Vertical finite long line source electromagnetic exploration apparent resistivity imaging method

Abstract

The invention discloses a vertical finite long line source electromagnetic exploration apparent resistivity imaging method, which comprises the following steps: (1) based on a uniform half-space model, deducing a radial electric field response analytic expression of vertical finite long line source well-to-ground electromagnetism on the ground; (2) setting a geoelectric model; (3) calculating parameter input; (4) performing initialization setting; (5) carrying out resistivity iterative calculation; and (6) judging whether abnormal bodies exist or not and identifying abnormal body distribution. According to the method, the monotonous relation between the electric field and the resistivity is introduced, the numerical solution path more suitable for the electromagnetic response law is adopted, and the purposes of shortening the apparent resistivity calculation time and achieving rapid imaging can be achieved.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, and in particular to a vertical finite-length line source electromagnetic exploration apparent resistivity imaging method. Background Technology

[0002] In geophysical electromagnetic exploration, changes in the electrical properties of the subsurface medium can affect the propagation of electromagnetic waves, thereby causing changes in the observed electric field response. Analyzing the propagation characteristics of the electromagnetic field and inverting the observation data is the key to constructing subsurface geological models.

[0003] However, traditional inversion methods typically rely on prior knowledge to establish an initial geological model and then iteratively refine it to make the forward modeling results increasingly approximate actual observation data. While this method is widely used, each iteration requires a new numerical forward modeling calculation, which is extremely computationally demanding, especially when dealing with complex three-dimensional structures. This results in a lengthy inversion process, becoming a major technical bottleneck for achieving real-time interpretation. Summary of the Invention

[0004] The purpose of this invention is to provide a vertical finite-length line source electromagnetic exploration resistivity imaging method that improves the efficiency and accuracy of resistivity calculation and enhances the ability to identify underground anomalies, in order to address the shortcomings of existing technologies.

[0005] The objective of this invention is achieved through the following technical solution: A vertical finite-length line source electromagnetic exploration resistivity imaging method includes: Based on the uniform half-space model, the vertical finite-length line source is regarded as an electric dipole model. The analytical expression of the radial electric field response of the well electromagnetic field of the vertical finite-length line source on the ground is derived, and it is determined that the electric field response has a monotonically decreasing relationship with the conductivity of the underground medium. A vertical finite-length current source is placed perpendicular to the ground into an underground medium to generate an electromagnetic field; multiple receivers are arranged on the ground surface to receive the radial electric field response signal generated by the current source. The radial electric field response data of the ground is obtained. The input includes the current magnitude, the starting and ending depths of the vertical finite-length current source, the emission frequency and the radial distance. The conductivity search interval is set. The electric field response is calculated according to the analytical formula of the radial electric field response. The electric field response is calculated by comparing the preset value and the measured value of the electric field response with the measured value through the recursive bisection method, and the interval is adjusted until convergence. The conductivity value of the underground medium is calculated iteratively, and the reciprocal is taken to obtain the apparent resistivity value. Draw an apparent resistivity distribution map of the underground medium based on the obtained apparent resistivity values; Anomalies were identified and their distribution was determined based on the apparent resistivity distribution map.

[0006] Furthermore, the analytical expression for the radial electric field response is derived by introducing the magnetic vector potential and using the Hankel transform and its inverse transform to solve the quasi-static Maxwell's equations neglecting displacement current in the frequency domain. The analytical expression for the radial electric field response is:

[0007] In the formula: E r线 σ1 is the radial electric field intensity, and σ2 is the dielectric conductivity. ε The medium constant, μ Permeability, λ Let be the integration constant. ω Angular frequency, f Where h1 is the transmission frequency, h2 is the depth of the starting point of the line source, and J1 is the depth of the ending point of the line source. λ r) is a first-order Bessel function.

[0008] Furthermore, the calculation steps of the recursive bisection method are as follows: Define the solution interval for underground conductivity [σ] min ,σ max and accuracy β And calculate the initial value σ. mid = (σ min +σ max ) / 2; The initial value σ mid Substituting into the analytical expression for the radial electric field response, the theoretical value of the electric field response is calculated. E r0 and compared with the measured electric field response value E r When comparing, the measured electric field response value E r Greater than the theoretical value of electric field response E r0 At that time, determine whether the difference meets the precision requirement. β If the condition is met, then output σ at this time. mid Otherwise, adjust the solution interval to [σ]. mid , σ max When the measured electric field response value E r Less than the theoretical value of electric field response E r0 At that time, determine whether the difference meets the precision requirement. β If the condition is met, then output σ at this time. mid Otherwise, adjust the solution interval to [σ]. min , σ mid Repeat the above steps until the conductivity value at each measuring point is obtained.

[0009] Furthermore, based on the location of the measuring point and its corresponding apparent resistivity, Kriging interpolation is used to draw an apparent resistivity contour map within the measuring point area.

[0010] Furthermore, when anomalies and spatial distribution characteristics of anomalous bodies appear in a certain area of ​​the apparent resistivity contour map, it can be determined that there are anomalous bodies in the underground medium, and it can be distinguished as low-resistivity or high-resistivity bodies.

[0011] Furthermore, when a vertical finite-length current source is located below the anomalous body, the apparent resistivity anomaly location closely matches the actual anomalous body location.

[0012] The present invention also provides a computer-readable storage medium storing program code that, when executed, can implement the above-described vertical finite-length line source electromagnetic exploration resistivity imaging method.

[0013] The present invention has the following beneficial effects: This invention constructs a forward model of the electric field response, decomposing a finite-length line source into a superposition of multiple electric dipoles. Simultaneously, utilizing the monotonic relationship between the electric field amplitude and the resistivity of the medium, a recursive bisection method is employed to solve the problem, transforming the nonlinear equation solution into an efficient interval convergence process. Furthermore, this invention supports the generation of apparent resistivity contour maps based on the actual survey network layout, clearly presenting the lateral variations of underground electrical structures and effectively delineating the planar distribution range of anomalies. Moreover, by analyzing the apparent resistivity response characteristics of the line source and the anomaly at different relative positions, this invention can infer the burial depth information of the anomaly, achieving a comprehensive judgment of the anomaly's spatial location. Attached Figure Description

[0014] Figure 1 A schematic diagram of the process for vertical finite-length line source electromagnetic exploration resistivity imaging provided in an embodiment of the present invention; Figure 2 This is a contour map of the apparent resistivity when the surrounding rock resistivity is 100 Ω·m in Embodiment 1 of the present invention; Figure 3 This is a contour map of the apparent resistivity when the surrounding rock resistivity is 1000 Ω·m in Embodiment 1 of the present invention; Figure 4 This is a contour map of the apparent resistivity when the surrounding rock resistivity is 10000 Ω·m in Embodiment 1 of the present invention; Figure 5 This is a screenshot of the final display of the time taken from data input to completion of the apparent resistivity calculation for all measurement points in Embodiment 2 of the present invention;

[0015] Figure 6 This is a contour map of apparent resistivity when the formation resistivity is 500 Ω·m and the anomaly resistivity is 10 Ω·m in Embodiment 2 of the present invention. Figure 7 This is a contour map of apparent resistivity when the formation resistivity is 500 Ω·m and the anomaly resistivity is 10000 Ω·m in Embodiment 2 of the present invention. Figure 8 In Embodiment 2 of the present invention x Apparent resistivity curve of the measuring line at position =200; Figure 9 In Embodiment 2 of the present invention y Apparent resistivity curve of the measuring line at the =0 position.

[0016] Figure 10 This is a schematic diagram of the radial electric field response obtained at three measuring points with radial distances of 50m, 400m, and 800m from the emission source, respectively, when they are at different ground conductivity levels. Detailed Implementation

[0017] To better understand the present invention, the present invention will be further described in detail below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0018] Definitions of terms used in this invention: Subsurface electrical structure: refers to the geological structure below the Earth's surface that has electromagnetic-related physical properties. Electrical properties generally refer to electrical parameters such as resistivity and conductivity.

[0019] Apparent resistivity: A core parameter in geophysical exploration that characterizes the changes in the electrical conductivity of rocks in heterogeneous media.

[0020] Electromagnetic forward modeling: Geophysical forward modeling using electromagnetic correlation methods. For electromagnetic exploration methods, the forward modeling problem aims to solve the electric and magnetic field components on the coordinates by solving Maxwell's equations, given the known electrical parameters of the stratigraphic structure.

[0021] Recursive binary search: By continuously dividing the interval to be searched into half and judging the interval where the target value may be located based on the result of the intermediate value, the search range is reduced by half, gradually approaching the target solution until the predetermined accuracy requirement is met.

[0022] This invention provides a vertical finite-length line source electromagnetic exploration resistivity imaging method, comprising: Based on the uniform half-space model, the vertical finite-length line source is regarded as an electric dipole model. The analytical expression of the radial electric field response of the well electromagnetic field of the vertical finite-length line source on the ground is derived, and it is determined that the electric field response has a monotonically decreasing relationship with the conductivity of the underground medium. A vertical finite-length current source is placed perpendicular to the ground into an underground medium to generate an electromagnetic field; multiple receivers are arranged on the ground surface to receive the radial electric field response signal generated by the current source. The radial electric field response data of the ground is obtained. The input includes the current magnitude, the starting and ending depths of the vertical finite-length current source, the emission frequency and the radial distance. The conductivity search interval is set. The electric field response is calculated according to the analytical formula of the radial electric field response. The electric field response is calculated by comparing the preset value and the measured value of the electric field response with the measured value through the recursive bisection method, and the interval is adjusted until convergence. The conductivity value of the underground medium is calculated iteratively, and the reciprocal is taken to obtain the apparent resistivity value. Draw an apparent resistivity distribution map of the underground medium based on the obtained apparent resistivity values; Anomalies were identified and their distribution was determined based on the apparent resistivity distribution map.

[0023] Preferably, the spacing between the survey lines of multiple surface receivers is 50-100 meters, and the number of survey points on each survey line is 20-50, so as to cover the exploration area and reduce boundary effects.

[0024] The analytical expression for the radial electric field response is derived by introducing the magnetic vector potential and using the Hankel transform and its inverse transform to solve the quasi-static Maxwell's equations neglecting displacement current in the frequency domain. The analytical expression for the radial electric field response is:

[0025] In the formula: E r线 σ1 is the radial electric field intensity, and σ2 is the dielectric conductivity. ε The medium constant, μ Permeability, λ Let be the integration constant. ω Angular frequency, f Where h1 is the transmission frequency, h2 is the depth of the starting point of the line source, and J1 is the depth of the ending point of the line source. λ r) is a first-order Bessel function; The calculation steps of the recursive bisection method are as follows: Define the solution interval for underground conductivity [σ] min ,σ max and accuracy β And calculate the initial value σ. mid = (σ min +σ max ) / 2; The initial value σ mid Substituting into the analytical expression for the radial electric field response, the theoretical value of the electric field response is calculated. E r0 and compared with the measured electric field response value E r When comparing, the measured electric field response value E r Greater than electric field response Theoretical value E r0At that time, determine whether the difference meets the precision requirement. β If the condition is met, then output σ at this time. mid Otherwise, adjust the solution interval to [σ]. mid , σ max When the measured electric field response value E r Less than the theoretical value of electric field response E r0 At that time, determine whether the difference meets the precision requirement. β If the condition is met, then output σ at this time. mid Otherwise, adjust the solution interval to [σ]. min , σ mid Repeat the above steps until the conductivity value at each measuring point is obtained.

[0026] The apparent resistivity imaging includes: converting the final output conductivity result into an apparent resistivity value. ρ = 1 / σ And read the corresponding measurement point coordinates ( x, y, 0); Using the Kriging interpolation principle, the resistivity value of each grid node is calculated based on the resistivity values ​​of the surrounding measuring points to form a continuous resistivity data volume. Then, the final resistivity result and its corresponding measuring point coordinates are used to perform apparent resistivity imaging.

[0027] This invention can analyze the characteristics of anomalous bodies by drawing contour maps based on apparent resistivity, including the spatial distribution of low-resistivity and high-resistivity bodies; and evaluate the range and depth of anomalous response by changing the position of the line source relative to the anomalous body.

[0028] Specifically, the present invention can verify the accuracy of the method by setting the anomaly body as a cube with a size of 200m×200m×100m and a burial depth of 500-1500 meters, placing the line source above or below the anomaly body, comparing the apparent resistivity anomaly pattern, distinguishing the electrical contrast, and restoring the real geological structure. It has been verified that when the vertical finite-length current source is located below the anomaly body, the location of the apparent resistivity anomaly highly matches the location of the real anomaly body.

[0029] Furthermore, this invention also verifies the monotonically decreasing relationship between the electric field response and the conductivity of the underground medium. Specifically, a forward modeling simulation was established with the starting depth of the line source at 450m and the ending depth at 500m, the current magnitude at 100A, the frequency at 100Hz, and the receiving point coordinates at (50,0,0), (400,0,0), and (800,0,0), with radial distances from the transmitting source of 50m, 400m, and 800m, respectively. The conductivity range of the ground was set to 10. -4~1S / m, combining the electric field responses at the same measuring point and frequency under different ground conductivity conditions, yields schematic diagrams of the radial electric field responses obtained at the same measuring point under different parameter conditions, as shown in the figure. Figure 10 As shown, at the same receiving point, there is a one-to-one correspondence between Er and resistivity, and Er is a monotonically decreasing function of the conductivity of the underground medium. Therefore, there is an obvious "binary" characteristic between the radial electric field response value and the resistivity value at each measuring point, thus determining that the conductivity can be calculated using the bisection method.

[0030] The present invention also provides a computer-readable storage medium having program instructions stored thereon, the instructions being adapted to be loaded by a processor and executed to realize automated data processing and calculation result output.

[0031] Example 1 The vertical finite-length line source electromagnetic exploration resistivity imaging method provided in this embodiment, such as... Figure 1 As shown, it includes: S1: Based on the uniform half-space model, the vertical finite-length line source is considered as an electric dipole model. By introducing the magnetic vector potential and utilizing the Hankel transform and its inverse transform, the quasi-static Maxwell's equations, neglecting displacement current, are solved in the frequency domain to derive the analytical expression for the radial electric field response. It is determined that the electric field response has a monotonically decreasing relationship with the conductivity of the underground medium. The analytical expression for the radial electric field response is:

[0032] In the formula: E r线 σ1 is the radial electric field intensity, and σ2 is the dielectric conductivity. ε The medium constant, μ Permeability, λ Let be the integration constant. ω Angular frequency, f Where h1 is the transmission frequency, h2 is the depth of the starting point of the line source, and J1 is the depth of the ending point of the line source. λ r) is a first-order Bessel function; S2: Geoelectric Model Setup: A uniform half-space geodetic model is constructed. To facilitate verification of the calculation accuracy of the method of this invention, the resistivity of the surrounding rock is set to 100Ω·m, 1000Ω·m, and 10000Ω·m (the preset resistivity of the surrounding rock is only for verification purposes and does not affect the normal procedure in this embodiment). A vertical finite-length current source is placed perpendicular to the ground surface into the surrounding rock. Harmonic current is emitted into the surrounding rock through the vertical finite-length current source, generating an electromagnetic field in the surrounding rock. Multiple receivers are arranged on the ground surface to receive the radial electric field response signal generated by the current source. In this embodiment, 21 measuring lines are symmetrically arranged on the left and right sides with the emission source as the center. Each measuring line is 100m apart, and the measuring point spacing is 50m. Each measuring line contains 41 measuring points. After removing the emission source point, there are a total of 860 measuring points. S3: Input of calculation parameters: Obtain electric field response data and emission parameters during electromagnetic forward modeling and actual measurement, and store them in computer memory in digital format; The above data and parameters include the radial electric field. E r Radial distance r of measuring point, transmitting current I ,frequency f and the depth of the line source starting point h 1 and endpoint depth h 2 In this embodiment, the emission current I= 10 A， frequency f= 10 Hz, Line source starting point depth h 1 =1000m, final depth h 2 =1010m, radial electric field E r The radial distance r of the measuring point should be entered as the measured value; S4: Initialization settings: Set the conductivity search range [σ] in the program. min ,σ max and accuracy β， The conductivity range is set according to the actual exploration area, and the calculation accuracy must meet the exploration accuracy requirements. In this embodiment, σ min Take 10 -16 S / m (corresponding to resistivity 10) 16 Ω·m), σ max Take 10 6 S / m (corresponding to resistivity 10) -6 Ω·m), β Setting it to 0.001 can meet the needs of almost all exploration scenarios; S5: Resistivity Iterative Calculation: First calculate the conductivity at the midpoint of the conductivity interval as σ.mid = (σ min + σ max ) / 2, and calculate its corresponding theoretical electric field value. E r0 Based on the obtained theoretical value of the electric field E r0 Calculate its value and the measured value. E r The absolute value of the difference δ=| E r0 - E r | Determine if δ is less than the precision. β If δ < β Then the output is the conductivity σ at this time. mid This represents the final conductivity calculation result; if δ < β Based on E r The monotonically decreasing relationship between the conductivity σ and the conductivity σ is used to determine... E r0 and E r The magnitude of this value adjusts the conductivity range; if E r0 > E r ,because E r Since σ is monotonically decreasing relative to σ, we can conclude that σ is decreasing at this point. mid The conductivity is less than the actual conductivity, so the conductivity range is adjusted to [σ]. mid , σ max ];like E r0 < E r ,because E r Since σ is monotonically decreasing relative to σ, we can conclude that σ is decreasing at this point. mid The conductivity is greater than the actual conductivity, and the conductivity range is adjusted to [σ]. min , σ mid Then, the resistivity is iterated and calculated until the conductivity at all measuring points is obtained. S6: Apparent Resistivity Imaging: Converts the final output conductivity into an apparent resistivity value. ρ = 1 / σ And read the corresponding measurement point coordinates ( x , y Using the Kriging interpolation principle, the resistivity value of each grid node is calculated based on the resistivity values ​​of surrounding measurement points, forming a continuous resistivity data volume. The final resistivity result and its corresponding measurement point coordinates are then used to perform apparent resistivity imaging. Figure 2 , Figure 3 , Figure 4 The figure shows the apparent resistivity contour maps when the surrounding rock resistivity is 100Ω·m, 1000Ω·m and 10000Ω·m respectively in this embodiment; the Kriging interpolation principle is to quantitatively describe the spatiotemporal structure characteristics of data with distance through the variogram, construct the Kriging equation system with unbiasedness and minimization of estimation variance as constraints, solve for the optimal weight coefficients of each known sample point, and thus achieve linear unbiased optimal estimation of unknown points; S7: Results are as follows Figure 2 , Figure 3 , Figure 4 As shown in the figure, there are no obvious regions of low apparent resistivity (low resistivity anomaly) or high apparent resistivity (high resistivity anomaly); the apparent resistivity values ​​are all close to the assumed surrounding rock resistivity. When the surrounding rock resistivity is 100 Ω·m, the calculated apparent resistivity ranges from 99.8 to 104, with a maximum relative error of 0.04%; when the surrounding rock resistivity is 1000 Ω·m, the calculated apparent resistivity ranges from 997 to 1011, with a maximum relative error of 0.011%; and when the surrounding rock resistivity is 10000 Ω·m, the calculated apparent resistivity ranges from 9990 to 10102, with a maximum relative error of 0.012%. The small relative errors indicate that the method of the present invention has high calculation accuracy and good numerical stability under different resistivity conditions.

[0033] Example 2 The vertical finite-length line source electromagnetic exploration resistivity imaging method provided in this embodiment includes: S1: Based on the uniform half-space model, the vertical finite-length line source is considered as an electric dipole model. By introducing the magnetic vector potential and utilizing the Hankel transform and its inverse transform, the quasi-static Maxwell's equations, neglecting displacement current, are solved in the frequency domain to derive the analytical expression for the radial electric field response. It is determined that the electric field response has a monotonically decreasing relationship with the conductivity of the underground medium. The analytical expression for the radial electric field response is:

[0034] In the formula: E r线 σ1 is the radial electric field intensity, and σ2 is the dielectric conductivity. ε The medium constant, μ Permeability, λ Let be the integration constant. ω Angular frequency, f Where h1 is the transmission frequency, h2 is the depth of the starting point of the line source, and J1 is the depth of the ending point of the line source. λ r) is a first-order Bessel function; S2: Geoelectric Model Setup: To facilitate verification of the calculation and detection accuracy of the method of this invention, this embodiment embeds an anomaly in a uniform half-space geodetic model. The resistivity of the stratum is 500 Ω·m. The resistivity of the anomaly is set to 10 Ω·m and 10000 Ω·m respectively (the preset resistivity is only for verification purposes and does not affect the normal procedure of this embodiment). The size of the anomaly is 250m × 600m × 100m (x, y, z order); the four corners above the anomaly... The coordinates of the first point are (150, 300, -950), (400, 300, -950), (150, -300, -950), and (400, -300, -950), respectively. The coordinates of the four lower corners are (150, 300, -1050), (400, 300, -1050), (150, -300, -1050), and (400, -300, -1050), respectively. The coordinates of the center point are (275, 0, -1000). The coordinate range of the horizontal projection anomaly is... x =150~400, y =-300~300, such as Figure 6 , Figure 7 As shown in the black box in the middle. A vertical finite-length line source was placed below the anomaly for detection simulation. 21 measuring lines were arranged, symmetrically distributed to the left and right of the source. Each measuring line was 100m apart, and the measuring point spacing was 50m. Each measuring line contained 41 measuring points. After removing the source location, there were a total of 860 measuring points. S3: Input of calculation parameters: Obtain electric field response data and emission parameters during electromagnetic forward modeling and actual measurement, and store them in computer memory in digital format; The above data and parameters include the radial electric field. E r Radial distance r of measuring point, transmitting current I ,frequency f and the depth of the line source starting point h 1 and endpoint depth h 2 In this embodiment, the radial electric field emits current. I= 10 A， frequency f= 10 Hz, Line source starting point depth h 1 =1000m, final depth h 2 =1010m, radial electric field E r The radial distance r of the measuring point should be entered as the measured value; S4: Initialization settings: Set the conductivity search range [σ] in the program. min ,σ maxand accuracy β， The conductivity range is set according to the actual exploration area, and the calculation accuracy must meet the exploration accuracy requirements. In this embodiment, σ min Take 10 -16 S / m (corresponding to resistivity 10) 16 Ω·m), σ max Take 10 6 S / m (corresponding to resistivity 10) -6 Ω·m), β Setting it to 0.001 can meet the needs of almost all exploration scenarios; S5: Resistivity Iterative Calculation: First calculate the conductivity at the midpoint of the conductivity interval as σ. mid = (σ min + σ max ) / 2, and calculate its corresponding theoretical electric field value. E r0 Based on the obtained theoretical value of the electric field E r0 Calculate its value and the measured value. E r The absolute value of the difference δ=| E r0 - E r | Determine if δ is less than the precision. β If δ < β Then the output is the conductivity σ at this time. mid This represents the final conductivity calculation result; if δ < β Based on E r The monotonically decreasing relationship between the conductivity σ and the conductivity σ is used to determine... E r0 and E r The magnitude of this value adjusts the conductivity range; if E r0 > E r ,because E r Since σ is monotonically decreasing relative to σ, we can conclude that σ is decreasing at this point. mid The conductivity is less than the actual conductivity, so the conductivity range is adjusted to [σ]. mid , σ max ];like E r0 < E r ,because E r Since σ is monotonically decreasing relative to σ, we can conclude that σ is decreasing at this point. mid The conductivity is greater than the actual conductivity, and the conductivity range is adjusted to [σ]. min , σ midThen, iterative resistivity calculations are performed until the conductivity at all measuring points is obtained; in this embodiment, the total calculation time from data input to completion of the apparent resistivity calculation for all measuring points is only 26.26 seconds. Figure 5 As shown, traditional inversion methods based on least squares or Gauss-Newton typically require hours to days to complete the interpretation of data of a similar scale. S6: Apparent Resistivity Imaging: Converts the final output conductivity into an apparent resistivity value. ρ = 1 / σ And read the corresponding measurement point coordinates ( x , y Using the Kriging interpolation principle, the resistivity value of each grid node is calculated based on the resistivity values ​​of surrounding measurement points, forming a continuous resistivity data volume. The final resistivity result and its corresponding measurement point coordinates are then used to perform apparent resistivity imaging. Figure 6 , Figure 7 The figure shows the apparent resistivity contour maps of the anomalous body with resistivity of 10 Ω·m and 10000 Ω·m in this embodiment. The black box in the figure represents the projection of the anomalous body on the ground. The blue color mark is set as the low resistivity area, that is, the area with an apparent resistivity value of less than 390 Ω·m, and the red color mark is set as the high resistivity area, that is, the area with an apparent resistivity value of greater than 550 Ω·m. S7: Identification of Anomalous Bodies: From Figure 6 , Figure 7 As can be seen, the anomalies caused by both low-resistivity and high-resistivity anomalies are clearly identifiable in the contour map. In the y-direction, the center positions of both anomalies can be accurately located, and the anomaly ranges are basically defined within the black border. (Drawing) x =200 and y The apparent resistivity curves of the two measuring lines with a value of 0 are shown in the figure. Figure 8 , Figure 9 As shown, the vertical axis represents the apparent resistivity. At low resistance, y When the apparent resistivity of the measuring line is 390 Ω·m and the value is 0, x The coordinate values ​​are 115.14 and 406.75 respectively; x When the apparent resistivity of the measuring line is 390 Ω·m at a constant value of 200, y The coordinate values ​​are -202.92 and 203.37 respectively; at high resistance, y When the apparent resistivity of the measuring line is 550 Ω·m and the value is 0, x The coordinate values ​​are 142.04 and 428.41 respectively; x When the apparent resistivity of the measuring line is 550 Ω·m at a constant value of 200, yThe coordinate values ​​are 163.25 and 165.53, respectively. The anomaly regions of the contour lines are accurately limited to the range of the assumed anomaly, indicating that this imaging method can accurately locate the anomaly with a very fast calculation speed and can effectively delineate the approximate range of the anomaly. It also shows that when a vertical finite-length current source is located below the anomaly, the apparent resistivity anomaly location is highly consistent with the actual anomaly location.

[0035] This invention constructs a method for calculating and imaging apparent resistivity in electromagnetic exploration using a vertical finite-length line source. Based on a uniform half-space model, it derives an analytical expression for the radial electric field response at the surface and uses a bisection algorithm to iteratively calculate apparent resistivity. This simplifies the apparent resistivity calculation process into an efficient interval convergence process. By inputting the measured electric field value into the bisection iterative process, the apparent resistivity value of the corresponding subsurface medium can be obtained. In other words, by introducing a monotonic relationship between electric field and resistivity, and employing a numerical solution path more suitable for electromagnetic response laws, the invention shortens the apparent resistivity calculation time and achieves rapid imaging. Furthermore, when calculating apparent resistivity, this invention allows for flexible setting of the conductivity search interval and accuracy threshold according to actual exploration needs, and dynamically adjusts the interval until convergence based on the iteration results. More precise bisection control helps improve the accuracy of the mapping from electric field response to resistivity. In addition, the apparent resistivity contour map generation method based on Kriging interpolation constructed in this invention is simpler and has a lower computational load than traditional inversion imaging, helping to save data processing time and clearly present the subsurface electrical structure.

[0036] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., digital versatile discs (DVDs)), or semiconductor media (e.g., solid state disks (SSDs)).

[0037] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0038] The embodiments described above are merely preferred embodiments of this application and are not intended to limit the scope of this application. Any modifications and improvements made by those skilled in the art to the technical solutions of this application without departing from the spirit of this application should fall within the protection scope defined by the claims of this application.

Claims

1. A vertical finite-length line source electromagnetic exploration resistivity imaging method, characterized in that, include: Based on the uniform half-space model, the vertical finite-length line source is regarded as an electric dipole model. The analytical expression of the radial electric field response of the well electromagnetic field of the vertical finite-length line source on the ground is derived, and it is determined that the electric field response has a monotonically decreasing relationship with the conductivity of the underground medium. A vertical finite-length current source is placed perpendicular to the ground into an underground medium to generate an electromagnetic field; multiple receivers are arranged on the ground surface to receive the radial electric field response signal generated by the current source. To acquire ground radial electric field response data, input parameters include current magnitude, depth of the starting and ending points of the vertical finite-length current source, emission frequency, and radial distance. Set the conductivity search interval, calculate the electric field response value according to the radial electric field response analytical formula, compare the preset electric field response value with the measured value using the recursive bisection method, adjust the interval until convergence, iteratively calculate the conductivity value of the underground medium, and take the reciprocal to obtain the apparent resistivity value. Draw an apparent resistivity distribution map of the underground medium based on the obtained apparent resistivity values; Determine the presence of abnormalities and identify their distribution based on the apparent resistivity distribution map.

2. The vertical finite-length line source electromagnetic exploration resistivity imaging method according to claim 1, characterized in that: The analytical expression for the radial electric field response is derived by introducing the magnetic vector potential and using the Hankel transform and its inverse transform to solve the quasi-static Maxwell's equations neglecting displacement current in the frequency domain. The analytical expression for the radial electric field response is: In the formula: E r线 σ1 is the radial electric field intensity, and σ2 is the dielectric conductivity. ε The dielectric constant is μ Permeability, λ Let be the integration constant. ω Angular frequency, f Where h1 is the transmission frequency, h2 is the depth of the starting point of the line source, and J1 is the depth of the ending point of the line source. λ r) is a first-order Bessel function.

3. The vertical finite-length line source electromagnetic exploration resistivity imaging method according to claim 1, characterized in that: The calculation steps of the recursive bisection method are as follows: Define the solution interval for underground conductivity [σ] min ,σ max and accuracy β And calculate the initial value σ. mid = (σ min + σ max ) / 2; The initial value σ mid Substituting into the analytical expression for the radial electric field response, the theoretical value of the electric field response is calculated. E r0 and compared with the measured electric field response value E r Comparison, when the measured electric field response value E r Greater than the theoretical value of electric field response E r0 At that time, determine whether the difference meets the precision requirement. β If the condition is met, then output σ at this time. mid Otherwise, adjust the solution interval to [σ]. mid ,σ max When the measured electric field response value E r Less than the theoretical value of electric field response E r0 At that time, determine whether the difference meets the precision requirement. β If the condition is met, then output σ at this time. mid Otherwise, adjust the solution interval to [σ]. min ,σ mid Repeat the above steps until the conductivity value at each measuring point is obtained.

4. The vertical finite-length line source electromagnetic exploration resistivity imaging method according to claim 3, characterized in that: Based on the location of the measuring point and its corresponding apparent resistivity, Kriging interpolation is used to draw an contour map of apparent resistivity within the measuring point area.

5. The vertical finite-length line source electromagnetic exploration resistivity imaging method according to claim 4, characterized in that: When an anomaly appears in a certain area of ​​the apparent resistivity contour map, it can be determined that there is an abnormal body in the underground medium and the spatial distribution characteristics of the abnormal body, and it can be distinguished as a low-resistivity body or a high-resistivity body.

6. The vertical finite-length line source electromagnetic exploration resistivity imaging method according to claim 5, characterized in that: When a vertical finite-length current source is located below an anomalous body, the apparent resistivity anomaly location closely matches the actual anomalous body location.

7. A computer-readable storage medium, characterized in that: It stores program code that, when executed, can implement the vertical finite-length line source electromagnetic exploration resistivity imaging method as described in claims 1-6.

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