A self-calibration method for the receiving coil of a transient electromagnetic instrument

Abstract

The present invention provides a self-calibration method for the receiving coil of a transient electromagnetic instrument, belonging to the field of instruments in geophysical exploration; the transmitter of the transient electromagnetic instrument outputs two completely identical excitation pulse signals, and two damping resistors R with different resistances are respectively connected in parallel on the receiving coil d1 and R d2 , the receiver receives and records the output response signals D1 and D2; since in the two measurements, the excitation pulse and the receiving channel are stable, and at the same time when the system is static, the earth response remains consistent, so only the response of the receiving coil changes during the measurement, that is, the self-inductance L and the total capacitance C can be quantified by solving the response equation of the receiving coil; finally, according to the condition that the optimal damping coefficient ξ of the receiving coil is 1, the optimal damping resistor DR for correcting the receiving coil is determined. The present invention can effectively improve the shallow underground detection accuracy of the transient electromagnetic method.

Description

Technical Field

[0001] The present invention belongs to the field of instruments in geophysical exploration, and more specifically, relates to a self-calibration method for a receiving coil of a transient electromagnetic method instrument. Background Art

[0002] The transient electromagnetic method (TEM) is a non-invasive geophysical exploration method that can obtain the underground conductivity distribution from several meters to kilometers deep. The transient electromagnetic method is based on Faraday's law of electromagnetic induction. By injecting current into a loop laid on the ground, after the current stabilizes, the current is suddenly turned off. The rapid change of the current will generate a pulsed magnetic field underground. The target body underground is excited by the pulsed magnetic field and will generate induced eddy currents, thereby generating a secondary induced magnetic field. By using a magnetic field sensor on the ground surface to receive the induced magnetic field intensity at different times, the electrical parameter information of the underground target body at different depths can be obtained. Currently, the transient electromagnetic method has been successfully applied to mineral and geothermal exploration, as well as engineering and hydrogeological surveys.

[0003] As can be seen from the above, the transient electromagnetic method obtains the electrical parameter information of the underground target body by observing the secondary induced magnetic field of the underground target body. On the one hand, the induced eddy currents generated by the underground target body are weak, and the intensity of the secondary induced magnetic field received by the receiving coil of the transient electromagnetic instrument is low, especially the late signals reflecting deep target bodies are weak; this requires the receiving coil to have high sensitivity and broadband frequency response. The output signal of a high-sensitivity receiving coil has an intensity sufficient to suppress the background noise of the preamplifier, thereby increasing the detection depth of the transient electromagnetic instrument; in addition, a receiving coil with broadband frequency response can receive undistorted early signals to obtain the conductivity of shallow underground target bodies.

[0004] The prior art improves the sensitivity of the receiving coil by increasing the number of turns of the receiving coil and increasing the size of the receiving coil. However, whether increasing the number of turns of the coil or increasing the size of the coil will result in an increase in the self-inductance and parasitic capacitance in the receiving coil, thereby reducing the bandwidth of the receiving coil and making it difficult to simultaneously correct the two indicators of sensitivity and bandwidth. Summary of the Invention

[0005] To solve the deficiencies of the prior art, the present invention proposes a self-calibration method for a receiving coil of a transient electromagnetic instrument. Without the help of additional equipment, an optimal damping resistor DR is matched for the receiving coil. By calculating the division equation of the responses of two different damping resistors and using the gradient descent method to solve the equation, the resistance value of DR is determined, thereby improving the sensitivity and bandwidth of the receiving coil and enhancing the detection capabilities of the transient electromagnetic instrument for shallow and deep layers.

[0006] The technical solution adopted by the present invention to solve its technical problems is: a self-calibration method for the receiving coil of a transient electromagnetic instrument is proposed, which specifically includes the following steps:

[0007] The transmitter of the transient electromagnetic instrument outputs two completely identical excitation pulse signals, and two damping resistors R with different resistances are respectively connected in parallel on the receiving coil d1 and R d2 , and the receiver receives and records the output response signals D1 and D2;

[0008] According to the basic principle of the transient electromagnetic method and the composition of its measuring equipment, the data d(t) measured by the transient electromagnetic instrument can be regarded as the convolution of four responses of the system, and we get:

[0009] d(t) = p(t) * g(t) * h(t) * r(t)

[0010] where p(t) is the derivative of the transmitted current, that is, the excitation signal, and g(t), h(t) and r(t) are the responses of the underground anomaly, the response of the receiving coil and the impulse response of the receiver respectively;

[0011] To simplify the calculation, the time-domain response function is transformed into the frequency-domain form, and the transfer function obtained is:

[0012] D(s) = P(s) · G(s) · H(s) · R(s)

[0013] where s = j2πf, j is the imaginary unit, f is the frequency, D(s) is the Laplace transform of d(t); P(s) is the Laplace transform of p(t); G(s) is the Laplace transform of g(t); H(s) is the Laplace transform of h(t); R(s) is the Laplace transform of r(t);

[0014] According to the equivalent circuit of the receiving coil: the self-inductance of the coil, the parasitic capacitance are connected in series with the inherent resistance of the receiving coil; among them, the parasitic capacitance is respectively connected in parallel with the damping resistor, the front door switch circuit and the preamplifier, so the input signal v(t) and the output response u(t) of the system can be expressed as:

[0015]

[0016] where C and R e respectively represent the total capacitance of the receiving coil and the total resistance connected in parallel with the parasitic capacitance C c of the coil, and R represents the internal resistance of the receiving coil; after Laplace transform, the transfer function of the receiving coil can be obtained:

[0017]

[0018] When the input signal of the system is a pulse signal and the damping coefficient ξ = 1, the response of the system decays within a relatively short time without oscillation. The damping coefficient is related to the self-inductance L of the receiving coil, the parasitic capacitance C of the receiving coil, and the damping resistance R d is related to;

[0019] D1 and D2 are obtained by collecting two different damping resistances R d1 and R d2 During two measurements, the excitation signal and the pulse response of the receiver are both stable. At the same time, when the system is in a static state, the response signal of the underground anomaly remains consistent, and only the response of the receiving coil changes. Thus, it can be obtained that:

[0020]

[0021] Solve the above equation to determine the self-inductance L of the receiving coil and the total capacitance C of the receiving coil. According to the condition of the optimal damping coefficient ξ = 1, determine the optimal damping resistance DR. Connect the optimal damping resistance DR in parallel with the receiving coil to obtain a receiving coil with the best comprehensive performance of sensitivity and bandwidth, thereby completing the self-calibration of the receiving coil.

[0022] Furthermore, calculate the total capacitance C of the receiving coil and the total resistance R e connected in parallel with it, where the total impedance of the front door switch circuit and the preamplifier is calculated as:

[0023]

[0024] Among them, C a is the low-pass filter capacitor of the preamplifier, R i and R a are the current-limiting resistance and input resistance of the preamplifier respectively; R on is the internal resistance of the front door switch circuit, C s and C d are the parasitic capacitances of the front door switch circuit respectively, || represents the parallel resistance calculation operator; among them, C and R e can be obtained from the total impedance Z:

[0025]

[0026]

[0027] Among them, C c is the parasitic capacitance of the receiving coil.

[0028] Furthermore, the damping coefficient ξ is related to the internal resistance R of the receiving coil, the self-inductance L, the total resistance R c connected in parallel with the parasitic capacitance C eThere is a relationship with the total capacitance C of the receiving coil; and the optimal total resistance R is determined according to the damping coefficient ξ = 1 ebest , where the damping coefficient ξ and R, L, C, R e The relationship can be expressed as:

[0029]

[0030] When ξ = 1, R can be obtained e The relationship with R and L, the result is:

[0031]

[0032] Furthermore, solve the self - inductance L of the receiving coil and the equivalent total capacitance C of the receiving coil. The calculation method is:

[0033] Use two damping resistors R with unequal resistance values d1 and R d2 Measure the responses as D1 and D2 respectively, make D1 / D2. When R d1 <R d2 At this time, the ratio function is less than 1, and at the same time it tends to 0 near the cut - off frequency ; when R d1 >R d2 At this time, the ratio function is greater than 1 and there is a maximum value near the cut - off frequency f0. Using this difference, L and C can be more accurately fitted and determined. Further, the ratio function is optimized into the following objective function:

[0034]

[0035] Among them, Represents the iterative fitting data, which is a complex vector of size n s ×1, where n s Represents the number of frequency samples. The objective function Θ only depends on L, C and s; the gradient - descent method is used to optimize the objective function, so as to calculate the optimal solutions of L and C. The formula for calculating the gradient - descent direction is:

[0036]

[0037] Among them, J T Represents the transpose of the Jacobian matrix of the objective function with respect to the gradient operator , r represents the residual, and its calculation formula is:

[0038]

[0039] After determining L and C, the total resistance R when paralleling R d1 can be calculated e1 and paralleling R d2The total resistance R at that time e2 , according to the formula obtained and Finally, the optimal damping resistance DR is determined.

[0040] The beneficial effects brought by the technical solution adopted by the present invention are as follows: The present invention provides a self-calibration method for the receiving coil of a transient electromagnetic instrument. By using a receiving coil connected with unequal damping resistors, two sets of secondary field data are obtained, and then the self-inductance L and the total capacitance C of the receiving coil are quantified by solving the response equation of the receiving coil. According to the optimal damping coefficient, the size of the optimal damping resistance is determined, so that the self-calibration of the receiving coil of the transient electromagnetic instrument can be completed without the aid of other equipment. This method has strong practicability, and the calibrated receiving coil has higher sensitivity and a wider measurement frequency band comprehensive performance, which can effectively improve the detection depth and the resolution of shallow detection of the transient electromagnetic instrument. Description of the Drawings

[0041] Figure 1 is a flowchart of a self-calibration method for the receiving coil of a transient electromagnetic instrument according to the present invention;

[0042] Figure 2 is an equivalent circuit diagram of the receiving coil of the transient electromagnetic instrument;

[0043] Figure 3 are the impulse responses corresponding to the receiving coils with three different damping resistances R d1 <R d2 <R d3 ;

[0044] Figure 4 is the ratio of the transfer functions between the data measured with R d1 , R d3 and the data measured with R d2 ;

[0045] Description of the Reference Numerals:

[0046] (a) is the receiving coil with a damping resistor, (b) is the damping resistor, (c) is the front door switch circuit, and (d) is the equivalent circuit of the preamplifier; C a is the low-pass filter capacitor of the preamplifier, R i and R a are respectively the current-limiting resistor and the input resistor of the preamplifier, R on is the internal resistance of the front door switch circuit, C s and C d are the parasitic capacitances of the switch circuit, C c is the parasitic capacitance of the receiving coil, R is the internal resistance of the receiving coil, L is the self-inductance of the receiving coil, and R d is the damping resistor. Detailed implementation mode

[0047] In order to clearly understand the purpose, technical solution and effect of the present invention, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0048] Refer to Figure 1 , Figure 1 which is a flowchart of a self - calibration method for the receiving coil of a transient electromagnetic instrument of the present invention. The embodiment provides a self - calibration method for the receiving coil of a transient electromagnetic instrument, including the following steps:

[0049] S1: The transmitter of the transient electromagnetic instrument outputs two completely identical excitation pulse signals, and two damping resistors R d1 and R d2 with unequal resistances are respectively connected in parallel on the receiving coil. The receiver receives and records the output response signals D1 and D2;

[0050] S2: Calculate the response function of the receiving coil.

[0051] In this embodiment, step S2 is specifically: According to the basic principle of the transient electromagnetic method and the composition of its measuring equipment, the data d(t) measured by the transient electromagnetic instrument can be regarded as the convolution of four responses of the system, and we get:

[0052] d(t) = p(t)*g(t)*h(t)*r(t)

[0053] where p(t) is the derivative of the transmitting current, that is, the excitation signal, and g(t), h(t) and r(t) are respectively the response of the underground anomaly, the response of the receiving coil and the impulse response of the receiver;

[0054] S3: Convert the time - domain response function into a frequency - domain form.

[0055] In this embodiment, step S3 is specifically: Perform a Laplace transform on the time - domain response function to obtain the frequency - domain response function:

[0056] D(s) = P(s)·G(s)·H(s)·R(s)

[0057] where s = j2πf, j is the imaginary unit, f is the frequency, D(s) is the Laplace transform of d(t); P(s) is the Laplace transform of p(t); G(s) is the Laplace transform of g(t); H(s) is the Laplace transform of h(t); R(s) is the Laplace transform of r(t);

[0058] S4: Calculate the total impedance of the multiplexer and the pre - amplifier.

[0059] In this embodiment, step S4 is specifically: Refer to Figure 2, according to the equivalent circuit of the receiving coil: the self-inductance of the coil, the parasitic capacitance is in series with the inherent resistance of the receiving coil; among them, the parasitic capacitance is respectively in parallel with the damping resistance, the front door switch circuit, and the preamplifier, and calculate the total impedance of the multiplexer and the preamplifier:

[0060]

[0061] Among them, C a is the low-pass filter capacitor of the preamplifier, R i and R a are respectively the current-limiting resistance and the input resistance of the preamplifier; R on is the internal resistance of the front door switch circuit, C s and C d are the parasitic capacitances of the front door switch circuit, || represents the parallel resistance calculation operator, that is, a||b = a*b / (a + b).

[0062] It should be understood that the receiving coil of the prior art is Figure 2 the part of the circuit that does not include the damping resistance R d .

[0063] S5: Calculate the total capacitance C of the receiving coil and the total resistance R e connected in parallel with it.

[0064] In this embodiment, step S5 is specifically: referring to Figure 2 , the real part of the total impedance Z calculated in step S4 represents the total resistance R ec of the multiplexer and the preamplifier, and the imaginary part represents the total capacitance C ec , where the total capacitance C ec can be equivalently in parallel with the parasitic capacitance of the receiving coil, and the total resistance R ec can be equivalently in parallel with the damping resistance:

[0065]

[0066]

[0067] Among them, C c is the parasitic capacitance of the receiving coil.

[0068] S6: Calculate the transfer function of the receiving coil.

[0069] In this embodiment, step S6 is specifically: referring to Figure 2 , and the total capacitance C and the total resistance R e obtained in step S5, and obtain the time-domain response function of the receiving coil:

[0070]

[0071] Among them, C and R e respectively represent the total capacitance of the receiving coil and the total resistance in parallel with the parasitic capacitance C of the coil, and R represents the internal resistance of the receiving coil; after Laplace transform, the transfer function of the receiving coil can be obtained: c

[0072]

[0073] S7: Calculate D2 / D1 according to the frequency-domain response function of the receiving coil obtained in step S3.

[0074] In this embodiment, step S7 is specifically: when the input signal of the system is a pulse signal and the damping coefficient ξ = 1, the response of the system decays within a relatively short time without oscillation (refer to Figure 3 ), and the damping coefficient is related to the self-inductance L of the receiving coil, the parasitic capacitance C of the receiving coil, and the damping resistance R d ;

[0075] D1 and D2 are collected by two different damping resistances R d1 and R d2 . During the two measurements, the excitation signal and the impulse response of the receiver are stable. At the same time, when the system is in a static state, the response signal of the underground anomaly remains consistent, and only the response of the receiving coil changes. Thus, we can obtain:

[0076]

[0077] S8: Solve the self-inductance L of the receiving coil and the equivalent total capacitance C of the receiving coil.

[0078] In this embodiment, step S8 is specifically: using two damping resistances R with different resistances d1 and R d2 to measure the responses as D1 and D2 respectively, making D1 / D2. When R d1 < R d2 , the ratio function is less than 1 and approaches 0 near the cut-off frequency ; when R d1 > R d2 , the ratio function is greater than 1 and has a maximum value near the cut-off frequency f0. Using this difference phenomenon, we can more accurately fit and determine L and C (refer to Figure 4 ), and further optimize the ratio function into the following objective function:

[0079]

[0080] Among them, represents the iterative fitting data, which is a complex vector of size n s ×1, where n​s denotes the number of frequency samples, and the objective function Θ only depends on L, C, and s. The gradient descent method is used to optimize the objective function to calculate the optimal solutions of L and C. The formula for calculating the gradient descent direction is:

[0081] g = Re(J T r)

[0082] where J T denotes the transpose of the Jacobian matrix of the objective function with respect to the gradient operator , and r denotes the residual, and its calculation formula is:

[0083]

[0084] S9: Calculate the optimal total resistance R when the optimal damping coefficient ξ = 1 ebest .

[0085] In this embodiment, step S9 is specifically: where the relationship between the damping coefficient ξ and R, L, C, R e can be expressed as:

[0086]

[0087] When ξ = 1, the relationship between R ebest and R, L can be obtained, and the result is:

[0088]

[0089] S10: After determining L and C, R e1 and R e2 can be calculated.

[0090] In this embodiment, step S9 is specifically: According to the formula obtain while Finally, determine the optimal damping resistance DR, and connect the optimal damping resistance DR in parallel on the receiving coil to obtain a receiving coil with the best comprehensive performance of sensitivity and bandwidth, thereby completing the self-calibration of the receiving coil.

[0091] The present invention provides a self-calibration method for a receiving coil of a transient electromagnetic instrument. By using a receiving coil connected with unequal damping resistors, two sets of secondary field data are acquired, and then the self-inductance L and the total capacitance C of the receiving coil are quantified by solving the response equation of the receiving coil. According to the optimal damping coefficient, the size of the optimal damping resistance is determined, so as to complete the self-calibration of the receiving coil of the transient electromagnetic instrument without relying on other devices. This method has strong practicability, and the calibrated receiving coil has higher sensitivity and a wider measurement frequency band, which can effectively improve the detection depth and the resolution of shallow detection of the transient electromagnetic instrument.

[0092] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A self - calibration method for the receiving coil of a transient electromagnetic instrument, characterized in that, The self-calibration method of the receiving coil of the transient electromagnetic instrument includes the following steps: The transmitter of the transient electromagnetic instrument outputs two completely identical excitation pulse signals, and two damping resistors R d1 and R d2 with unequal resistances are respectively connected in parallel on the receiving coil; the receiver receives and records the output response signals D1 and D2; According to the basic principle of the transient electromagnetic method and the composition of its measuring equipment, the data d(t) measured by the transient electromagnetic instrument can be regarded as the convolution of four responses of the system, and we get: d(t) = p(t) * g(t) * h(t) * r(t) where p(t) is the derivative of the transmitting current, that is, the excitation signal, and g(t), h(t), and r(t) are the responses of the underground anomaly, the response of the receiving coil, and the impulse response of the receiver, respectively; To simplify the calculation, the time-domain response function is transformed into the frequency-domain form, and the transfer function is obtained as: D(s) = P(s)·G(s)·H(s)·R(s) where s = j2πf, j is the imaginary unit, f is the frequency, D(s) is the Laplace transform of d(t); P(s) is the Laplace transform of p(t); G(s) is the Laplace transform of g(t); H(s) is the Laplace transform of h(t); R(s) is the Laplace transform of r(t); According to the equivalent circuit of the receiving coil: the self-inductance of the coil, the parasitic capacitance are in series with the inherent resistance of the receiving coil; among them, the parasitic capacitance is in parallel with the damping resistance, the front door switch circuit, and the preamplifier respectively. Therefore, the input signal v(t) and the output response u(t) of the system can be expressed as: Among them, C and R e respectively represent the total capacitance of the receiving coil and the total resistance in parallel with the parasitic capacitance C c of the coil, and R represents the internal resistance of the receiving coil; after Laplace transform, the transfer function of the receiving coil can be obtained: When the input signal of the system is a pulse signal and the damping coefficient ξ = 1, the response of the system decays within a relatively short time without oscillation. The damping coefficient is related to the self-inductance L of the receiving coil, the parasitic capacitance C of the receiving coil, and the damping resistance R d are related; D1 and D2 are obtained by two different damping resistors R d1 and R d2 collected. In the two measurements, the excitation signal and the impulse response of the receiver are both stable. At the same time, when the system is in a static state, the response signals of the underground anomalies remain consistent, and only the response of the receiving coil changes. Thus, it can be obtained that: Solve the above equation to determine the self-inductance L of the receiving coil and the total capacitance C of the receiving coil. According to the condition of the optimal damping coefficient ξ = 1, determine the optimal damping resistance DR. Connect the optimal damping resistance DR in parallel on the receiving coil to obtain a receiving coil with the best comprehensive performance of sensitivity and bandwidth, thereby completing the self-calibration of the receiving coil.

2. The self - calibration method for the receiving coil of a transient electromagnetic instrument according to claim 1, characterized in that, Calculate the total capacitance C of the receiving coil and the total resistance R connected in parallel therewith e , where the total impedance of the front door switch circuit and the preamplifier is calculated as: Among them, C a is the low-pass filter capacitor of the preamplifier, R i and R a are the current-limiting resistor and input resistor of the preamplifier respectively; R on is the internal resistance of the front door switch circuit, C s and C d are the parasitic capacitances of the front door switch circuit respectively, || represents the parallel resistance calculation operator; among them, C and R e can be obtained from the total impedance Z: Among them, C c is the parasitic capacitance of the receiving coil.

3. The self - calibration method for the receiving coil of a transient electromagnetic instrument according to claim 2, characterized in that, The damping coefficient ξ is related to the internal resistance R, self-inductance L of the receiving coil, and the total resistance R in parallel with the parasitic capacitance C of the receiving coil c of the receiving coil e and there is a relationship with the total capacitance C of the receiving coil; and the optimal total resistance R is determined according to the damping coefficient ξ = 1 ebest , where the relationship between the damping coefficient ξ and R, L, C, R e can be expressed as: When ξ = 1, R can be obtained e The relationship with R and L is as follows:

4. The self - calibration method for the receiving coil of a transient electromagnetic instrument according to claim 3, characterized in that, Solve for the self-inductance L of the receiving coil and the equivalent total capacitance C of the receiving coil. The calculation method is: Use two damping resistors R with unequal resistances d1 and R d2 Measure the responses as D1 and D2 respectively, and make D1 / D2. When R d1 < R d2 The ratio function is less than 1 and approaches 0 near the cut-off frequency When R d1 > R d2 The ratio function is greater than 1 and has a maximum value near the cut-off frequency f0. Using this difference, L and C can be determined by relatively accurate fitting. Further, the ratio function is optimized into the following objective function: Among them, represents the iterative fitting data, which is a complex vector of size n s ×1, where n s represents the number of frequency samples. The objective function Θ only depends on L, C, and s. The gradient descent method is used to optimize the objective function, thereby calculating the optimal solutions of L and C. The formula for calculating the gradient descent direction is: Among them, represents the transpose of the Jacobian matrix of the objective function with respect to the gradient operator , r represents the residual, and its calculation formula is: After determining L and C, the total resistance R when d1 parallel R is calculated. e1 and the total resistance R when d2 parallel R is e2 , according to the formula is obtained and finally, the optimal damping resistance DR is determined.

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