A method for extracting adverse geological features from tunnel geophysical inversion data

Abstract

The present invention discloses a method for extracting adverse geological features from tunnel geophysical inversion data, comprising the following steps: pre-processing face data and advance drilling data to obtain a set of interpolation points of a target type of adverse geological body, performing interpolation calculations on the point set to obtain a voxel model of the adverse geological body; using advance drilling data to perform quality assessment on the interpolation results of the adverse geological body; using geophysical inversion data to construct a geophysical field voxel model, obtaining the intersection of the geophysical field voxel model with the adverse geological body voxel model to obtain an adverse geological feature voxel model; mapping the coordinates of the adverse geological feature voxel model to the geophysical inversion data, extracting a local coordinate set and resampling it according to the corresponding accuracy to obtain a set of coordinate points of the adverse geological feature. The present invention can integrate the adverse geological prior information revealed by the face data and the advance drilling data, accurately extract the adverse geological features in the multimodal geophysical inversion data, and facilitate the clarification of the geophysical response characteristics of the adverse geological body.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering geological detection, and in particular to a method for extracting adverse geological features from tunnel geophysical inversion data. Background Art

[0002] Since the 21st century, railway construction has entered a climax, creating unprecedented opportunities for the development of tunnel technology. At the same time, it has also put forward higher requirements for tunnel engineering geological exploration and disaster prevention. The use of multiple types of geophysical advanced detection technology to detect, model and analyze the spatial distribution and attribute information of unfavorable geological bodies ahead of the tunnel face is an indispensable part of tunnel construction. Extracting unfavorable geological characteristics from geophysical inversion data such as seismic wave fields, electromagnetic fields, and electric fields that are continuously updated during tunnel excavation, establishing a corresponding relationship with the actual unfavorable geological conditions, and then obtaining the geophysical response laws of unfavorable geological bodies in the tunnel will help to more accurately grasp the unfavorable geological conditions ahead of the tunnel face, which is of great significance to the dynamic optimization design and precise safety control of tunnel construction.

[0003] Existing methods for extracting adverse geological features rely on expert judgment and manual sketching. Geophysical methods have a wide detection range but exhibit variations in geophysical response characteristics under different geological settings. Drilling and sketching methods have a narrow detection range but high accuracy. Furthermore, multi-source data are independent and dispersed, with varying accuracy and scale, making it difficult to fuse and extract key features. Because face data and advance drilling data can intuitively reflect actual geological information, including key features such as the type, morphology, and spatial distribution of adverse geological bodies, accurately extracting corresponding adverse geological features from multimodal geophysical field data, using these directly revealed adverse geological conditions as a reference, is an urgent challenge.

[0004] At present, there are two main methods for extracting adverse geological features from geophysical inversion data: 1) Extraction of adverse geological features based on unsupervised classification: This type of method analyzes existing geological data, artificially sets the number of geological unit categories, and then divides the geophysical inversion data into geological units through an unsupervised clustering algorithm. The geological unit category that is most likely to be an adverse geological body in the classification analysis results is the adverse geological feature. This type of method is easy to implement and has a fast extraction speed, but it can only roughly classify geophysical inversion data, and because it takes into account fewer factors, it is difficult to ensure the accuracy of the adverse geological features extracted in a complex geological environment. 2) Extraction of adverse geological features based on deep learning: This type of method first constructs a mapping relationship between the geophysical field and the adverse geological body through artificial labeling, and then uses deep learning methods to learn and identify adverse geological features. This type of method can effectively identify multiple types of adverse geological features, but the prerequisite is that a large amount of training data is required.

[0005] Therefore, there is an urgent need for an extraction method that can be applied to a variety of geophysical inversion data, has wide applicability, and can accurately extract adverse geological features in multimodal geophysical inversion data. Summary of the Invention

[0006] In order to solve the problems existing in the prior art, the present invention provides a method for extracting adverse geological features from tunnel geophysical inversion data. By fusing the adverse geological prior information revealed by the face data and the advance drilling data, the adverse geological features in the multimodal geophysical inversion data are accurately extracted, which is conducive to clarifying the geophysical response characteristics of the adverse geological body and solving the problems mentioned in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solution: a method for extracting adverse geological features from tunnel geophysical inversion data, comprising the following steps:

[0008] S1. Preprocessing the tunnel face data and the advance drilling data to obtain a set of interpolation points of the target type of undesirable geological body, performing interpolation calculation on the set of points to obtain a voxel model of the undesirable geological body;

[0009] S2. Using the advanced drilling data, perform a quality assessment on the interpolation result of the poor geological body;

[0010] S3, constructing a geophysical field voxel model using the geophysical inversion data, and obtaining an intersection between the geophysical field voxel model and the adverse geological body voxel model to obtain an adverse geological feature voxel model;

[0011] S4. Mapping the coordinates of the adverse geological feature voxel model to the geophysical inversion data, extracting the local coordinate set and resampling it according to the corresponding accuracy to obtain the adverse geological feature coordinate point set.

[0012] Preferably, the step S1 specifically includes the following:

[0013] S101, selecting target adverse geological features to extract multiple tunnel face data within a tunnel mileage section, and manually marking the adverse geological body contours in the corresponding tunnel face image data based on the adverse geological information of the target type recorded in each tunnel face data;

[0014] S102, each tunnel face image is divided into m partitions with equal horizontal spacing, and then into n partitions with equal horizontal spacing, for a total of m×n partitions. The center point of each partition is taken, and the shortest distance from the point to the contour of the unfavorable geological body described in S101 is calculated. It is then determined whether the point and the contour of the unfavorable geological body described in S101 form an inclusion relationship. If so, the attribute value of the point is assigned to be the negative value of the distance. If not, the attribute value of the point is assigned to be the positive value of the distance, thereby obtaining a point set Ps1;

[0015] S103, selecting target adverse geological features to extract multiple advance drilling data within the tunnel mileage section, and dividing the corresponding drilling data into two categories based on the adverse geological information of the target type recorded in each advance drilling data: one category is adverse geological bodies belonging to the target type, and the other category is adverse geological bodies not belonging to the target type, thereby obtaining multiple segments of classified drilling data, extracting segment nodes from the multiple segments of drilling data, obtaining a point set Ps2, assigning a value of 0 to the attribute values of all points in Ps2, and merging Ps1 and Ps2 to obtain a point set Ps3;

[0016] S104. Combine the tunnel construction design drawings and the tunnel construction mileage information corresponding to the face data, map the coordinates of the point set Ps3 to the tunnel construction mileage three-dimensional coordinate system to obtain the three-dimensional point set Ps_i to be interpolated, calculate the axis-aligned bounding box of the three-dimensional point set Ps_i to be interpolated and divide the space into dense voxels, set interpolation parameters, interpolate and calculate the attribute value of each voxel unit of the three-dimensional point set to be interpolated to obtain the interpolation result of the poor geological body, extract the voxel units whose attribute values are not greater than 0 in the interpolation result, and obtain the voxel model of the poor geological body.

[0017] Preferably, in step S102, the tunnel face image is divided into equal intervals, and the number of horizontal and vertical divisions is no less than 20.

[0018] Preferably, in step S104, the interpolation calculation uses hierarchical B-spline interpolation, and the accuracy of the spatial division is not less than 0.1 meter.

[0019] Preferably, the step S2 specifically includes the following:

[0020] S201, encrypting the multiple segments of drilling data in S103 at equal intervals, marking each point as to whether it belongs to a target type of unfavorable geological body, mapping the point set coordinates to a three-dimensional coordinate system of tunnel construction mileage, and obtaining a three-dimensional drilling point set Ps_d;

[0021] S202, determining the relative positional relationship between each point in the three-dimensional drilling point set Ps_d and the voxel model of the unfavorable geological body described in step S1, obtaining the ratio of the number of points with correct relative positional relationship to the total number of points, and obtaining the model accuracy;

[0022] S203: Based on the preset model accuracy, determine whether the quality of the voxel model of the poor geological body being evaluated meets the standard. If the quality meets the standard, proceed to the next step of processing. If the quality does not meet the standard, it is necessary to return to step S1.

[0023] Preferably, in step S202, the correct relative position relationship indicates that the three-dimensional drilling point of the bad geological body of the target type is located inside the bad geological body voxel model of step S1, or the three-dimensional drilling point of the bad geological body that does not belong to the target type is located outside the bad geological body voxel model of step S1. In other cases, the relative position relationship is incorrect.

[0024] Preferably, the step S3 specifically includes the following:

[0025] S301. Select target adverse geological features to extract geophysical inversion data within the tunnel mileage section, and construct a geophysical field voxel model based on the geophysical field mode. If the geophysical field is a two-dimensional geophysical field, resample the data to the same resolution as the adverse geological body voxel model, construct a voxel model with a thickness of 1 in the Z-axis direction, and then map the coordinates of the voxel model to a three-dimensional coordinate system of the tunnel mileage to obtain a geophysical field voxel model. If the geophysical field is three-dimensional geophysical inversion data, resample the data to the same resolution as the adverse geological body voxel model, construct a voxel model, and then map the coordinates of the voxel model to a three-dimensional coordinate system of the tunnel mileage to obtain a geophysical field voxel model.

[0026] S302: Obtain the intersection of the bad geological volume voxel model and the geophysical field voxel model to obtain a bad geological feature voxel model.

[0027] Preferably, in step S301, the two-dimensional geophysical inversion data resampling method uses a bilinear interpolation method, and the three-dimensional geophysical inversion data resampling method uses a trilinear interpolation method.

[0028] Preferably, the step S4 specifically includes the following:

[0029] S401, mapping the coordinates of the adverse geological feature voxel model to the local coordinate system of the geophysical field voxel model, extracting the three-dimensional coordinates corresponding to the center of each voxel, and obtaining a local coordinate set of the geophysical field;

[0030] S402. Resample the local coordinate set according to the accuracy of the geophysical inversion data to obtain a set of coordinate points of adverse geological features.

[0031] Preferably, in step S402, if the geophysical inversion data expresses a two-dimensional geophysical field, the resampling method uses a bilinear interpolation method; if the geophysical inversion data expresses a three-dimensional geophysical field, the resampling method uses a trilinear interpolation method.

[0032] The beneficial effects of the present invention are:

[0033] 1) The present invention provides a method for extracting adverse geological features from tunnel geophysical inversion data. This method can integrate prior adverse geological information revealed by tunnel face data and advanced horizontal drilling data, enabling three-dimensional reconstruction and quality assessment of adverse geological environments before tunnel excavation. This method is beneficial for accurately extracting adverse geological features from multimodal geophysical inversion data.

[0034] 2) The present invention provides a method for extracting adverse geological features from tunnel geophysical inversion data. The process of obtaining the intersection of adverse geological features uniformly converts multimodal geophysical inversion data into a voxel model, which can be applied to a variety of geophysical inversion data and has wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The figure is a flow chart of the steps of the method for extracting adverse geological features from tunnel geophysical inversion data according to the present invention. DETAILED DESCRIPTION

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0037] See also Figure 1 The present invention provides a technical solution: a method for extracting adverse geological features from tunnel geophysical inversion data, which specifically includes the following steps:

[0038] Step S1: pre-processing the tunnel face data and the advance drilling data to obtain a set of interpolation points of a target type of poor geological body, performing interpolation calculation on the set of points to obtain a voxel model of the poor geological body.

[0039] It specifically includes the following sub-steps:

[0040] Step S101: Select target adverse geological features to extract multiple tunnel face data within a tunnel mileage section, and manually plot the adverse geological body contour in the corresponding tunnel face image data based on the adverse geological information of the target type recorded in each tunnel face data;

[0041] Step S102: Each tunnel face image is divided into m partitions with equal horizontal spacing, and then into n partitions with equal horizontal spacing, for a total of m×n partitions. The center point of each partition is taken, and the shortest distance from the point to the contour of the unfavorable geological body described in step S101 is calculated. It is then determined whether the point and the contour of the unfavorable geological body described in step S101 form an inclusion relationship. If so, the attribute value of the point is assigned to the negative value of the distance; if not, the attribute value of the point is assigned to the positive value of the distance, thereby obtaining a point set Ps1.

[0042] Step S103: Select target adverse geological features to extract multiple advance drilling data within the tunnel mileage section. According to the adverse geological information of the target type recorded in each advance drilling data, the corresponding drilling data are divided into two categories: one category belongs to the target type of adverse geological body, and the other category does not belong to the target type of adverse geological body, to obtain multiple segments of classified drilling data, extract segment nodes in the multiple segments of drilling data to obtain a point set Ps2, assign 0 to the attribute values of all points in Ps2, merge Ps1 and Ps2 to obtain a point set Ps3;

[0043] Step S104: Combine the tunnel construction design drawings and the tunnel construction mileage information corresponding to the face data, map the coordinates of the point set Ps3 to the tunnel construction mileage three-dimensional coordinate system to obtain the three-dimensional point set Ps_i to be interpolated, calculate the axis-aligned bounding box of the three-dimensional point set Ps_i to be interpolated and divide the space into dense voxels, set interpolation parameters, interpolate and calculate the attribute value of each voxel unit of the three-dimensional point set to be interpolated to obtain the interpolation result of the poor geological body, extract the voxel units whose attribute values are not greater than 0 in the interpolation result, and obtain the voxel model of the poor geological body.

[0044] Furthermore, in step S102, the tunnel face image is divided into equal intervals, and the number of horizontal and vertical divisions is preferably no less than 20.

[0045] Furthermore, in step S104, the interpolation calculation algorithm uses hierarchical B-spline interpolation, and the accuracy of the space division in step S104 is not less than 0.1 meters.

[0046] Step S2: Using the advanced drilling data, perform a quality assessment on the interpolation result of the poor geological body.

[0047] It specifically includes the following sub-steps:

[0048] Step S201: Encrypt the multiple segments of drilling data in step S103 at equal intervals, mark each point as belonging to a target type of unfavorable geological body, and map the point set coordinates to the tunnel construction mileage three-dimensional coordinate system to obtain a three-dimensional drilling point set Ps_d;

[0049] The above-mentioned equally spaced dense drilling polylines should ensure that the distance between any point in the three-dimensional drilling point set Ps_d and its nearest neighbor point is no more than 0.1 meters;

[0050] Step S202: determine the relative positional relationship between each point in the three-dimensional drilling point set Ps_d and the voxel model of the unfavorable geological body described in step S1, and obtain the ratio of the number of points with correct relative positional relationship to the total number of points to obtain the model accuracy;

[0051] Step S203: determine whether the quality of the voxel model of the poor geological body being evaluated meets the standard based on the preset model accuracy. If the quality meets the standard, proceed to the next step of processing. If the quality does not meet the standard, return to step S1.

[0052] Furthermore, in step S202, the correct relative position relationship indicates that the three-dimensional drilling point of the bad geological body of the target type is located inside the voxel model of the bad geological body described in step S1, or the three-dimensional drilling point of the bad geological body that does not belong to the target type is located outside the voxel model of the bad geological body described in step S1. In other cases, the relative position relationship is incorrect.

[0053] Furthermore, the preset value of the preset model accuracy is not less than 80%.

[0054] Step S3: construct a geophysical field voxel model using the geophysical inversion data, and obtain the intersection of the geophysical field voxel model and the adverse geological body voxel model to obtain an adverse geological feature voxel model.

[0055] It specifically includes the following sub-steps:

[0056] Step S301: Select the target adverse geological features to extract geophysical inversion data within the tunnel mileage section, and construct a geophysical field voxel model based on the geophysical field mode. If it is a two-dimensional geophysical field, resample the data to the same resolution as the adverse geological body voxel model, construct a voxel model with a thickness of 1 in the Z-axis direction, and then map the voxel model coordinates to the tunnel mileage three-dimensional coordinate system to obtain the geophysical field voxel model; if it is three-dimensional geophysical inversion data, resample the data to the same resolution as the adverse geological body voxel model, construct a voxel model, and then map the voxel model coordinates to the tunnel mileage three-dimensional coordinate system to obtain the geophysical field voxel model;

[0057] Step S302: Obtain the intersection of the bad geological volume voxel model and the geophysical field voxel model to obtain a bad geological feature voxel model.

[0058] Furthermore, in step S301, the two-dimensional geophysical inversion data resampling method uses a bilinear interpolation method, and the three-dimensional geophysical inversion data resampling method uses a trilinear interpolation method.

[0059] Step S4: Mapping the coordinates of the adverse geological feature voxel model to the geophysical inversion data to obtain a set of adverse geological feature coordinate points.

[0060] It includes the following sub-steps:

[0061] Step S401: Mapping the coordinates of the adverse geological feature voxel model to the local coordinate system of the geophysical field voxel model, extracting the three-dimensional coordinates corresponding to the center of each voxel, and obtaining a local coordinate set of the geophysical field;

[0062] Step S402: resample the local coordinate set according to the accuracy of the geophysical inversion data to obtain a set of coordinate points of adverse geological features.

[0063] Furthermore, in step S402, if the geophysical inversion data expresses a two-dimensional geophysical field, the resampling method uses a bilinear interpolation method; if the geophysical inversion data expresses a three-dimensional geophysical field, the resampling method uses a trilinear interpolation method.

[0064] It should be noted that if the geophysical inversion data expresses a two-dimensional geophysical field, the Z-axis information of the corresponding geophysical field local coordinate set will be discarded.

[0065] The present invention provides a method for extracting adverse geological features from tunnel geophysical inversion data, which can integrate adverse geological prior information revealed by face data and advance drilling data, realize three-dimensional reconstruction and quality assessment of the adverse geological environment before tunnel excavation, and is conducive to the accurate extraction of adverse geological features in multimodal geophysical inversion data; the process of obtaining the intersection of adverse geological features uniformly converts multimodal geophysical inversion data into a voxel model, which can be applied to a variety of geophysical inversion data and has wide applicability.

[0066] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for extracting adverse geological features from tunnel geophysical inversion data, characterized in that: The following steps are involved: S1. Preprocessing the tunnel face data and the advance drilling data to obtain a set of interpolation points of the target type of undesirable geological body, performing interpolation calculation on the set of points to obtain a voxel model of the undesirable geological body; S2. Using the advanced drilling data, perform a quality assessment on the interpolation result of the poor geological body; S3, constructing a geophysical field voxel model using the geophysical inversion data, and obtaining an intersection between the geophysical field voxel model and the adverse geological body voxel model to obtain an adverse geological feature voxel model; S4. Mapping the coordinates of the adverse geological feature voxel model to the geophysical inversion data, extracting the local coordinate set and resampling it according to the corresponding accuracy to obtain the adverse geological feature coordinate point set.

2. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 1, characterized in that: The step S1 specifically includes the following: S101, selecting target adverse geological features to extract multiple tunnel face data within a tunnel mileage section, and manually marking the adverse geological body contours in the corresponding tunnel face image data based on the adverse geological information of the target type recorded in each tunnel face data; S102, each tunnel face image is divided into m partitions with equal horizontal spacing, and then into n partitions with equal horizontal spacing, for a total of m×n partitions. The center point of each partition is taken, and the shortest distance from the point to the contour of the unfavorable geological body described in S101 is calculated. It is then determined whether the point and the contour of the unfavorable geological body described in S101 form an inclusion relationship. If so, the attribute value of the point is assigned to be the negative value of the distance. If not, the attribute value of the point is assigned to be the positive value of the distance, thereby obtaining a point set Ps1; S103, selecting target adverse geological features to extract multiple advance drilling data within the tunnel mileage section, and dividing the corresponding drilling data into two categories based on the adverse geological information of the target type recorded in each advance drilling data: one category is adverse geological bodies belonging to the target type, and the other category is adverse geological bodies not belonging to the target type, thereby obtaining multiple segments of classified drilling data, extracting segment nodes from the multiple segments of drilling data, obtaining a point set Ps2, assigning a value of 0 to the attribute values of all points in Ps2, and merging Ps1 and Ps2 to obtain a point set Ps3; S104. Combine the tunnel construction design drawings and the tunnel construction mileage information corresponding to the face data, map the coordinates of the point set Ps3 to the tunnel construction mileage three-dimensional coordinate system to obtain the three-dimensional point set Ps_i to be interpolated, calculate the axis-aligned bounding box of the three-dimensional point set Ps_i to be interpolated and divide the space into dense voxels, set interpolation parameters, interpolate and calculate the attribute value of each voxel unit of the three-dimensional point set to be interpolated to obtain the interpolation result of the poor geological body, extract the voxel units whose attribute values are not greater than 0 in the interpolation result, and obtain the voxel model of the poor geological body.

3. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 2, characterized in that: In step S102, the tunnel face image is divided into equal intervals, and the number of horizontal and vertical divisions is not less than 20.

4. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 2, characterized in that: In step S104, the interpolation calculation uses hierarchical B-spline interpolation, and the accuracy of the spatial division is not less than 0.1 meters.

5. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 1, characterized in that: The step S2 specifically includes the following: S201, encrypting the multiple segments of drilling data in S103 at equal intervals, marking each point as to whether it belongs to a target type of unfavorable geological body, mapping the point set coordinates to a three-dimensional coordinate system of tunnel construction mileage, and obtaining a three-dimensional drilling point set Ps_d; S202, determining the relative positional relationship between each point in the three-dimensional drilling point set Ps_d and the voxel model of the unfavorable geological body described in step S1, obtaining the ratio of the number of points with correct relative positional relationship to the total number of points, and obtaining the model accuracy; S203: Based on the preset model accuracy, determine whether the quality of the voxel model of the poor geological body being evaluated meets the standard. If the quality meets the standard, proceed to the next step of processing. If the quality does not meet the standard, it is necessary to return to step S1.

6. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 5, characterized in that: In step S202, the correct relative position relationship indicates that the three-dimensional drilling point of the bad geological body of the target type is located inside the bad geological body voxel model of step S1, or the three-dimensional drilling point of the bad geological body that does not belong to the target type is located outside the bad geological body voxel model of step S1. In other cases, the relative position relationship is incorrect.

7. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 1, characterized in that: The step S3 specifically includes the following: S301. Select target adverse geological features to extract geophysical inversion data within the tunnel mileage section, and construct a geophysical field voxel model based on the geophysical field mode. If the geophysical field is a two-dimensional geophysical field, resample the data to the same resolution as the adverse geological body voxel model, construct a voxel model with a thickness of 1 in the Z-axis direction, and then map the coordinates of the voxel model to a three-dimensional coordinate system of the tunnel mileage to obtain a geophysical field voxel model. If the geophysical field is three-dimensional geophysical inversion data, resample the data to the same resolution as the adverse geological body voxel model, construct a voxel model, and then map the coordinates of the voxel model to a three-dimensional coordinate system of the tunnel mileage to obtain a geophysical field voxel model. S302: Obtain the intersection of the bad geological volume voxel model and the geophysical field voxel model to obtain a bad geological feature voxel model.

8. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 7, characterized in that: In step S301, the two-dimensional geophysical inversion data resampling method uses a bilinear interpolation method, and the three-dimensional geophysical inversion data resampling method uses a trilinear interpolation method.

9. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 1, characterized in that: The step S4 specifically includes the following: S401, mapping the coordinates of the adverse geological feature voxel model to the local coordinate system of the geophysical field voxel model, extracting the three-dimensional coordinates corresponding to the center of each voxel, and obtaining a local coordinate set of the geophysical field; S402. Resample the local coordinate set according to the accuracy of the geophysical inversion data to obtain a set of coordinate points of adverse geological features.

10. The method for extracting adverse geological features from tunnel geophysical inversion data according to claim 9, characterized in that: In step S402, if the geophysical inversion data expresses a two-dimensional geophysical field, the resampling method uses a bilinear interpolation method; if the geophysical inversion data expresses a three-dimensional geophysical field, the resampling method uses a trilinear interpolation method.

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