Method for determining transmit-receive distance based on detection depth of controllable source audio magnetotelluric method

Abstract

The invention discloses a method for determining transmit-receive distance based on detection depth of a controllable source audio magnetotelluric method, and the method comprises the steps: carrying out the simulation calculation of an electromagnetic field of a uniform geodetic model through employing a fast Hankel transformation method, mainly calculating the Cannius apparent resistivity and impedance phase under the conditions of different transmit-receive distances and different geodetic resistivity; determining the lowest far-field frequency, and concluding a formula for calculating the lowest far-field frequency by using a field source condition; and a detection depth calculation formula is further deduced according to the formula. Verifying the correctness of the calculation formula of the lowest far-field frequency and the calculation formula of the detection depth by using a field test mode, determining the lowest far-field frequency of the actually measured data and the corresponding apparent resistivity, calculating the actually measured detection depth, and comparing the actually measured detection depth with a theoretical value calculated by using a formula derived by induction; in order to conveniently judge the lowest far-field frequency in the CSAMT data, AMT data is also collected for comparison.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geophysical prospecting technology and method, and particularly relates to a method for determining the transmitting-receiving distance based on the detection depth of the controllable source audio magnetotelluric method. BACKGROUND

[0002] The controllable source audio magnetotelluric method (CSAMT) is a geophysical method for studying the electrical properties and geological characteristics of the underground by using an artificial controllable field source to excite an alternating electromagnetic field in the earth and observing the distribution of the electromagnetic field. In practical applications, the mutually orthogonal electric field and magnetic field components are observed to calculate the Cagniard apparent resistivity, so as to achieve the detection of the underground geological conditions. The CSAMT is widely used in the fields of geothermal resources, solid minerals, hydrogeology, engineering geology exploration, etc. The theoretical basis of the CSAMT is the basic theory of magnetotelluric sounding, that is, when the alternating electromagnetic field propagates in the underground medium, due to the effect of the skin depth, signals of different frequencies have different penetration depths, and the frequency response of the observed magnetotelluric field will reflect the vertical distribution of the electrical properties of the underground medium.

[0003] In theory, the effective detection depth of the electromagnetic method is related to the formation resistivity and the frequency of the electromagnetic signal. When the formation resistivity is constant, the lower the signal frequency, the deeper the detection depth. However, this is only true under the premise of plane electromagnetic waves, and the electromagnetic field of the artificial source is much more complex. Most of the actually collected data contains both plane electromagnetic wave data and non-plane electromagnetic wave data. This leads to many problems in the process of applying the controllable source audio magnetotelluric method in practice. In order to ensure the reliability of the detection, only the plane wave data, i.e. the far zone data, is used in actual work. For the relationship between the field source and the far zone: the mutually orthogonal electric field component and the magnetic field component reach the far zone at the same time, at this time the transmitting-receiving distance needs to reach 13 times the skin depth; the simulation calculation shows that the minimum transmitting-receiving distance is greater than 7 times the skin depth to ensure that the error between the collected CSAMT data and the MT data is within 1%; the transmitting-receiving distance greater than 3-6 times the exploration depth can collect far zone data; when the transmitting-receiving distance is greater than half of the wavelength of the electromagnetic wave emitted by the electric dipole source, it can be approximately considered to enter the far zone; in theory, the maximum detection depth of the Cagniard apparent resistivity is 0.3r (r is the transmitting-receiving distance). The conclusions of the above theoretical research on the relationship between the transmitting-receiving distance and the detection depth are inconsistent, and the influence of the non-uniformity of the underground medium is not considered, and the explicit mathematical relationship between the field source and the detection depth is not given.

[0004] This invention first uses a uniform half-space as the research object, calculating the Carnia apparent resistivity and impedance phase of the receiving point under different transmit / receive distances and resistivity conditions of the equatorial dipole device. It then analyzes and summarizes the relationship between transmit / receive distance, earth resistivity, and the far-field region, and uses this relationship to derive a formula for calculating the detection depth under non-uniform earth conditions. The correctness of the formula is then verified through field source experiments. This provides guidance for the field source deployment of CSAMT and a theoretical basis for evaluating the applicability of the method. Summary of the Invention

[0005] The purpose of this invention is to provide a method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method.

[0006] The method for determining the transmit / receive distance based on the detection depth using controlled-source audio-frequency magnetotelluric method employs the following technical solution: S100: Establishing the CSAMT theoretical calculation model: S101: Based on the basic theory of CSAMT, set the electromagnetic field calculation parameters, including the distance between the transmitter and receiver, the frequency of the alternating current sent underground by the transmitter through the power supply electrode AB, and the uniform earth resistivity. Simulate and calculate the amplitude and phase data of the orthogonal electromagnetic field components at the ground measuring point, and then calculate the Carnia apparent resistivity and impedance phase; S102: Use the fast Hankel transform algorithm of the electromagnetic field of the horizontal layered earth dipole source to calculate the electromagnetic field distribution: establish the integral expressions of the electric field components and the magnetic field components, introduce the spatial frequency, current intensity, dipole moment length, and dipole moment direction angle parameters, convert the integral expression into a discrete summation form, and use Anderson filter coefficients for fast Hankel transform; S200: Perform uniform half-space model simulation calculations; S201: Fix the transmit / receive distance and change the ground resistivity to perform theoretical simulation: Set the transmit / receive distance to a fixed value, set the ground resistivity as a variable, set the acquisition frequency range and frequency density, calculate the corresponding apparent resistivity and impedance phase, and use a double logarithmic coordinate system to plot the apparent resistivity curve and impedance phase curve, identifying the near-zone, transition zone, and far-zone characteristics in the curves; S202: Fix the ground resistivity and change the transmit / receive distance to perform theoretical simulation: Set the uniform ground resistivity to a fixed value, set the transmit / receive distance r as a variable, set the acquisition frequency range and frequency density, calculate the corresponding apparent resistivity and impedance phase, and use a double logarithmic coordinate system to plot the apparent resistivity curve and impedance phase curve, identifying the near-zone, transition zone, and far-zone characteristics in the curves; S300: Determine the relationship between the lowest far-field frequency and parameters: S301: Define the criteria for determining the lowest far-field frequency: Define the first frequency point where the difference between the calculated and actual apparent resistivity values ​​is less than or equal to 1%. If no precise corresponding point exists, calculate using linear interpolation. S302: Analyze the relationship between earth resistivity and the lowest far-field frequency: Under fixed transmit / receive distance conditions, calculate the lowest far-field frequency corresponding to different resistivities; verify whether the ratio of the lowest far-field frequency to earth resistivity is a constant; analyze the variation law of this constant under different transmit / receive distances. S303: Analyze the relationship between transmit / receive distance and the lowest far-field frequency: Under fixed earth resistivity conditions, calculate the lowest far-field frequency corresponding to different transmit / receive distances; plot a scatter plot in a logarithmic coordinate system to observe the trend of the relationship; fit the data using a power function. S400: Establish an empirical formula system: S401: Derive the comprehensive relationship between transmit / receive distance, earth resistivity, and minimum far-field frequency. Based on the analysis results in S302 and S303, take the arithmetic mean of the fitting functions for different resistivities to obtain the empirical formula; S402: Establish the relationship between transmit / receive distance and detection depth: Substitute the empirical formula obtained in S401 into the detection depth formula to derive the formula for calculating the ratio of transmit / receive distance to detection depth, verifying that under uniform earth conditions, the detection depth is independent of earth resistivity and only related to transmit / receive distance; S403: Establish the relationship between transmit / receive distance and detection depth under non-uniform earth conditions. Substitute the empirical formula obtained in S401 into the detection depth formula, where the combined resistivity of the stratum between the transmitter and receiver is not equal to the resistivity of the stratum below the receiver point and cannot be canceled out during the calculation. Therefore, the detection depth is related to earth resistivity; S500: Optimize the field source deployment scheme: S501: Expand the transmit / receive distance range analysis: Calculate the ratio of transmit / receive distance to detection depth when the transmit / receive distance is in different ranges; analyze the ratio change law and determine the ratio range within the actual working range; S502: Formulate a field source deployment guidance scheme: Calculate the required transmit / receive distance according to the target detection depth or use the transmit / receive distance to detection depth ratio table to determine it.

[0007] Furthermore, the calculation of Carnia's apparent resistivity and impedance phase described in S101 includes: The formula for calculating the apparent resistivity ρ of Carnia is as follows: The formula for calculating the impedance phase φ is as follows: Where: μ is the magnetic permeability in air, with a value of 4π × 10⁻⁶. -7 H / m; ω is the angular frequency; The amplitudes of the electric field component and the magnetic field component are respectively: For electric field phase, This represents the magnetic field phase.

[0008] Furthermore, the integral expressions for the electric and magnetic field components described in S102 are converted into discrete summation forms, and a fast Hankel transform is performed using Anderson filter coefficients, including: electric field component amplitude Magnetic field component amplitude λ is the spatial frequency, which has the dimension of the reciprocal of distance; I is the current intensity; dl is the length of the dipole moment; and θ is the angle between the direction of the dipole moment and the line connecting the center of the dipole moment to the measuring point. ,in Let be the resistivity of the i-th layer. Equivalent reflection coefficient of the vertical magnetic field component The equivalent reflection coefficient of the horizontal electric field component ,in , , Let be the thickness of the i-th layer.

[0009] Let θ = π / 2, , ,in Take the interval Filter coefficients , right , Perform calculations, where The sampling interval is denoted as .

[0010] The Hankel filter coefficient algorithm used in this study is based on the Anderson filter coefficients, with a sampling range of 8.92 × 10⁻⁶. -14 ~4.94×10 21 The sampling interval is Δ=1.105. n-1 Δ min : where Δ min =9.38×10 -15 A total of 801 filtering coefficients are used. The large sampling range and high sampling density ensure computational accuracy and stability. By setting the strata as a single layer during calculation, it can be used to simulate uniform geodetic models.

[0011] Furthermore, in step S201, a dual logarithmic coordinate system is used to plot the apparent resistivity curve and the impedance phase curve, identifying the near-field, transition, and far-field characteristics of the curves, including: Analyzing the resistivity curve characteristics, the near-field segment exhibits a 45° upward slope, while the far-field segment approaches the actual ground resistivity and displays a horizontal straight line. The transition segment shows a distinct trough shape. Analyzing the impedance phase curve characteristics, the near-field phase value is close to 0°, and the far-field phase value is close to 45°, forming a continuous transition zone between the two regions. The frequency point where the difference between the calculated apparent resistivity and the actual ground resistivity does not exceed 1% is defined as the lowest far-field frequency. When no precise matching point is available, linear interpolation is performed using adjacent frequency points. In a double logarithmic coordinate system, linear fitting is performed on the lowest far-field frequency under different resistivity conditions to verify the existence of a power function relationship between the lowest far-field frequency and ground resistivity. By calculating the ratio of the lowest far-field frequency to the ground resistivity, it is verified that under a fixed transmit / receive distance, this ratio tends to a constant. When the combination of transmit / receive distance and ground resistivity parameters leads to significant non-plane wave effects, abnormal data points are identified and corrected to ensure the accuracy of the lowest far-field frequency determination.

[0012] Furthermore, the analysis of the influence of different transmit / receive distances on the resistivity curve and impedance phase curve in S202 includes: Multiple sets of uniform earth resistivity parameters were set, including 400 Ω·m, 1600 Ω·m, and 3200 Ω·m. Transmit / receive distance parameters were set within the commonly used range for practical operation, ranging from 4 km to 16 km. To improve the accuracy of the minimum far-field frequency calculation, a frequency sampling ratio of 20.125 was set, with a sampling frequency range of 0.125 Hz to 8192 Hz. Analysis of the resistivity curve characteristics revealed that under different transmit / receive distances, the curves in the far-field region tended to approach the set earth resistivity values ​​and exhibited overlap. Furthermore, the smaller the transmit / receive distance, the fewer frequency points where the curve overlapped with the earth resistivity value. Analysis of the impedance phase curve characteristics showed that the curve approached 45° in the far-field region, and the smaller the transmit / receive distance, the lower the frequency required for the curve to reach a 45° phase value. Based on the criterion that the difference between the calculated and actual apparent resistivity values ​​should not exceed 1%, the minimum far-field frequency parameters under different transmit / receive distance conditions were determined, providing a data foundation for establishing a model relating transmit / receive distance and the minimum far-field frequency.

[0013] Furthermore, in step S303, a scatter plot is drawn in a double logarithmic coordinate system to observe the relationship trend; the data is fitted using a power function, including: The minimum far-field frequency data corresponding to different transmit / receive distances were plotted as scatter plots in a log-log coordinate system. Observing the scatter plot distribution trend, when the earth resistivity is fixed, the minimum far-field frequency and transmit / receive distance exhibit a linear relationship in the log-log coordinate system. Based on the linear relationship characteristic, a power function relationship between the minimum far-field frequency and transmit / receive distance was determined, and a power function fitting model was established. Power function fitting was performed on multiple sets of experimental data, and the goodness of fit R² and coefficient of determination all reached 0.9999, verifying the high reliability of the model. The fitting results determined that the range of the power function exponent parameter is -2.131 to -2.134, providing key parameters for establishing a comprehensive relationship between transmit / receive distance, earth resistivity, and minimum far-field frequency.

[0014] Furthermore, in step S401, based on the analysis results in steps S302 and S303, the arithmetic mean of the fitting functions for different resistivities is taken to obtain an empirical formula, including: When the transmit / receive distance is constant, the ratio of the lowest far-field frequency to the resistivity is a constant. Therefore, the fitting function for a ground resistivity of 400 Ω·m is: After sorting, we get: Similarly, the fitting functions for earth resistivity of 1600 Ω·m and 3200 Ω·m are respectively: and , where ρ is the uniform resistivity of the earth (Ω·m).

[0015] Taking the arithmetic mean of the corresponding parameter values ​​in the above formula yields: This is an empirical formula derived from theoretical data statistics and deduction. The formula reveals the relationship between the minimum far-field frequency, the ground resistivity, and the transmit / receive distance under uniform ground conditions. In practical work, the detection depth is generally determined first, then the minimum far-field frequency is calculated, and then the transmit / receive distance is calculated. This can greatly simplify the deployment of the field source and reduce the workload of the field source test.

[0016] Furthermore, in step S402, a formula for calculating the ratio of transmit / receive distance to detection depth is derived, verifying that under uniform ground conditions, the detection depth is independent of the ground resistivity and only related to the transmit / receive distance, including: Under uniform ground conditions, Substitute into the detection depth formula We can obtain: The ratio of the transmission distance to the detection depth is . It can be seen that under uniform ground conditions, the detection depth is independent of the ground resistivity and only depends on the transmission and reception distance.

[0017] The formula described is an empirical formula for the transmit / receive distance *r* within the range of 4 km to 16 km. To investigate the relationship between transmit / receive distance and detection depth under normal circumstances, the ratio of transmit / receive distance to detection depth was simulated and calculated when the transmit / receive distance was within the range of 3 km to 128 km. Based on the ratio data, a curve was plotted. The curve is smooth and decreases as the transmit / receive distance increases, with the rate of decrease being initially rapid, then slowing down, and finally stabilizing.

[0018] Furthermore, in S403, the relationship between the detection depth, transmit / receive distance, and ground resistivity under non-uniform ground conditions is derived, including: For non-uniform ground conditions or differences in geological strata between the receiving and transmitting sites, empirical formulas will be used. Substitute into the detection depth formula The relationship between transmit / receive distance and detection depth under non-uniform ground conditions was derived. ,in The resistivity of the underground medium between the transmitting and receiving points. The resistivity at the lowest far-field frequency at the receiving point corresponds to the detection depth range. It can be seen that under non-uniform ground conditions, the detection depth is related to both the ground resistivity and the transmission / reception distance.

[0019] Furthermore, the S500 analysis extends the transmit / receive range, and a field source deployment guidance scheme is formulated, including: The study analyzes the variation of the transmit / receive distance to detection depth ratio with transmit / receive distance. The ratio decreases rapidly within the range of 3km to 16km, then slows significantly and gradually stabilizes beyond 16km. Through large-scale simulations, the ratio variation range within the 3km to 128km transmit / receive distance range is determined to be 10.779 to 12.736. For the commonly used transmit / receive distance range of 4km to 16km in practical applications, the ratio variation range within this range is determined to be 11.106 to 12.231. A calculation model for the transmit / receive distance to detection depth ratio is established, providing a precise mathematical calculation method. A lookup table for the transmit / receive distance to detection depth ratio is constructed, containing ratio data corresponding to commonly used transmit / receive distances, facilitating rapid on-site determination of field source deployment parameters. Combining the calculation model and the lookup table, the optimal transmit / receive distance parameters are optimized based on the target detection depth requirements, enabling efficient formulation of field source deployment schemes.

[0020] The beneficial effects of this invention are: 1. Based on theoretical calculations, a formula for calculating the minimum far-field frequency under uniform ground conditions was summarized. The formula shows that the minimum far-field frequency is jointly determined by the size of the transmitter-receiver distance and the resistivity of the underground medium between the transmitter and receiver. Field tests show that the calculation formula is still applicable under non-uniform ground conditions. As long as the comprehensive resistivity of the underground medium between the transmitter and receiver is correctly estimated, the minimum far-field frequency can be accurately estimated.

[0021] 2. Based on the minimum far-field calculation formula, a formula for calculating the detection depth under uniform ground conditions was derived, showing that the detection depth is only related to the transmitter-receiver distance and is independent of the ground resistivity. Within the normal operating range, the ratio of transmitter-receiver distance to detection depth is between 11.106 and 12.231; it decreases as the transmitter-receiver distance increases, with the rate of decrease being initially rapid, then slowing down, and finally stabilizing, similar to a power function.

[0022] 3. Furthermore, a general formula for the relationship between detection depth and transmit / receive distance under non-uniform ground conditions was derived. The formula shows that the detection depth is jointly determined by the transmit / receive distance, the comprehensive resistivity of the underground strata at the receiving point, and the comprehensive resistivity of the underground strata in the area between the transmitter and receiver. Comparing the measured detection depth from the field source test with the depth calculated using the formula, it can be seen that the calculated value is in high agreement with the measured value, indicating that the formula is stable and reliable.

[0023] 4. When implementing the CSAMT method in the field, not only should the source be placed on a low-resistivity rock layer, but the resistivity of the medium between the transmitter and receiver should also be considered. This is to obtain a sufficiently low minimum far-field frequency and achieve a sufficiently deep detection depth at a certain transmitter-receiver distance. If the resistivity of the medium is too high, the CSAMT method may not be applicable to this site. Attached Figure Description

[0024] Figure 1 A flowchart illustrating the method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method; Figure 2 A schematic diagram of the theoretical curves of Carnia apparent resistivity and impedance phase for different geoelectric models. Figure 3 A schematic diagram of the theoretically calculated Carnia apparent resistivity and impedance phase curves for different transmit and receive distances. Figure 4 This is a schematic diagram showing the relationship between the lowest far-field frequency and the transmit / receive distance. Figure 5 This is a schematic diagram of the ratio curve between transmit / receive distance and detection depth; Figure 6 A schematic diagram showing the layout of regional geological and experimental work; Figure 7 A schematic diagram showing the projected positions of each emission source on the MT profile; Figure 8 A schematic diagram comparing the apparent resistivity and impedance phase data curves of CSAMT with the AMT data curves of different emission sources. Figure 9 The diagram shows the apparent resistivity profile and the impedance phase profile of the Cania. Detailed Implementation

[0025] The present invention will be further described clearly and completely below, but the scope of protection of the present invention is not limited thereto.

[0026] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship.

[0027] Example 1 The method for determining the transmit / receive distance based on the detection depth using controlled-source audio-frequency magnetotelluric method employs the following technical solution: S100: Establishing the CSAMT theoretical calculation model: S101: Based on the basic theory of CSAMT, set the electromagnetic field calculation parameters, including the distance between the transmitter and receiver, the frequency of the alternating current sent underground by the transmitter through the power supply electrode AB, and the uniform earth resistivity. Simulate and calculate the amplitude and phase data of the orthogonal electromagnetic field components at the ground measuring point, and then calculate the Carnia apparent resistivity and impedance phase; S102: Use the fast Hankel transform algorithm of the electromagnetic field of the horizontal layered earth dipole source to calculate the electromagnetic field distribution: establish the integral expressions of the electric field components and the magnetic field components, introduce the spatial frequency, current intensity, dipole moment length, and dipole moment direction angle parameters, convert the integral expression into a discrete summation form, and use Anderson filter coefficients for fast Hankel transform; S200: Perform uniform half-space model simulation calculations; S201: Fix the transmit / receive distance and change the ground resistivity to perform theoretical simulation: Set the transmit / receive distance to a fixed value, set the ground resistivity as a variable, set the acquisition frequency range and frequency density, calculate the corresponding apparent resistivity and impedance phase, and use a double logarithmic coordinate system to plot the apparent resistivity curve and impedance phase curve, identifying the near-zone, transition zone, and far-zone characteristics in the curves; S202: Fix the ground resistivity and change the transmit / receive distance to perform theoretical simulation: Set the uniform ground resistivity to a fixed value, set the transmit / receive distance r as a variable, set the acquisition frequency range and frequency density, calculate the corresponding apparent resistivity and impedance phase, and use a double logarithmic coordinate system to plot the apparent resistivity curve and impedance phase curve, identifying the near-zone, transition zone, and far-zone characteristics in the curves; S300: Determine the relationship between the lowest far-field frequency and parameters: S301: Define the criteria for determining the lowest far-field frequency: Define the first frequency point where the difference between the calculated and actual apparent resistivity values ​​is less than or equal to 1%. If no precise corresponding point exists, calculate using linear interpolation. S302: Analyze the relationship between earth resistivity and the lowest far-field frequency: Under fixed transmit / receive distance conditions, calculate the lowest far-field frequency corresponding to different resistivities; verify whether the ratio of the lowest far-field frequency to earth resistivity is a constant; analyze the variation law of this constant under different transmit / receive distances. S303: Analyze the relationship between transmit / receive distance and the lowest far-field frequency: Under fixed earth resistivity conditions, calculate the lowest far-field frequency corresponding to different transmit / receive distances; plot a scatter plot in a logarithmic coordinate system to observe the trend of the relationship; fit the data using a power function. S400: Establish an empirical formula system: S401: Derive the comprehensive relationship between transmit / receive distance, earth resistivity, and minimum far-field frequency. Based on the analysis results in S302 and S303, take the arithmetic mean of the fitting functions for different resistivities to obtain the empirical formula; S402: Establish the relationship between transmit / receive distance and detection depth: Substitute the empirical formula obtained in S401 into the detection depth formula to derive the formula for calculating the ratio of transmit / receive distance to detection depth, verifying that under uniform earth conditions, the detection depth is independent of earth resistivity and only related to transmit / receive distance; S403: Establish the relationship between transmit / receive distance and detection depth under non-uniform earth conditions. Substitute the empirical formula obtained in S401 into the detection depth formula, where the combined resistivity of the stratum between the transmitter and receiver is not equal to the resistivity of the stratum below the receiver point and cannot be canceled out during the calculation. Therefore, the detection depth is related to earth resistivity; S500: Optimize the field source deployment scheme: S501: Expand the transmit / receive distance range analysis: Calculate the ratio of transmit / receive distance to detection depth when the transmit / receive distance is in different ranges; analyze the ratio change law and determine the ratio range within the actual working range; S502: Formulate a field source deployment guidance scheme: Calculate the required transmit / receive distance according to the target detection depth or use the transmit / receive distance to detection depth ratio table to determine it.

[0028] refer to Figure 1 The diagram shows a flowchart of a method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method.

[0029] Furthermore, the calculation of Carnia's apparent resistivity and impedance phase described in S101 includes: The formula for calculating the apparent resistivity ρ of Carnia is as follows: The formula for calculating the impedance phase φ is as follows: Where: μ is the magnetic permeability in air, with a value of 4π × 10⁻⁶. -7 H / m; ω is the angular frequency; The amplitudes of the electric field component and the magnetic field component are respectively: For electric field phase, This represents the magnetic field phase.

[0030] Furthermore, the integral expressions for the electric and magnetic field components described in S102 are converted into discrete summation forms, and a fast Hankel transform is performed using Anderson filter coefficients, including: electric field component amplitude Magnetic field component amplitude λ is the spatial frequency, which has the dimension of the reciprocal of distance; I is the current intensity; dl is the length of the dipole moment; and θ is the angle between the direction of the dipole moment and the line connecting the center of the dipole moment to the measuring point. ,in Let be the resistivity of the i-th layer. Equivalent reflection coefficient of the vertical magnetic field component The equivalent reflection coefficient of the horizontal electric field component ,in , , Let be the thickness of the i-th layer.

[0031] Let θ = π / 2, , ,in Take the interval Filter coefficients , right , Perform calculations, where The sampling interval is denoted as .

[0032] The Hankel filter coefficient algorithm used in this study is based on the Anderson filter coefficients, with a sampling range of 8.92 × 10⁻⁶. -14 ~4.94×10 21 The sampling interval is Δ=1.105. n-1 Δ min : where Δ min =9.38×10 -15 A total of 801 filtering coefficients are used. The large sampling range and high sampling density ensure computational accuracy and stability. By setting the strata as a single layer during calculation, it can be used to simulate uniform geodetic models.

[0033] refer to Figure 2 The figure shows a schematic diagram of the theoretical curves of Carnia apparent resistivity and impedance phase for different geoelectric models, where ρ is the uniform earth resistivity and r is the transmit / receive distance.

[0034] Furthermore, in step S201, a dual logarithmic coordinate system is used to plot the apparent resistivity curve and the impedance phase curve, identifying the near-field, transition, and far-field characteristics of the curves, including: fromFigure 2 It can be seen that the characteristics of the near region, transition region and far region of the curve are quite obvious: in the resistivity curves (a), (c) and (e), the near region rises at 45°, the far region approaches the resistivity of the earth and is a horizontal straight line, and the valley in the middle transition region is quite obvious; in the impedance phase curves (b), (d) and (f), the phase in the near region is close to 0°, the phase in the far region is close to 45°, and the middle is a transition zone.

[0035] For quantitative research purposes, the frequency that differs from the actual resistivity by 1% is defined as the lowest far-field frequency. If no corresponding value is available, linear interpolation is performed. The lowest far-field frequency (Hz) values ​​for each curve are shown in Table 1. Figure 2 It can be seen that in the logarithmic coordinate system, the lowest far-field frequencies corresponding to different resistivities can be connected by a straight line, indicating a power function relationship between earth resistivity and the lowest far-field frequency. To determine the relationship between earth resistivity and the lowest far-field frequency, the lowest far-field frequency is divided by the earth resistivity; their ratios are shown in Table 2. From the data in Table 2, it can be seen that the lowest far-field frequency increases proportionally with increasing resistivity. Analysis of the values ​​in Table 2 shows that: when the transmit / receive distance is 4 km, the values ​​are all close to 1.1950; when the transmit / receive distance is 8 km, the values ​​are all close to 0.2616; and when the transmit / receive distance is 16 km, the values ​​are all close to 0.615. The data corresponding to a transmit / receive distance of 4 km and a resistivity of 6400 Ω·m differ significantly from the data corresponding to other resistivities. This may be due to the excessively high earth resistivity, the small transmit / receive distance, and the relatively large influence of non-plane waves. Therefore, it can be determined that when the transmit / receive distance is constant, the ratio of the lowest far-field frequency to the earth resistivity is a constant.

[0036] Table 1. Lowest far-field frequency under different ground power conditions Resistance (Ω·m) r = 4 km r = 8 km r = 16 km 100 119.46 26.15 6.15 200 238.94 52.31 12.30 400 477.73 104.61 24.61 800 956.36 209.19 49.21 1600 1913.47 418.76 98.43 3200 3811.02 837.23 197.04 6400 7230.21 1674.21 393.85 Table 2. Ratio of lowest far-field frequency to earth resistivity Resistivity (Ω·m) r = 4 km r = 8 km r = 16 km 100 1.1946 0.2615 0.0615 200 1.1947 0.2616 0.0615 400 1.1943 0.2615 0.0615 800 1.1955 0.2615 0.0615 1600 1.1959 0.2617 0.0615 3200 1.1909 0.2616 0.0616 6400 1.1297 0.2616 0.0615 refer to Figure 3 The figure shows a schematic diagram of the theoretically calculated Carnia apparent resistivity and impedance phase curves for different transmit and receive distances.

[0037] Furthermore, the analysis of the influence of different transmit / receive distances on the resistivity curve and impedance phase curve in S202 includes: To investigate the impact of transmit / receive distance on the minimum far-field frequency, uniform ground resistivity ρ = 400 Ω·m, 1600 Ω·m, and 3200 Ω·m were given, and simulations were performed for different transmit / receive distances. The transmit / receive distance range was 4 km to 16 km, as this distance range is commonly used in practical applications. To accurately calculate the minimum far-field frequency, the sampling density was increased, and the common ratio of the sampling frequencies was 2. 0.125The sampling range remains 0.125Hz~8192Hz.

[0038] The calculation curves for different transmit / receive distances corresponding to ρ=400Ω·m are shown in the figure. Figure 3 As can be seen from the resistivity curves, the resistivity curves (a) for different transmit / receive distances all coincide with the given earth resistivity after entering the far field. The smaller the transmit / receive distance, the fewer points coincide with the earth resistivity. Correspondingly, the impedance phase curve (b) shows that the value approaches 45° after entering the far field; the smaller the transmit / receive distance, the later it approaches 45°. Based on the previously defined criteria for determining the lowest far-field frequency, the determined lowest far-field frequency data are shown in Table 3, in Hz.

[0039] Table 3. Minimum far-field frequencies corresponding to different transmit / receive distances. Transmitter-receiver distance (km) p = 400 Ω·m p = 1600 Ω·m p = 3200 Ω·m 4 473.15 1884.25 3785.27 5 288.68 1151.73 2312.53 6 193.69 775.13 1552.93 7 138.64 555.10 1109.82 8 104.37 417.68 835.82 9 81.23 325.07 650.26 10 65.01 260.20 519.78 11 53.19 212.74 425.93 12 44.35 177.47 354.96 13 37.52 150.16 300.39 14 32.14 128.53 256.45 15 27.90 111.64 223.31 16 24.38 97.51 195.05 refer to Figure 4 The figure shows a schematic diagram of the relationship between the lowest far-field frequency and the transmit / receive distance.

[0040] Furthermore, in step S303, a scatter plot is drawn in a double logarithmic coordinate system to observe the relationship trend; the data is fitted using a power function, including: Plot the data in Table 3 as a scatter plot in a log-log coordinate system, i.e. Figure 4 The lowest far-field frequency *f* and the transmit / receive distance *r* show a linear relationship in the figure. Based on this, it can be determined that for a given earth resistivity, the lowest far-field frequency and the transmit / receive distance have a power-like relationship. Therefore, a power-like function was used to fit these three sets of data, and the fitting results are shown in Table 4. Their R² (coefficient of determination) is 0.9999. Table 4 shows that the lowest far-field frequency is a power-like function of the transmit / receive distance, with the exponent ranging from -2.131 to -2.134, where *f* is the lowest far-field frequency (Hz).

[0041] Table 4. Fitting function between minimum far-field frequency and transmit / receive distance p (Ω·m) Fitting function [R 2 ]]> 400 f = 8906.4 r -2.133 ]] 0.9999 1600 f=35443r -2.131 ]]> 0.9999 3200 f=71452r -2.134 ]]> 0.9999 Furthermore, in step S401, based on the analysis results in steps S302 and S303, the arithmetic mean of the fitting functions for different resistivities is taken to obtain an empirical formula, including: When the transmit / receive distance is constant, the ratio of the lowest far-field frequency to the resistivity is a constant. Therefore, the fitting function for a ground resistivity of 400 Ω·m is: After sorting, we get: Similarly, the fitting functions for earth resistivity of 1600 Ω·m and 3200 Ω·m are respectively: and , where ρ is the uniform resistivity of the earth (Ω·m).

[0042] Taking the arithmetic mean of the corresponding parameter values ​​in the above formula yields: This is an empirical formula derived from theoretical data statistics and deduction. The formula reveals the relationship between the minimum far-field frequency, the ground resistivity, and the transmit / receive distance under uniform ground conditions. In practical work, the detection depth is generally determined first, then the minimum far-field frequency is calculated, and then the transmit / receive distance is calculated. This can greatly simplify the deployment of the field source and reduce the workload of the field source test.

[0043] refer to Figure 5 The figure shows a schematic diagram of the ratio curve between the transmit / receive distance and the detection depth.

[0044] Furthermore, in step S402, a formula for calculating the ratio of transmit / receive distance to detection depth is derived, verifying that under uniform ground conditions, the detection depth is independent of the ground resistivity and only related to the transmit / receive distance, including: Under uniform ground conditions, Substitute into the detection depth formula We can obtain: The ratio of the transmission distance to the detection depth is . It can be seen that under uniform ground conditions, the detection depth is independent of the ground resistivity and only depends on the transmission and reception distance.

[0045] The formula described is an empirical formula for the transmit / receive distance *r* within the range of 4 km to 16 km. To investigate the relationship between transmit / receive distance and detection depth under normal circumstances, the ratio of transmit / receive distance to detection depth was simulated and calculated when the transmit / receive distance is within the range of 3 km to 128 km. The data are shown in Table 5, and curves were plotted. Figure 5 The curve is smooth and decreases as the transmission distance increases, with the rate of decrease being fast at first, then slow, and finally stabilizing.

[0046] Table 5. Ratio of Transmit / Receive Range to Detection Depth Furthermore, the S500 analysis extends the transmit / receive range, and a field source deployment guidance scheme is formulated, including: When the transmission distance increases from 3km to 16km, the ratio decreases rapidly, then the rate of decrease slows down and gradually approaches horizontal. Within the range calculated in this study, the maximum value is 12.736 (r=3km), and the minimum value is 10.779 (r=128km). In actual operation, the transmission distance is generally between 4km and 16km, with a maximum ratio of 12.231 and a minimum of 11.106. Specific values ​​can be calculated using the formula or obtained from Table 5.

[0047] Example 2 The receiving area for this experiment is located in Zhantian Township, Ningdu County, Jiangxi Province. Figure 6The western part of the receiving area, about 1 km away, is the interface between the Cretaceous red sandstone strata (red beds) and the Caledonian granite body. The red beds are typical low-resistivity layers, while the granite body is a typical high-resistivity layer. This allows for the placement of field sources on different rock strata with significant differences in electrical properties for comparative analysis.

[0048] The survey line direction is northeast-east. The CSAMT observation system uses an equatorial dipole device. The experiment was designed with four transmission sources. Sources 1-3 are located northwest of the receiving area, and source 4 is located southeast of the receiving area (see...). Figure 6 The power supply electrodes of each transmitter are equidistant and oriented in the same direction. Furthermore, the angle (sector angle) formed by the line connecting the midpoint of the receiving electrode and the midpoint of the power supply electrode to the central axis of the power supply electrode is less than 30°. Specific parameter information for each source is shown in Table 6. In addition, to better distinguish between the near-field, transition, and far-field regions, AMT data were also collected at the same locations as the CSAMT measurement points for analysis and comparison.

[0049] Table 6 Information on each source and table Field source number Stratum code Transmitter-receiver distance (km) Power supply AB distance (m) AB direction (°) Sector angle (°) No. 1 source [K2m] 11.8 1050 72° 2~4 No. 2 source [K2m] 8.5 1050 72° 4~8 No. 3 source [Nh2-Z1h] 3.7 1050 72° 0~8 No. 4 source 2-4 ]]> ​ 7.8 1050 72° 4~9 refer to Figure 6 The diagram shown is a schematic diagram of the regional geological and experimental work layout.

[0050] Experimental area (see) Figure 6 The receiving location is within the Caledonian Wanyangshan Sequence magmatic rock (ηγS12-4), consisting of medium- to coarse-grained porphyritic biotite monzogranite; fine-grained syenogranite (ξγS12-5) is also exposed locally. Sources 1 and 2 are located in the Late Cretaceous Ganzhou Group Maodian Formation (K2m), primarily composed of purplish-red layered sandstone, conglomerate, or complex conglomerate, sandstone-conglomerate, interbedded with fine sandstone-conglomerate lenses, or andesite. Source 3 is located in the Late Sinian to Early Sinian Hongshan Formation (Nh2-Z1h), its lithology mainly consisting of biotite schist, silicic biotite schist, graphite-quartz schist, biotite granulite interbedded with magnetite, pyrite biotite granulite, schist interbedded with marble lenses or diopside. Source 4 is located within the same Caledonian Wanyangshan Sequence magmatic rock (ηγS12-4) as the receiving location. 2-4 In the rock mass.

[0051] In this experiment, the apparent resistivity was measured at the outcrops of the strata near each source location using a small quadrupole method. The results (Table 7) show that the apparent resistivity of the strata where sources 1, 2, and 3 are located is roughly the same, all less than 500 Ω·m. The results measured in the surface exposed rocks are relatively high. Based on previous geophysical exploration experience, the apparent resistivity of Cretaceous red sandstone is generally less than 100 Ω·m, which is a low-resistivity rock layer. On the other hand, the rock mass where source 4 is located has a higher resistivity, reaching 3475~4083 Ω·m, which is a high-resistivity layer.

[0052] Table 7 Apparent resistivity of rock layers near the source refer to Figure 7 The figure shows a schematic diagram of the projection positions of each emission source on the MT cross-section.

[0053] To gain a more comprehensive understanding of the overall electrical structure in the test area, an MT test line was collected (see...). Figure 7 The survey line runs southeast, and although it forms an angle with the path from the transmitter to the receiver, the lithology and electrical structure of the underground strata it passes through are basically consistent with the experimental area. Therefore, it can be used to visually represent the relative positions of each transmitter and receiver area in the experimental area, as well as the electrical properties of the underground rock strata. From the projection positions of each transmitter in the MT profile, it can be seen that transmitters 1-3 are located in a low-resistivity rock layer (apparent resistivity less than 100 Ω·m) with a thickness of 600m to 1500m, and the area between the transmitter and receiver is also a low-resistivity rock layer. This can be used to study the influence of the transmitter-receiver distance on the detection depth. Source 4 is located in the same high-resistivity rock mass as the receiver. The profile shows that the resistivity between the transmitter and receiver is less than 2000 Ω·m from the surface to a depth of 1000m. This source is used for comparison with source 2 to study the influence of different geoelectric conditions on the data. Because outcrop testing measures the complete apparent resistivity of rock above the groundwater level, while MT profile testing measures the apparent resistivity of a large area of ​​rock mass, and in its natural state the underground rock mass is below the water level and the rock is water-saturated, the apparent resistivity value in MT profile is lower than that of outcrop testing, but is closer to the true Kania apparent resistivity.

[0054] Both CSAMT and AMT data were obtained using the GDP-32 instrument. Ⅱ Data was acquired in a scalar manner, with the CSAMT acquisition frequency range of 0.125~8192Hz. The AMT arrangement (measurement point positions, pole spacing, magnetic probe placement, etc.) was identical to that of the CSAMT, used for comparison with CSAMT data at various transmit / receive distances. Two CSAMT arrangements were acquired for each transmitter, with 6 physical points per arrangement, a point spacing of 50m, point numbers ranging from 375 to 925, and a measurement line azimuth of 72°. The standard deviation (SEM) of the acquired data was less than 50mrad. The formula for calculating the standard deviation is shown in the formula below. Where: N is the number of acquisition cycles, The electric or magnetic field phase value (in mrad) is the value of the j-th cycle. The AMT observation duration is 1.5 hours, and the lowest effective frequency is 1 Hz.

[0055] The AMT (Automated Media Transformer) acquires time-domain data, which includes resistivity and impedance phase. Therefore, it requires software to perform a Fourier transform to convert the data into frequency-domain data for comparative analysis. The AMT data preprocessing software includes MTFT and MTEdit. MTFT is used to perform Fourier transforms of the AMT time-domain data into frequency-domain data, while MTEdit is used to perform correlation analysis on the AMT frequency-domain data.

[0056] To preserve the authenticity of the data, only obvious outliers in the data are removed, and then the sounding curve is directly generated and the apparent resistivity and impedance phase pseudo-profiles are plotted.

[0057] The key to data analysis is determining the lowest far-field frequency. In homogeneous and layered geotechnical environments, the principles of CSAMT data analysis are: for near-field data, apparent resistivity increases at a 45° angle with decreasing frequency, and the impedance phase approaches zero; the resistivity curve in the transition zone often shows a transition zone "trough," i.e., a false low-resistivity anomaly. A false slope often accompanies the low-frequency side of this trough, trending towards the near-field frequency band, and the impedance phase shows a significant change related to the slope of the apparent resistivity; far-field data varies with the geotechnical resistivity, and the frequency of the first far-field data point is the lowest far-field frequency. Due to the complexity of the subsurface strata in the test area, the measured CSAMT sounding curves are even more complex and variable. Not all measured apparent resistivity data curves will show a typical transition zone "trough," making it quite difficult to determine the lowest far-field frequency from the measured curves. To accurately identify the lowest far-field frequency of each source's CSAMT curve, the specific approach is to first select a typical curve and compare it with the corresponding AMT curve. Based on their shape and trend, the lowest far-field frequency of each source is initially determined. Then, the value is verified based on the pseudo-profile, and finally, the accurate value of the lowest far-field frequency of each source is determined.

[0058] The effect of non-planar electromagnetic waves on the impedance phase curve is much greater than that on the apparent resistivity curve. Therefore, in the comparative analysis, both the apparent resistivity and impedance phase parameters of the Kania wave are considered.

[0059] refer to Figure 8 The figure shows a comparison of the CSAMT apparent resistivity and impedance phase data curves with the AMT data curves for different emission sources.

[0060] Figure 8This is a comparison chart of typical CSAMT and AMT curves. The AMT Carnia apparent resistivity curve is generally G-shaped, with the apparent resistivity rising from 128 to 12 Hz, and the curve flattening in the low-frequency range. The impedance phase curve rises, falls, and rises again from high to low frequencies, with inflection points at 256 Hz and 22.5 Hz, respectively. For source 1 CSAMT data (a), the apparent resistivity and impedance phase curves above 11.3 Hz are consistent with the AMT curves. The data from 5.63 to 1.41 Hz is a transitional "trough," after which the near-field region begins. Comparative analysis determines that the lowest far-field frequency is 11.3 Hz, corresponding to a Carnia apparent resistivity of 311 Ω·m. The CSAMT apparent resistivity data curve (b) of source 2 does not have a clear transition band "trough". The curve after 22.5Hz is consistent with the AMT curve, while the curve shape and trend below 22.5Hz are inconsistent with AMT. The impedance phase curve shape is consistent with the AMT curve above 22.5Hz, while the CSAMT curve shape and trend below 22.5Hz are inconsistent with AMT. Therefore, the lowest far-field frequency can be set at 22.5Hz, corresponding to a Cagnia apparent resistivity of 323Ω·m. The CSAMT data curve (c) of source 3 has a clear inflection point at 180Hz, and then quickly enters the near-field region with a 45° rise, without a clear transition band "trough". The impedance phase curve above 180Hz is consistent with the trend of AMT. Therefore, the lowest far-field frequency can be set at 180Hz, corresponding to a Cagnia apparent resistivity of 127Ω·m. The CSAMT data curve (d) from source 4 is a typical curve that can distinguish the near field, transition period, and far field. The apparent resistivity curve shows a clear transition band "trough" in the 360Hz~128Hz range. After that, it rises with a 45° decrease in frequency in the near field. The impedance phase curve stabilizes at around zero in the range below 128Hz. In the 128Hz~360Hz range, it transitions to the far field with a certain slope. Therefore, the lowest far field frequency of the curve can only be set at 512Hz, and the corresponding Carnia resistivity at this frequency is 137Ω·m.

[0061] refer to Figure 9 The figure shown is a schematic diagram of the apparent resistivity pseudo-profile and the impedance phase pseudo-profile of Cania.

[0062] The preceding analysis only examined the comparison of a few typical curves; now, the analysis of the entire cross-section will proceed as follows. For example... Figure 9As shown, the apparent resistivity pseudo-profile from the Kanya profile reveals significant lateral fluctuations in the apparent resistivity contours. While a single profile makes it difficult to discern the boundary between the far-field and transition regions, combining it with the phase pseudo-profile provides a clearer distinction. In the phase pseudo-profile (a1) of source 1, a distinct transition band characteristic is observed from 1 to 8 Hz, with the phase rapidly increasing from 0 milliradians. The apparent resistivity profile does not show a clear low-resistivity anomaly in the transition band, but the apparent resistivity gradient increases below 1 Hz, indicating a clear near-field electrical characteristic. Based on this comprehensive analysis, the next frequency after 8 Hz, 11.3 Hz, can be identified as the lowest far-field frequency. Similarly, the lowest far-field frequencies for sources 2 and 3 can be determined to be 22.5 Hz and 180 Hz, respectively. In the apparent resistivity pseudo-profile of source 4, a clear low-resistivity anomaly appears between 64 and 360 Hz. The phase profile also shows a rapid phase increase from 0 milliradians within this frequency range, thus determining the lowest far-field frequency to be 512 Hz.

[0063] In summary, the lowest far-field frequencies of the CSAMT data from sources 1 to 4 are 11.3 Hz, 22.5 Hz, 128 Hz, and 512 Hz, respectively.

[0064] Calculating the lowest far-field frequency requires knowing the combined resistivity of the strata in the area between the transmitter and receiver, and the challenge lies in determining this combined resistivity. This study employs outcrop testing, combined with existing MT profile data, and uses a comprehensive estimation method to determine the frequency. Based on the preceding description of the geological and geophysical background of the test site, the combined resistivity of sources 1, 2, and 3 can be set at 100 Ω·m, and the combined resistivity of source 4 can be set at 2000 Ω·m. The lowest far-field frequency of each source, calculated using the formula... The calculation results are shown in Table 8. It can be seen that the relative errors between the calculated and measured values ​​for sources 1, 2, and 4 are less than 9%, while the calculated value for source 3 differs significantly from the theoretical value. This is because source 3 is very close to the receiving point, and the high-resistivity granite mass significantly influences the overall resistivity of the strata, leading to a lower estimate of its overall resistivity and consequently a lower calculated value. Therefore, the lowest far-field frequency calculated using this formula matches the measured value very well, proving the correctness of the theoretical fitting formula.

[0065] Table 8 Comparison of Measured and Calculated Values ​​of Lowest Far-Field Frequency Under uniform ground conditions, the ratio of CSAMT transmit / receive distance to detection depth can be expressed as follows: This can also be obtained by referring to the corresponding values ​​in Table 5. If the ground is not uniform or the geological strata at the receiving and transmitting sites are different, then the formula will change because... and The resistivity ρ in the two equations is not equal. To distinguish them, the former is denoted as... Let ρ1 represent the resistivity of the underground medium between the transmitter and receiver, denoted as ρ2, and let ρ3 represent the resistivity within the depth range corresponding to the lowest far-field frequency at the receiving point. The formula... Substitute into the formula have to: , where the units for r and D are both km.

[0066] Due to the influence of the non-uniform resistivity of the underground medium, simply discussing the ratio of transmitter / receiver distance to detection depth is meaningless; therefore, this study will not examine the ratio of transmitter / receiver distance to detection depth. It can be seen that the detection depth is affected by three factors simultaneously: the transmitter-receiver distance, the receiving point, and the resistivity of the underground strata between the transmitter and receiver. When = At that time, it was the same as the formula. They've reached an agreement.

[0067] As shown in Table 9, the formula is used based on the measured lowest far-field frequency and the corresponding apparent resistivity. The measured detection depth of each source at the same receiving point was calculated. The detection depth was calculated using the formula... The calculated values ​​are shown in the table. As can be seen from the data, except for source No. 3, the relative errors between the calculated and measured values ​​are all less than 4%. The larger calculation error for source No. 3 is also due to the deviation in the estimated comprehensive resistivity of the underground medium between the source and the receiving point. Therefore, it is proven that under non-uniform geodetic conditions, the calculation formula... It is reliable.

[0068] From the formula This also explains why the field source needs to be placed in a low-impedance region. Typically, actual CSAMT projects have specific requirements for the working location and detection depth, meaning that D and ρ2 in the formula remain constant. Placing the field source in a low-impedance region has two advantages: first, the low-impedance region has a smaller ρ1, which can reduce the transmit-receive distance r; second, a large transmit current is easily obtained in a low-impedance region. This significantly increases the energy of the received signal and greatly improves the signal-to-noise ratio, which is especially important in working areas with severe electromagnetic interference. Furthermore, from the formula... It can also be seen that, for a given transmit / receive distance, the detection depth of a field source arranged in a high-resistivity region increases with the overall resistivity. The rise and fall. As can be seen from Table 9, the transmit and receive distance of source No. 4, which is arranged on the high-resistivity rock mass, is not much different from that of source No. 2, but the detection depth is less than one-seventh of that of source No. 2, only 177m. It can be said that the detection of source No. 4 was a failure.

[0069] Table 9 Comparison of Measured and Theoretical Values ​​of Detection Depth In this field source test verification process, the fundamental reason for the error between the measured and theoretical values ​​is the inability to accurately predict the actual comprehensive earth resistivity. Although this study employed methods such as on-site small quadrupole measurements on outcrop rocks and reference to MT measurement results to approach the true value as closely as possible, these are all local measurements and cannot accurately measure the overall comprehensive earth resistivity at a certain depth underground. Therefore, in practical application of the formula... , , and At that time, the most crucial thing is to accurately predict the overall resistivity of the earth.

[0070] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0071] This invention discloses a method for determining the transmit / receive distance based on controlled-source audio-frequency magnetotelluric (CSAMT) for sounding depth. First, the electromagnetic field of a uniform geodetic model is simulated using the Fast Hankel Transform (FMT) method. This primarily involves calculating the Carnia apparent resistivity and impedance phase under different transmit / receive distances and geoelectric conditions to determine the lowest far-field frequency. Based on this, a formula for calculating the lowest far-field frequency using field source conditions is derived. Furthermore, a formula for calculating the sounding depth is derived from this formula. By designing four field sources with different transmit / receive distances and geoelectric conditions, and receiving data at the same location, the lowest far-field frequency and its corresponding apparent resistivity of the measured data are determined through analysis and comparison. To facilitate the determination of the lowest far-field frequency in the CSAMT data, AMT data is also collected for comparison. The correctness of the formulas for calculating the lowest far-field frequency and the sounding depth is verified through field experiments.

Claims

1. A method for determining the transmit / receive distance based on the detection depth of the controlled-source audio-frequency magnetotelluric method, characterized in that, include: Establish a CSAMT theoretical calculation model, set the electromagnetic field model parameters according to the basic theory of CSAMT, and calculate the apparent resistivity and impedance phase of Carnia. The electromagnetic field model parameters include the distance between the transmitter and the receiver, the frequency at which the transmitter sends alternating current into the ground through the power supply electrode AB, and the uniform resistivity of the earth. The electromagnetic field distribution is calculated using the fast Hankel transform algorithm for a horizontally layered geoelectric couple source. A uniform half-space model simulation was performed, and the characteristic regions of the apparent resistivity curve and impedance phase curve were analyzed by changing the earth resistivity and transmitter-receiver distance parameters. The relationship between the lowest far-field frequency and parameters is determined, the criteria for determining the lowest far-field frequency are defined, and the correlation between earth resistivity, transmit / receive distance and the lowest far-field frequency is analyzed. The criteria for determining the lowest far-field frequency are defined as the first frequency point where the difference between the calculated value and the actual value of the apparent resistivity is ≤1%. If there is no precise corresponding point, it is calculated by linear interpolation. Establish an empirical formula system, derive the comprehensive relationship between transmit / receive distance, earth resistivity and minimum far-field frequency, and establish a quantitative relationship between transmit / receive distance and detection depth under uniform and non-uniform earth conditions. Optimize the field source deployment scheme, calculate the required transmit / receive distance based on the target detection depth and the empirical formula system, and provide a field source deployment guidance scheme.

2. The method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method as described in claim 1, characterized in that, The electromagnetic field fast Hankel transform algorithm using a horizontally layered geodetic dipole source is used to calculate the electromagnetic field distribution, including: Integral expressions for the electric and magnetic field components are established, incorporating spatial frequency, current intensity, dipole moment length, and dipole moment direction angle as parameters; parameters for the layered medium are defined, along with hyperbolic cotangent function expressions for recursively calculating the equivalent reflection coefficients of the vertical magnetic field component and the horizontal electric field component; the electromagnetic field components are expressed in discrete summation form; and a fast Hankel transform is performed using Anderson filter coefficients.

3. The method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method as described in claim 1, characterized in that... By varying the earth resistivity and transmitter / receiver distance parameters, the characteristic regions of the apparent resistivity curve and impedance phase curve are analyzed, including: With a fixed transmit / receive distance, the resistivity of the earth was changed, and the frequency range and frequency density of the acquisition were set to conduct a theoretical simulation: the transmit / receive distance was set to a fixed value, the uniform resistivity ρ was set as a variable, and the apparent resistivity curve and impedance phase curve were plotted using a double logarithmic coordinate system to analyze the relationship between the lowest far-field frequency and the resistivity of the earth. With a fixed earth resistivity, a theoretical simulation was conducted by varying the transmit / receive distance: the uniform earth resistivity was set as a fixed value, the transmit / receive distance r was set as a variable, the acquisition frequency range and frequency density were set, and the influence of different transmit / receive distances on the resistivity curve and impedance phase curve was analyzed.

4. The method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method as described in claim 1, characterized in that, An empirical formula system was established, summarizing the comprehensive relationship between transmit / receive distance, earth resistivity, and the lowest far-field frequency, including: Under a fixed transmit / receive distance, the ratio between the lowest far-field frequency and the earth resistivity remains constant. Based on this characteristic, for specific earth resistivity values, the corresponding fitting functions are established as follows: When the earth resistivity is 400 Ω·m, its fitting function is: After sorting, we get: ; For a ground resistivity of 1600 Ω·m, the corresponding fitting formula is: ; When the earth resistivity is 3200 Ω·m, the fitting formula becomes ; ρ represents the resistivity of uniform ground, with units of Ω·m. The arithmetic mean of the fitted parameters under different resistivity conditions is used to derive an empirical formula applicable to a wide range of situations. .

5. The method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method as described in claim 1, characterized in that, Establish a quantitative relationship between transmit / receive distance and probe depth under both uniform and non-uniform geodetic conditions, including: Under uniform ground conditions, empirical formulas Substitute into the detection depth formula We can obtain: Where D is the detection depth, To determine the skin depth, the ratio of the transmit / receive distance to the detection depth is further calculated. ; For non-uniform ground conditions or differences in geological strata between the receiving and transmitting sites, empirical formulas will be used. Substitute into the detection depth formula The relationship between the transmitter / receiver distance and the detection depth under non-uniform ground conditions was derived. ,in The resistivity of the underground medium between the transmitting and receiving points. The resistivity within the detection depth range corresponding to the lowest far-field frequency at the receiving point; The formulas described are applicable to the 4km~16km transmit / receive distance range commonly used in actual work. Based on the calculation results, a curve of the ratio of transmit / receive distance to detection depth is plotted.

6. The method for determining the transmit / receive distance based on the detection depth using the controlled-source audio-frequency magnetotelluric method as described in claim 1, characterized in that, Based on the target detection depth and the aforementioned empirical formula system, the required transmit / receive distance is calculated, and a field source deployment guidance scheme is provided, including... The relationship between the transmit / receive distance and the detection depth ratio was analyzed and determined through large-scale simulation calculations. For the commonly used transmit / receive distance range in practical work, the variation range of the ratio of transmit / receive distance to detection depth within this range is determined; a calculation model for the ratio of transmit / receive distance to detection depth is established; a lookup table for the ratio of transmit / receive distance to detection depth is constructed, containing the ratio data corresponding to commonly used transmit / receive distances; combining the calculation model and the lookup table, the optimal transmit / receive distance parameters are optimized and determined according to the target detection depth requirements, thereby realizing the formulation of the field source deployment scheme.

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