurement electrodes M and N and the corresponding potential difference are accurately recorded for each measurement, thereby enabling advanced detection in front of the tunnel and obtaining DC resistivity data of the required detection area.

[0064] Step Six: Calculate the effective range and Gaussian variation model of the borehole transient electromagnetic y and z axes: Since the advance borehole is only distributed along the x-axis, the effective range and Gaussian variation model of the borehole transient electromagnetic y and z axes cannot be directly calculated using Step Four. Therefore, a smoothing constraint is used to invert the DC resistivity data from Step Five to obtain the DC resistivity advance detection inversion result under the smoothing constraint. The specific objective function is:

[0065] (4)

[0066] in, The model smoothing constraint weighting matrix for DC resistivity can be constructed using zero-order, first-order, and second-order derivative operators.

[0067] Since the DC resistivity advance detection inversion result under smoothing constraints is a complete three-dimensional rectangular space in front of the drilling face (rather than the borehole transient electromagnetic results which only have circular resistivity profiles at each site), taking the x-axis as an example, all the resistivity curves along the x-axis of the inversion result under DC resistivity smoothing constraints are extracted, superimposed, and averaged to obtain a uniquely determined discrete resistivity distribution curve along the x-axis. Subsequently, the calculation of the experimental half-variation and the fitting of the Gaussian variation model are exactly the same as in step four; therefore, the effective ranges along the x, y, and z axes under DC resistivity smoothing constraints are calculated according to the method in step four, and combined with the effective range in the x-axis direction of the borehole transient electromagnetic in step four, the effective ranges and Gaussian variation models in the y and z-axis directions of the borehole transient electromagnetic are calculated, specifically as follows:

[0068] Let the effective path lengths of the x-axis, y-axis, and z-axis under DC resistivity smoothing constraints be respectively , , The effective travel distance of the transient electromagnetic drilling in the x-axis direction is The effective travel distance in the y and z axes of the transient electromagnetic borehole drilling is calculated using the following formula. , :

[0069] (5)

[0070] (6)

[0071] Next, the calculated , Substituting into formula (3), we obtain the Gaussian variation model of the transient electromagnetic y and z axes of the borehole.

[0072] Step 7: Calculate the effective range and Gaussian variation model for any direction of the borehole transient electromagnetic circuit: Based on the effective range and Gaussian variation models for the x, y, and z axes of the borehole transient electromagnetic circuit obtained in Steps 4 and 6, the effective range and Gaussian variation model for any direction are calculated as follows:

[0073] Define the angle between any direction and the plane containing the x and y axes as The angle between this arbitrary direction and the positive x-axis direction on the plane containing the x and y axes is... like Figure 4 As shown, the effective range in any direction is... The calculation formula is:

[0074] (7)

[0075] The effective distance in any direction will be calculated. Substituting into formula (3), we obtain the Gaussian variation model in any direction.

[0076] Step 8: Construct the covariance constraint matrix: Discretize the desired detection area into a 3D inversion mesh, and calculate the covariance value of any two mesh cells using an arbitrary-direction Gaussian variation model. The specific formula is as follows:

[0077] (8)

[0078] Where C(h) is the covariance function value. Once the direction is determined, this function value is only related to the lag distance h. Therefore, in the same direction, two grid cells with the same lag distance h have the same covariance value.

[0079] Assume there are a total of [number] grid cells. There are , and the corresponding covariance matrix to be constructed has dimensions of . This matrix is ​​a symmetric matrix, where the value of any i-th row and j-th column is... Let represent the covariance value between the i-th and j-th grid cells. Then, the formula for the covariance constraint matrix is:

[0080] (9).

[0081] Step 9: DC Resistivity Lead Probe Inversion with Covariance Constraints: The DC resistivity probe data is inverted using the covariance constraint matrix. The specific objective function is:

[0082] (10)

[0083] in, This is the data weighting matrix for the DC resistivity method; Potential difference data acquired using the DC resistivity method; This is the positive analog operator for the DC resistivity method; This is the predicted resistivity model in the DC resistivity method; This is the regularization factor for the covariance constraint term in the DC resistivity method; This is the covariance constraint matrix.

[0084] Based on the above inversion results and the borehole transient electromagnetic inversion results, the geological conditions of the area to be explored are obtained.

[0085] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A combined advanced detection method based on borehole transient electromagnetic and direct current resistivity, characterized in that, The method comprises the following steps: Step one, establish a coordinate system with the tunnel axis as the x-axis, parallel to the tunnel roof and floor as the y-axis, and perpendicular to the tunnel roof and floor as the z-axis, and drill an advanced borehole along the x-axis at the center of the tunnel working face; Step two, perform transient electromagnetic detection on the detection points at different positions in the advanced borehole to obtain the borehole transient electromagnetic data of all the detection points; Step three, after radial inversion and processing of the borehole transient electromagnetic data of each detection point, the resistivity profile distribution of all the detection points is obtained; Step four, the resistivity values with the same y and z coordinates in the resistivity profile distribution of each detection point are extracted as a discrete curve along the x-axis, and the average value of the corresponding superposition of each discrete curve is obtained to obtain a curve x(k), wherein the value of k is the x-axis coordinate of each detection point; the experimental semivariogram is calculated according to the curve x(k), then the Gaussian variogram model is fitted and the parameters are estimated, and finally the effective range of the borehole transient electromagnetic x-axis direction and the Gaussian variogram model are obtained; Step five, obtain the direct current resistivity data of the required detection area; Step six, after inversion of the direct current resistivity data in step five using the smoothing constraint to obtain the result, the effective range of the x-axis, y-axis and z-axis under the direct current resistivity smoothing constraint is calculated in the manner of step four, and the effective range of the borehole transient electromagnetic y-axis and z-axis is calculated in combination with the effective range of the borehole transient electromagnetic x-axis direction in step four, and the Gaussian variogram model is obtained; Step seven, the effective range and the Gaussian variogram model in any direction are calculated according to the effective range and the Gaussian variogram model of the borehole transient electromagnetic x-axis, y-axis and z-axis obtained in steps four and six; Step eight, the three-dimensional discrete of the inversion grid of the required detection area is performed, and the covariance value of any two grid units is calculated using the Gaussian variogram model in any direction, so as to construct a covariance constraint matrix; Step nine, the direct current resistivity detection data is inverted using the covariance constraint matrix, and the geological conditions of the required detection area are obtained according to the inversion result and the borehole transient electromagnetic inversion result.

2. The method according to claim 1, wherein the method is characterized by, After the drilling, the coordinates, elevation, axial direction and depth mark of the hole are recorded.

3. The method for combined advanced detection based on borehole transient electromagnetic and direct current resistivity according to claim 1, characterized in that, The specific formula of the radial inversion in step three is: （1） wherein, is a weighting matrix for borehole transient electromagnetic observation data; is the observation data of borehole transient electromagnetic at the ith survey point, i from 1 to N; is a forward modeling operator for borehole transient electromagnetic; is a predicted resistivity model for borehole transient electromagnetic; is a regularization factor for the model constraint term of borehole transient electromagnetic; is a model smoothing constraint weighting matrix for borehole transient electromagnetic.

4. The method of claim 1, wherein the method is characterized by, The calculation formula of the experimental semivariogram in step four is: （2） Wherein, N(h) is the number of selected lag distance; The specific formula of the Gaussian variogram model function is: （3） in, This represents the variance of all discrete points in the borehole transient electromagnetic inversion result; For the effective travel distance in the x-axis direction of the transient electromagnetic drilling, targeting The values ​​are optimized using least squares to find an optimal value. The value minimizes the residual between the Gaussian variation model curve and the previously calculated experimental semivariogram; the optimal value is... Substituting the value back into formula (3), we obtain the Gaussian variation model of the borehole transient electromagnetic x-axis direction.

5. The method according to claim 4, wherein, In the step six, the effective ranges of x-axis, y-axis and z-axis are respectively 、 、 , the effective range of x-axis of the borehole transient electromagnetic method is ; the effective ranges of y-axis and z-axis of the borehole transient electromagnetic method are calculated by the following formula 、 : （4） （5） Then the calculated , are substituted into formula (3) respectively, and the Gaussian variation model of the y and z axis direction of the drilling transient electromagnetic method is obtained.

6. The method according to claim 5, wherein, The specific formula of step seven is: Let the angle between any direction and the plane of the x, y axes be Let the angle between the arbitrary direction and the positive direction of the x axis be Then the effective range of the arbitrary direction is The calculation formula is: （6） The effective range of the calculation of any direction Substitute equation (3), so that the Gaussian variation model of any direction is obtained.

7. The method according to claim 6, wherein, The specific formula of the covariance value of any two grid units calculated in step eight is: （7） Wherein, C(h) is the covariance function value.

8. The method according to claim 7, wherein, In step nine, the direct current resistivity detection data is inverted using the covariance matrix, and the objective function is: （8） wherein, is a data weighting matrix for the direct current resistivity method; is a potential difference data collected by the direct current resistivity method; is a forward simulation operator for the direct current resistivity method; is a predictive resistivity model in the direct current resistivity method; is a regularization factor for the covariance constraint term of the direct current resistivity method; is a covariance constraint matrix.

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