A resistivity CT imaging method based on dual-channel cross-hole radar

Abstract

The present invention relates to the field of resistivity CT imaging technology, solving the technical problems of inter-hole resistivity CT technology, such as low resolution, poor reliability, and low measurement efficiency, which cannot meet the needs of practical engineering applications. In particular, it relates to a resistivity CT imaging method based on dual-channel cross-hole radar, comprising the following steps: S1, drilling holes 1 and 2 on both sides of the measured area to form an inter-hole profile; S2, gridding the inter-hole profile, dividing the inter-hole profile into rectangular grid cells with M vertical rows and N horizontal columns, wherein the number of cells in the grid is M×N, and M≥N. The present invention not only improves the resolution and reliability of resistivity CT results, but also can obtain three physical images of wave velocity, skin depth, and resistivity through a single data acquisition, thus strengthening the foundation for comprehensive geophysical interpretation, greatly improving work efficiency, and making construction easier and faster.

Description

Technical Field

[0001] The present invention relates to the technical field of resistivity CT imaging, and in particular to a resistivity CT imaging method based on dual-channel cross-hole radar. Background Art

[0002] Cross-hole resistivity CT images are widely used in engineering fields such as dam leakage, anti-seepage wall quality, goaf and karst detection, as well as in metal mine exploration. These measurements are typically performed using specialized cross-hole resistivity CT equipment, which requires multiple transmitting and receiving electrodes. Currently used technology, such as that described in Chinese invention patent application number 2019101126936, produces resistivity CT images.

[0003] Cross-hole radar is a digital electromagnetic wave CT technology with relatively high resolution and good reliability. Currently, the results of this technology are limited to wave velocity CT and attenuation CT (equivalent to skin depth CT) imaging, and there is no method for resistivity CT imaging.

[0004] The traditional hole resistivity CT technology uses the direct current method for observation, and the data processing is based on the principle of electrostatic field. The main problems of this technology are:

[0005] 1. Many electrodes are arranged during measurement, the on-site construction is cumbersome, the measurement speed is slow, and the efficiency is low;

[0006] 2. The results have low resolution and large errors, which cannot meet actual requirements;

[0007] In summary, the results have low resolution and poor reliability, cannot meet the actual requirements of engineering, and are rarely used in practice. Summary of the Invention

[0008] In response to the shortcomings of the existing technology, the present invention provides a resistivity CT imaging method based on dual-channel cross-hole radar, which solves the technical problems of cross-hole resistivity CT technology, such as low result resolution, poor reliability, and low measurement efficiency, which cannot meet the actual application needs of engineering.

[0009] To solve the above technical problems, the present invention provides the following technical solution: a resistivity CT imaging method based on dual-channel cross-hole radar, comprising the following steps:

[0010] S1, drill hole 1 and hole 2 on both sides of the measured area to form an inter-hole profile;

[0011] S2. Gridding the inter-hole cross section into rectangular grid cells with M vertical rows and N horizontal columns. The number of cells in the grid cell is M×N, and M≥N.

[0012] S3. Perform data collection. M transmitting points and receiving points are set in hole 1 and hole 2 according to the grid units. Each transmitting point transmits M times. For each transmission, the receiving point moves one position to receive the electromagnetic wave signal emitted by the transmitting point and records the dual-channel data of the ray. At the same time, M transmitting points are connected to M receiving points to obtain M×M rays.

[0013] S4. Perform ray tracing to calculate the lengths of different cells that any ray passes through in the grid cells to obtain a number of unit path lengths. The sum of the unit path lengths should be equal to the length of the ray.

[0014] S5, constructing a travel time equation group, combining the travel time equations of the M×M rays in sequence to form the travel time equation group of the overall inter-hole profile;

[0015] S6. Solve for the wave velocity v i Construct the decoupling matrix C and use the least squares method or joint algebraic iteration method to solve the travel time equations to obtain the wave velocity v of the unit i , according to the wave velocity v of the unit i Construct decoupling matrix C;

[0016] S7, constructing a conductivity attenuation equation group, and establishing the conductivity attenuation equation group according to the amplitude attenuation data of the measured electromagnetic wave;

[0017] S8. Construct a resistivity CT image and a skin depth CT image within the inter-hole profile, solve the conductivity attenuation equation group to obtain the conductivity distribution within the inter-hole profile, and calculate the resistivity distribution and skin depth distribution within the inter-hole profile based on the conductivity distribution. Finally, generate a resistivity CT image and a skin depth CT image based on the resistivity distribution and skin depth distribution.

[0018] Furthermore, in step S3, the specific process includes the following steps:

[0019] S31. Number the cells i in the grid. Each cell i corresponds to an independent variable to be determined, the wave velocity v. i , skin depth δ i and resistivity ρ i , i represents the i-th unit in the grid, i = 1, 2, 3, ...;

[0020] S32, placing the radar's transmitting antenna and receiving antenna in hole 1 and hole 2 respectively, with the transmitting antenna and receiving antenna being located at corresponding units in hole 1 and hole 2 as transmitting points and receiving points respectively;

[0021] S33, an electromagnetic wave signal is transmitted from the transmitting point corresponding to the bottom of hole 1 as the starting point, and at the same time, the receiving antenna in hole 2 is gradually moved upward from the hole bottom to the hole mouth with the receiving point corresponding to the M vertical rows of units, and the receiving time and amplitude of the transmitting antenna and the receiving antenna are recorded to obtain dual-channel data for a ray;

[0022] S34, repeat step S33 to cover M transmitting points, place the transmitting antenna at the location of each transmitting point, and gradually move the receiving point from the bottom of the hole to the hole mouth each time to obtain dual-channel data of the M transmitting points;

[0023] S35. Connect the electromagnetic wave propagation paths from one transmitting point to M receiving points to obtain M rays, and obtain a total of M×M rays from the M transmitting points.

[0024] Furthermore, in step S5, the travel time equations are expressed as:

[0025]

[0026] In the above formula, N represents the number of units, A ij is the path length of the jth ray in the i-th unit, v i is the wave velocity in the ith unit, T j is the travel time difference between the transmitted signal and the received signal of the jth ray, which is a known quantity.

[0027] Furthermore, in step S6, the expression of the decoupling matrix C is:

[0028]

[0029] The equivalent unit length matrix B is formed by multiplying the unit length matrix A and the decoupling matrix C. The expression of the equivalent unit length matrix B is:

[0030]

[0031] In the above formula, k represents the number of units on the ray, v represents the wave velocity, A is the unit length matrix as mentioned above, B is the equivalent unit length matrix, j represents the ray, v J represents the wave velocity of the jth ray.

[0032] Furthermore, in step S7, the conductivity decay equation group is expressed as:

[0033]

[0034] In the above formula, B ij is the equivalent path length of the jth ray in the i-th unit, v i is the wave velocity in the i-th unit, σ iis the conductivity in the i-th unit, F j is the equivalent amplitude attenuation ratio of the j-th ray.

[0035] Furthermore, the equivalent amplitude attenuation ratio F j The calculation formula is:

[0036]

[0037] In the above formula, μ is the magnetic permeability, which is approximately a constant and has a value of 4π×10 -7 , E i is the amplitude of the radar transmission signal, E r is the amplitude of the radar received signal, R is the path length of the ray, the distance from the transmitting point to the receiving point, and θ1 and θ2 are the angles between the ray and the optimal directions of the transmitting antenna and the receiving antenna, respectively.

[0038] Further, in step S8, the resistivity ρ i The calculation formula is:

[0039]

[0040] In the above formula, σ i is the conductivity in the i-th unit.

[0041] Furthermore, in step S8, the skin depth δ i The calculation formula is:

[0042]

[0043] In the above formula, μ is the magnetic permeability, which is approximately a constant and has a value of 4π×10 -7 ,ρ i is the resistivity, v i , δ i are the wave velocity and skin depth in the i-th unit respectively.

[0044] By means of the above technical solution, the present invention provides a resistivity CT imaging method based on dual-channel cross-hole radar, which has at least the following beneficial effects:

[0045] 1. The resistivity CT imaging method proposed in this invention can achieve higher resolution, better reliability, more convenient operation, and higher efficiency in cross-hole resistivity exploration. Through a single cross-hole radar measurement, three types of images—wave velocity CT, skin depth CT, and resistivity CT—can be simultaneously obtained, greatly improving the comprehensiveness and reliability of geological interpretation.

[0046] 2. The present invention adopts the wave field theory and the observation method of cross-hole radar. By measuring the travel time and attenuation of electromagnetic waves, it realizes CT imaging of the resistivity distribution of cross-hole radar, completely replacing the position of existing resistivity CT equipment.

[0047] 3. The present invention not only improves the resolution and reliability of resistivity CT results, but also can obtain three physical images of wave velocity, skin depth and resistivity through one data acquisition, making the foundation of comprehensive geophysical interpretation more solid, and also greatly improving work efficiency and making construction more convenient and quick.

[0048] 4. The present invention linearizes the equation containing resistivity attenuation by using a cross-hole radar observation method and a decoupling matrix, so that the resistivity CT image can be directly reconstructed from the projection using the Radon principle, so that the result has high resolution and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0050] Figure 1 Schematic diagram of dividing the hole cross section into grid units in the present invention;

[0051] Figure 2 This is a schematic diagram of the principle of data acquisition by the cross-hole radar of the present invention;

[0052] Figure 3 Schematic diagram of the wave velocity distribution image in the present invention;

[0053] Figure 4 Schematic diagram of the skin depth distribution image in the present invention;

[0054] Figure 5 is a schematic diagram of a resistivity distribution image in the present invention;

[0055] Figure 6 This is a schematic diagram of the drilling sampling verification results of the present invention. DETAILED DESCRIPTION

[0056] To make the above-mentioned objectives, features, and advantages of the present invention more clearly understood, the present invention is further described below in detail with reference to the accompanying drawings and specific embodiments. This will enable a full understanding of how this application uses technical means to solve technical problems and achieve technical effects, and to implement the invention accordingly.

[0057] Please refer to Figures 1-6, shows a specific implementation of this embodiment, in which the inter-hole cross-section is meshed to obtain M×N units, and the wave velocity v in a unit i is calculated by the corresponding equation group. i , conductivity σ i and skin depth δ i , then calculate the wave velocity v in each cell i in the grid cell i and resistivity σ i , obtain the resistivity data of M×N units, and finally directly generate CT images based on the wave velocity, resistivity and skin depth data. This not only improves the resolution and reliability of the resistivity CT results, but also allows the acquisition of three physical images of wave velocity, skin depth and resistivity in the same data acquisition, greatly improving work efficiency and comprehensive interpretation capabilities, making on-site construction more convenient and faster.

[0058] This embodiment proposes a resistivity CT imaging method based on a dual-channel cross-hole radar, comprising the following steps:

[0059] S1. Drill holes 1 and 2 on both sides of the measured area to form the hole cross section. Please refer to Figure 1 , is a schematic diagram of a grid unit. A vertical hole 1 and a hole 2 are drilled on both sides of the measured area. At this time, a double-channel cross-hole structure is formed between hole 1, hole 2 and the measured area. The cross-hole section is constructed to explain the grid unit more clearly. Therefore, according to Figure 1 Be able to clearly understand the specific meaning of the inter-hole profile and grid unit.

[0060] S2. Grid the inter-hole profile, dividing the inter-hole profile into rectangular grid cells with M vertical rows and N horizontal columns. Each cell corresponds to the velocity and resistivity variables to be determined. The number of cells in the grid cell is M×N, and M≥N.

[0061] Please refer to Figure 1 , the inter-hole profile is gridded and divided into rectangular grid units. The length and width of the grid units can be different, so it can be divided into M rows vertically and N columns horizontally. The M≥N condition must be satisfied, and the total number of units in the grid unit is M×N.

[0062] S3. Perform data collection. M transmitting points and receiving points are set in hole 1 and hole 2 according to the grid units. Each transmitting point transmits M times repeatedly. The receiving point moves one position to receive each time it transmits, and a total of M×M electromagnetic wave records are obtained. Each record has two-channel data, recording the transmitting signal and the receiving signal respectively. For each transmission, the receiving point moves one position to receive the electromagnetic wave signal emitted by the transmitting point and record the dual-channel data of the ray. At the same time, M×M rays are obtained by connecting the M transmitting points to the M receiving points. The line connecting the transmitting point and the receiving point is the channel for electromagnetic wave propagation, which is called a ray.

[0063] In order to explain step S3 more clearly and completely, the specific process of implementing this step includes the following steps:

[0064] S31. Number the cells i in the grid. Each cell i corresponds to an independent variable to be determined, the wave velocity v. i , skin depth δ i and resistivity ρ i , i represents the i-th unit in the grid, i = 1, 2, 3, ...;

[0065] S32, placing the radar's transmitting antenna and receiving antenna in hole 1 and hole 2 respectively, with the transmitting antenna and receiving antenna being located at corresponding units in hole 1 and hole 2 as transmitting points and receiving points respectively;

[0066] S33, an electromagnetic wave signal is transmitted from the transmitting point corresponding to the bottom of hole 1 as the starting point, and at the same time, the receiving antenna in hole 2 is gradually moved upward from the hole bottom to the hole mouth with the receiving point corresponding to the M vertical rows of units, and the receiving time and amplitude of the transmitting antenna and the receiving antenna are recorded to obtain dual-channel data for a ray;

[0067] S34, repeat step S33 to cover M transmitting points, place the transmitting antenna at the location of each transmitting point, and gradually move the receiving point from the bottom of the hole to the hole mouth each time to obtain dual-channel data of the M transmitting points;

[0068] S35. Connect the electromagnetic wave propagation paths from one transmitting point to M receiving points to obtain M rays, and obtain a total of M×M rays from the M transmitting points.

[0069] In steps S31 to S35, as Figure 2As shown in the figure, a transmitting antenna is placed in hole 1 on the left, and a receiving antenna is placed in hole 2 on the right. The hole spacing between holes 1 and 2 is L, and the hole depth is D. A dual-channel radar is then used, with one channel recording the transmitted signal and the other channel recording the received signal. The transmitting antenna starts at the bottom of the hole and moves upward point by point after transmission. For each transmitting point, the receiving antenna moves point by point from the bottom of the hole to receive until the recording of the transmission of the first point is completed after the hole mouth, which includes the time and amplitude records of the transmission and reception. After the transmitting point moves upward, the above receiving process is repeated. The line connecting the transmitting point to the receiving point is a ray, and a total of M×M rays are obtained across all transmitting points and receiving points.

[0070] S4. Perform ray tracing. Each ray must pass through N units from the emission point to the receiving point. Calculate the lengths of different units passed by any ray in the grid unit to obtain several unit path lengths. The sum of several unit path lengths should be equal to the length of the ray. The line connecting the emission point and the receiving point is the path of electromagnetic wave propagation, which is called the ray of the wave. Ray tracing is to calculate the length of the line segment of the ray in the grid unit it passes through, which is called the unit path length. The unit length of each ray constitutes a unit length matrix.

[0071] like Figure 1 As shown in the figure, ray tracing is to calculate the path length A within the unit i passed through ij , the path lengths within each unit i are connected end to end, and the sum of all unit paths is equal to the total length of the ray. Since the length and width of the unit are both known quantities, the conventional distance calculation method can be used to calculate the length of the ray in a unit. Since this technical means is relatively conventional, it will not be described in detail here.

[0072] S5. Construct a set of travel time equations. Combine the travel time equations of the M×M rays in sequence to form the overall travel time equation set for the inter-hole profile. For each ray, the travel time on each unit path is equal to the ratio of the unit path length to the unit wave velocity. The sum of the time consumed by each unit should be equal to the travel time difference between the received signal and the transmitted signal of the ray. This is the travel time equation for a ray. Combine the travel time equations of the M×M rays in sequence to form the overall travel time equation set for the inter-hole profile. The variables in the travel time equation set are the unit wave velocity, which is M×N in total, and the total number of equation sets is M×M. The number of equation sets is greater than the number of variables, and there is an optimal solution. The expression of the travel time equation set is:

[0073]

[0074] In the above formula, N represents the number of units, A ij is the path length of the jth ray in the i-th unit, v i is the wave velocity in the ith unit, T j is the travel time difference between the transmitted signal and the received signal of the jth ray, which is a known quantity.

[0075] First, we construct the travel time equation for each ray. Then, we combine the travel time equations for each of the M × M rays to form the overall travel time equation system for the profile. The physical meaning of this travel time equation system is the total time spent on the ray path, which is equal to the sum of the time spent on each element traversed. The time spent within an element is expressed as the ratio of the element path length to the wave velocity. The wave velocity within the element is the variable in this system of equations, and the element path length is the matrix coefficient of this equation. The measured travel time difference is the known quantity in this system of equations. The travel time difference is the time difference between the electromagnetic wave signal emitted by the transmitting antenna and the electromagnetic wave signal received by the receiving antenna. The number of velocity variables is equal to the number of elements (M × N), and the total number of equations is M × M. If the number of equations is greater than the number of variables, then an optimal solution exists.

[0076] S6. Solve for the wave velocity v i Construct the decoupling matrix C and use the least squares method or joint algebraic iteration method to solve the travel time equations to obtain the wave velocity v of the unit i , according to the wave velocity v of the unit i Construct the decoupling matrix C, which is a diagonal matrix with diagonal elements equal to the unit wave velocity v i , the other elements are zero;

[0077] The wave velocity v of element i in the walk-away equations can be automatically solved using the least squares method (LSM) or the combined algebraic iteration method (SART) i , then according to the wave speed v i Construct the decoupling matrix C, which is a diagonal matrix with diagonal elements being the wave velocity v i , the other elements are zero, and the expression of the decoupling matrix C is:

[0078]

[0079] The equivalent unit length matrix B is formed by multiplying the unit length matrix A and the decoupling matrix C. The expression of the equivalent unit length matrix B is:

[0080]

[0081] In the above formula, k represents the number of units on the ray, v represents the wave velocity, A is the unit length matrix as mentioned above, B is the equivalent unit length matrix, j represents the ray, v J represents the wave velocity of the jth ray.

[0082] S7. Constructing a conductivity attenuation equation group. The conductivity attenuation equation group is established based on the measured electromagnetic wave amplitude attenuation data. The measurement of the electromagnetic wave amplitude attenuation data can be achieved using existing equipment without any restrictions. Due to the introduction of the decoupling matrix C, the conductivity is linearized in the attenuation equation and becomes the only independent quantity. The coefficient matrix of the conductivity attenuation equation group is the product of the unit length matrix and the decoupling matrix. The right-hand term is the attenuation obtained by measuring the electromagnetic wave amplitude attenuation data.

[0083] The conductivity decay equations are expressed as:

[0084]

[0085] In the above formula, B ij is the equivalent path length of the jth ray in the i-th unit, v i is the wave velocity in the i-th unit, σ i is the conductivity in the i-th unit, F j is the equivalent amplitude attenuation ratio of the j-th ray.

[0086] Furthermore, the equivalent amplitude attenuation ratio F j The calculation formula is:

[0087]

[0088] In the above formula, μ is the magnetic permeability, which is approximately a constant and has a value of 4π×10 -7 , E i is the amplitude of the radar transmission signal, E r is the amplitude of the radar received signal, R is the path length of the ray, the distance from the transmitting point to the receiving point, and θ1 and θ2 are the angles between the ray and the optimal directions of the transmitting antenna and the receiving antenna, respectively.

[0089] like Figure 1 As shown, Figure 1 The angles θ1 and θ2 in the figure represent the angles between the ray direction and the dominant direction of the antenna transmission power, and are used to correct the transmission and reception energy.

[0090] S8. Construct the resistivity CT image and skin depth CT image within the inter-hole profile, solve the conductivity attenuation equation group to obtain the conductivity distribution within the inter-hole profile, and calculate the resistivity distribution and skin depth distribution within the inter-hole profile based on the conductivity distribution. Finally, generate the resistivity CT image and skin depth CT image based on the resistivity distribution and skin depth distribution. This is based on the Radon principle and is obtained by projection reconstruction to obtain the resistivity CT image and skin depth CT image, which has high resolution and reliability.

[0091] The above-mentioned known parameters can be used to solve the conductivity attenuation equations to obtain the resistivity σ of the i-th unit.i , by calculating the conductivity σ of all cells in the grid i The conductivity distribution within the inter-hole profile is calculated and finally obtained. Similar to the conductivity distribution, the resistivity distribution and skin depth distribution have the same meaning as the conductivity distribution. After the resistivity distribution and skin depth distribution within the entire inter-hole profile are obtained by calculation, the resistivity CT image and skin depth CT image can be generated by projection reconstruction according to the Radon principle.

[0092] Resistivity ρ i The calculation formula is:

[0093]

[0094] Skin depth δ i The calculation formula is:

[0095]

[0096] In the above formula, σ i is the conductivity in the i-th unit, μ is the magnetic permeability, which is approximately a constant and has a value of 4π×10 -7 ,ρ i is the resistivity, v i , δ i are the wave velocity and skin depth in the i-th unit respectively.

[0097] This embodiment not only improves the resolution and reliability of resistivity CT results, but also can obtain three physical images of wave velocity, skin depth and resistivity through a single data acquisition, thereby making the foundation of comprehensive geophysical interpretation more solid, greatly improving work efficiency and making construction more convenient and quick.

[0098] like Figure 3 and Figure 4 As shown, the wave velocity v in the cell i in the grid cell is calculated. i and skin depth δ i After that, the cross-hole radar wave velocity distribution image and cross-hole radar skin depth distribution image can be generated according to the wave velocity v and skin depth δ in all units, where Figure 3 The cross-hole radar wave velocity distribution image shown is used as an example to illustrate. Figure 3 The results shown are actual dual-channel cross-hole radar measurements, intermediate results from resistivity imaging calculations. The hole depth is 145m, the hole spacing is 50m, and the distance between the transmitting and receiving points is 1m. The lithology is granite, which has undergone varying degrees of metamorphism. Below 120m, metamorphic mudstone is present. The wave velocity values ​​range from 0.10 to 0.15m / ns, inferring a reasonable dielectric constant of 4-9.

[0099] by Figure 4The cross-hole radar skin depth distribution image shown is used as an example to illustrate. Figure 4 What is shown is Figure 3 The skin depth distribution graph, similar to the velocity distribution graph, is also an intermediate result of the resistivity calculation. The skin depth in the graph represents the distance an electromagnetic wave travels before it attenuates to 1 / e of its original value. Skin depths range from 10 to 20 meters, with skin depths exceeding 12 meters in dry granite and around 10 meters in mudstone.

[0100] like Figure 5 As shown in FIG, the resistivity CT image is the final result of the resistivity CT imaging method proposed in the present invention. The resistivity distribution in the figure is in the range of 650-1500Ωm, where the area with a resistivity above 900Ωm is granite, and the area below is metamorphic mudstone. Figure 6 As shown, the results are consistent with those revealed by the samples obtained from the drilling test. At the same time, the frequency of the dual-channel radar is 40MHz, the observation point distance is 1m, and the resolution of the results is between 1-2m.

[0101] The resistivity CT imaging method proposed in this application can provide higher resolution, better reliability, more convenient operation, and higher efficiency in cross-hole resistivity exploration. Through a single cross-hole radar measurement, three types of images—wave velocity CT, skin depth CT, and resistivity CT—can be obtained simultaneously, greatly improving the comprehensiveness and reliability of geological interpretation.

[0102] This application adopts the wave field theory and the observation method of cross-hole radar. By measuring the travel time and attenuation of electromagnetic waves, it realizes CT imaging of the resistivity distribution of cross-hole radar, completely replacing the position of existing resistivity CT equipment.

[0103] Moreover, no additional field work is required during the construction process, and the resistivity CT image can be obtained in the later data processing stage through the resistivity CT imaging method proposed in this application.

[0104] The above embodiments provide a detailed introduction to the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

Claims

1. A resistivity CT imaging method based on dual-channel cross-hole radar, characterized in that: The following steps are involved: S1, drill hole 1 and hole 2 on both sides of the measured area to form an inter-hole profile; S2. Gridding the inter-hole cross section into rectangular grid cells with M vertical rows and N horizontal columns. The number of cells in the grid cell is M×N, and M≥N. S3. Perform data collection. M transmitting points and receiving points are set in hole 1 and hole 2 according to the grid units. Each transmitting point transmits M times. For each transmission, the receiving point moves one position to receive the electromagnetic wave signal emitted by the transmitting point and records the dual-channel data of the ray. At the same time, M transmitting points are connected to M receiving points to obtain M×M rays. S4. Perform ray tracing to calculate the lengths of different cells that any ray passes through in the grid cells to obtain a number of unit path lengths. The sum of the unit path lengths should be equal to the length of the ray. S5, constructing a travel time equation group, combining the travel time equations of the M×M rays in sequence to form the travel time equation group of the overall inter-hole profile; S6. Solve for wave velocity Construct the decoupling matrix C and use the least squares method or joint algebraic iteration method to solve the travel time equations to obtain the wave velocity of the unit , according to the wave velocity of the unit Construct the decoupling matrix C, which is expressed as: ； The equivalent unit length matrix B is formed by multiplying the unit length matrix A and the decoupling matrix C. The expression of the equivalent unit length matrix B is: ； In the above formula, k represents the number of units on the ray, v represents the wave velocity, A is the unit length matrix as mentioned above, B is the equivalent unit length matrix, j represents the ray, represents the wave velocity of the jth ray; S7. Construct a conductivity attenuation equation group. The conductivity attenuation equation group is established based on the amplitude attenuation data of the measured electromagnetic wave. The expression is: ； In the above formula, is the equivalent path length of the j-th ray in the i-th unit, is the wave velocity in the ith unit, is the conductivity in the i-th unit, is the equivalent amplitude attenuation ratio of the j-th ray; S8. Construct a resistivity CT image and a skin depth CT image within the inter-hole profile, solve the conductivity attenuation equation group to obtain the conductivity distribution within the inter-hole profile, and calculate the resistivity distribution and skin depth distribution within the inter-hole profile based on the conductivity distribution. Finally, generate a resistivity CT image and a skin depth CT image based on the resistivity distribution and skin depth distribution.

2. The resistivity CT imaging method according to claim 1, wherein: In step S3, the specific process includes the following steps: S31. Number the cells i in the grid. Each cell i corresponds to an independent variable wave velocity to be determined. , skin depth and resistivity , i represents the i-th unit in the grid unit, ; S32, placing the radar's transmitting antenna and receiving antenna in hole 1 and hole 2 respectively, with the transmitting antenna and receiving antenna being located at corresponding units in hole 1 and hole 2 as transmitting points and receiving points respectively; S33, an electromagnetic wave signal is transmitted from the transmitting point corresponding to the bottom of hole 1 as the starting point, and at the same time, the receiving antenna in hole 2 is gradually moved upward from the hole bottom to the hole mouth with the receiving point corresponding to the M vertical rows of units, and the receiving time and amplitude of the transmitting antenna and the receiving antenna are recorded to obtain dual-channel data for a ray; S34, repeat step S33 to cover M transmitting points, place the transmitting antenna at the location of each transmitting point, and gradually move the receiving point from the bottom of the hole to the hole mouth each time to obtain dual-channel data of the M transmitting points; S35. Connect the electromagnetic wave propagation paths from one transmitting point to M receiving points to obtain M rays, and obtain a total of M×M rays from the M transmitting points.

3. The resistivity CT imaging method according to claim 1, wherein: In step S5, the travel time equations are expressed as: ； In the above formula, N represents the number of units, is the path length of the j-th ray in the i-th unit, is the wave velocity in the ith unit, is the travel time difference between the transmitted signal and the received signal of the jth ray, which is a known quantity.

4. The resistivity CT imaging method according to claim 1, wherein: Equivalent amplitude attenuation ratio The calculation formula is: ； In the above formula, is the magnetic permeability, which is approximately a constant and takes the value , is the amplitude of the radar transmission signal, is the amplitude of the radar receiving signal, R is the path length of the ray, and the distance from the transmitting point to the receiving point. and are the angles between the ray and the optimal directions of the transmitting antenna and the receiving antenna, respectively.

5. The resistivity CT imaging method according to claim 1, wherein: In step S8, the resistivity The calculation formula is: ； In the above formula, is the conductivity in the i-th unit.

6. The resistivity CT imaging method according to claim 1, characterized in that: In step S8, the skin depth The calculation formula is: ； In the above formula, is the magnetic permeability, which is approximately a constant and takes the value , is the resistivity, 、 are the wave velocity and skin depth in the i-th unit respectively.

Images