Method for calibrating very low frequency three-component coil based on sweep excitation

Abstract

The application belongs to the field of geophysical exploration, and particularly relates to a very low frequency three-component coil calibration method based on sweep excitation, which comprises the following steps: acquiring an alternating current and a time domain signal of a three-component coil, performing frequency domain transformation on the time domain signal to obtain a complex frequency domain response vector covering a sweep frequency range; constructing a linear equation set describing coil system errors based on the measured complex frequency domain response vector and a calculated excitation magnetic field reference vector in each attitude, solving the linear equation set by using a least square method to obtain a calibration matrix used for correcting measurement data; and correcting the measurement data of the three-component coil in a use state by using the calibration matrix. The application can accurately calibrate the systematic errors of the very low frequency three-component coil and effectively improve the measurement accuracy and data reliability of the very low frequency electromagnetic method.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of geophysical exploration, and in particular to a very low frequency three-component coil calibration method based on sweep excitation. BACKGROUND

[0002] Electromagnetic waves can be divided into long waves (≥1km), medium waves (100m~1km), short waves (10m~100m) and the like according to the size of their wavelength. The short wave signal has a wide available frequency spectrum, but the wavelength is short, the energy attenuation is serious, and the signal coverage range is small. The long wave signal has a wider coverage, but the frequency band resource is limited, and the data rate that can be carried is lower, which cannot meet the requirement of high-speed data transmission; however, due to its strong penetration ability, stable phase, strong diffraction ability and wide coverage, it not only plays a key role in special fields such as underwater communication, global navigation and military communication, but also provides a promising technical means for geophysical exploration.

[0003] Unlike the traditional method which needs large-scale artificial field source arrangement, such as controlled source audio-frequency magnetotelluric method (CSAMT) and airborne transient electromagnetic method (ATEM), the very low frequency electromagnetic method receives fixed long wave station signals, and naturally has the characteristics of frequency stability, good penetration and strong anti-interference ability. This characteristic not only greatly simplifies the field exploration process, but also has unique advantages in metal mine and karst exploration in extreme environments due to its long-distance propagation ability (coverage range up to thousands of kilometers).

[0004] The single-component coil is essentially a one-dimensional measuring device, which is only sensitive to the magnetic field component in its own direction. This design leads to two inherent defects: one is that it cannot perceive the magnetic field signal perpendicular to it, forming a significant detection blind area; the other is that it loses the information of the other two orthogonal directions, so it cannot determine the complete spatial direction of the magnetic field. In contrast, the three-component coil can accurately measure the magnetic field signal in space through three orthogonal single-component coils. However, the complexity of this structure also introduces new error sources: the accuracy of the output results will be disturbed by system errors such as bias, scale factor and inter-axis non-orthogonality.

[0005] The prior art either needs expensive auxiliary equipment, increasing the calibration cost, or the calibration process is relatively complex and has low automation degree, and the mathematical model cannot accurately solve the three major systematic errors of the inherent bias, scale factor and non-orthogonality of the very low frequency three-component coil in a unified framework. SUMMARY

[0006] The embodiment of the present application provides a very low frequency three-component coil calibration method based on sweep excitation, which solves the problem of the three major systematic errors of the inherent bias, scale factor and non-orthogonality of the very low frequency three-component coil.

[0007] According to the method, the three-component coil is calibrated based on the sweep excitation.

[0008] The time domain signal of the three-component coil is obtained by outputting the AC excitation current with a continuously changing frequency in the very low frequency range by using a programmable current source and driving the Helmholtz coil to generate a sweep magnetic field changing with time, and the three-component coil is rotated to K postures under the driving of the non-magnetic turntable, and the data is synchronously collected at each posture.

[0009] The time domain signal is subjected to frequency domain transformation to obtain a complex frequency domain response vector covering the sweep frequency range.

[0010] Based on the complex frequency domain response vector measured at each posture and the calculated excitation magnetic field reference vector, a linear equation set describing the coil system error is constructed, and the linear equation set is solved by using the least square method to obtain a calibration matrix for correcting the measurement data.

[0011] The measurement data of the three-component coil in the use state is corrected by using the calibration matrix.

[0012] Further, the frequency domain transformation of the time domain signal comprises generating in-phase reference signals and quadrature reference signals with the same frequency as the excitation frequency, multiplying the collected time domain signal, and performing integral operation in an integral number of signal periods to obtain a complex frequency domain response representing amplitude and phase information.

[0013] Further, the K postures comprise at least three linearly independent direction vectors.

[0014] Further, the linear equation set is:

[0015] ,

[0016] In the formula, is an observation value, represents a complex voltage vector actually measured and demodulated by the three-component coil at the target frequency under the th posture, , , three-axis, is a complex voltage vector actually measured and demodulated by the three-component coil at the target frequency under the th posture, is a complex voltage vector actually measured and demodulated by the three-component coil at the target frequency under the th posture; is a calibration matrix, off-diagonal elements respectively represent , , scale factor errors between three axes, off-diagonal elements represent , , non-orthogonal errors of three axes; is the excitation magnetic field reference vector, , represents the magnetic field components that should be induced theoretically by the three-axis sensor at the target frequency under the th posture, , , magnetic field components that should be induced theoretically by the three-axis sensor at the target frequency is the magnetic field component value of the axis that should be induced theoretically, is the magnetic field component value of the axis that should be induced theoretically, is the magnetic field component value of the axis that should be induced theoretically; , , and are the bias errors of the three axes respectively. , , bias errors of the three axes.

[0017] Further, the calculation formula of the excitation magnetic field reference vector is:

[0018] ,

[0019] wherein, is the Helmholtz coil constant, is the excitation current complex vector, is the directional projection vector under the th posture, , , are the cosine values of the included angles between the Helmholtz coil and the three-axis sensor respectively, , , is the cosine value of the included angle between the is the vacuum permeability, is the number of turns of the Helmholtz coil, is the radius of the Helmholtz coil.

[0020] Further, the bias errors are obtained by cutting off the Helmholtz coil current and collecting the output voltage of the three-axis sensor.

[0021] Further, the linear equations are solved using least square method, comprising:

[0022] The least square optimization problem is constructed as:

[0023] ,

[0024] For the optimization instruction, the calibration matrix is found by the optimization instruction to make the total value minimum.

[0025] Further, the measurement data of the three-component coil in use is corrected by the calibration matrix, comprising: removing the bias error from the product of the inverse of the calibration matrix and the measurement data to obtain the corrected magnetic field data.

[0026] Compared with the prior art, the application has at least the following beneficial effects: the application can accurately calibrate and correct the systematic error of the very low frequency three-component coil, and effectively improve the measurement accuracy and data reliability of the very low frequency electromagnetic method. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 The structural schematic diagram of the device provided by the embodiment of the application is provided;

[0028] Figure 2 The flowchart of the calibration method of the very low frequency three-component coil provided by the embodiment of the application is provided;

[0029] Figure 3 The schematic diagram of the spatial distribution of electromagnetic data before and after correction provided by the embodiment of the application is provided. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical scheme and advantages of the application clearer and more apparent, the application will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and not to limit the application.

[0031] Referring to Figure 1 The device used in the method of the application is shown in the figure, comprising a Helmholtz coil 1 fixed on a base, a non-magnetic turntable 2 arranged in the middle of the Helmholtz coil 1, a three-component coil to be measured fixed on the non-magnetic turntable 3 and rotating with the non-magnetic turntable 2, a programmable alternating current source, a data acquisition device and a data processing module. The programmable alternating current source applies a sweep excitation current to the Helmholtz coil 1, so that the Helmholtz coil 1 generates an alternating magnetic field with a known amplitude, a controllable phase and a stable amplitude at each frequency point. The three-component coil is fixed at the center position of the non-magnetic turntable 3. The data acquisition device synchronously acquires the time domain signals of the alternating excitation current and the three-component coil, and processes them through the data processing module.

[0032] According to some embodiments of the present application, based on Figure 1 the device shown in Figure 2 , the present application provides a calibration method of a very low frequency three-component coil. The calibration method comprises:

[0033] obtaining an alternating excitation current and a time domain signal of the three-component coil, the alternating excitation current and the time domain signal of the three-component coil being an alternating excitation current with a continuously changing frequency in a very low frequency range output by a programmable current source, and driving the Helmholtz coil 1 to generate a time-varying sweep magnetic field; the very low frequency range refers to an alternating excitation current with a frequency range between 3 kHz and 30 kHz;

[0034] Under the drive of the non-magnetic turntable 2, the three-component coil is rotated to K postures in turn, and the alternating excitation current and the time domain signal of the three-component coil are synchronously collected while each posture is kept stable, and the time domain signal includes a time domain voltage signal and a time domain current signal;

[0035] performing frequency domain transformation on the time domain signal to obtain a

[0036] Based on the complex frequency domain response vector measured at each posture and the calculated excitation magnetic field reference vector, a linear equation set describing the error of the coil system is constructed, and the least square method is used to solve the linear equation set to obtain a calibration matrix for correcting the measurement data of the three-component coil;

[0037] The calibration matrix is used to correct the measurement data of the three-component coil in the use state.

[0038] In some embodiments, the plurality of postures includes at least three linearly independent direction vectors, and linear independence refers to a set of direction vectors being called linearly independent if none of the direction vectors in the set can be expressed as a linear combination of the other direction vectors. For example:

[0039] Posture one: make the main direction of the axis of the three-component coil parallel to the magnetic field direction generated by the Helmholtz coil;

[0040] Posture two: make the main direction of the axis of the three-component coil parallel to the magnetic field direction generated by the Helmholtz coil;

[0041] Posture three: make the main direction of the axis of the three-component coil parallel to the magnetic field direction generated by the Helmholtz coil;

[0042] And add intermediate angles to the above orthogonal angles, a total of K (K is greater than or equal to 3) angles.

[0043] In some embodiments, the first direction projection vector is defined as the direction projection vector of the second attitude :

[0044]

[0045] are the cosine values of the included angle between the Helmholtz coil and the three-component coil, respectively.

[0046] In some embodiments, when the second attitude is kept stationary, two signals are synchronously collected by the data acquisition module:

[0047] The first signal is the alternating excitation current flowing through the Helmholtz coil

[0048] The second signal is the three-channel induced voltage signal output by the three-component coil, i.e., the time-domain signal of the three-component coil.

[0049] In some embodiments, in order to obtain the amplitude and phase information at the target frequency point , the collected time-domain signal needs to be transformed into the frequency domain, including: generating in-phase reference signals and quadrature reference signals with the same frequency as the excitation frequency, multiplying them with the collected time-domain signal, and performing integration operation within an integer number of signal periods to obtain the complex frequency-domain response representing the amplitude and phase information. Specifically, a digital synchronous demodulation method is used, and the specific method is as follows:

[0050] For the time-domain voltage signal collected at the target frequency point , the in-phase reference signal and the quadrature reference signal are multiplied by the in-phase reference signal is a positive integer,

[0051]

[0052]

[0053] , thereby obtaining the complex frequency-domain response representing the voltage amplitude and phase information is the real part of the voltage frequency-domain response, andis the imaginary part of the voltage frequency-domain response.​​​​​​​​​​​​​​​​​

[0054] For the target frequency The time-domain current signal acquired below Multiply by the in-phase reference signal respectively Orthogonal reference signal and in an integer number of periods T ( M is a positive integer. Integrate within )

[0055] ,

[0056] ,

[0057] This yields the complex frequency domain response representing the current amplitude and phase information. , Let the real part of the current frequency domain response be . This represents the imaginary part of the current frequency domain response.

[0058] In some implementations, for a standard Helmholtz coil, the Helmholtz coil constant is... The calculation formula is as follows: ,

[0059] In the formula, The permeability of free space, The number of coil turns. Where is the radius of the coil.

[0060] In some implementations, in In this posture, targeting the target frequency Excitation magnetic field reference vector The calculation formula is as follows:

[0061] ,

[0062] In the formula, The constant of the Helmholtz coil is . The excitation current is a complex vector. In order to be in The directional projection vector under the next attitude.

[0063] In some implementations, ideally, the three-component coil only measures the magnetic field along its own axis; however, in practice, the following errors exist: scale factor error. (Error between the actual sensitivity and nominal value of the three-component coil), non-orthogonality error (the three axes of the three-component coil are not physically perfectly perpendicular, and the three-component coils will couple with each other), bias error (From environmental noise or zero-point drift of the circuit). Therefore, for in In this posture, targeting the target frequency A linear model between the measured values and the true values is established as follows:

[0064] ,

[0065] wherein, is the observed value, represents the actual measured and demodulated complex voltage vector of the three-axis at the target frequency , , , , , is the actual measured and demodulated complex voltage vector of the x-axis, is the actual measured and demodulated complex voltage vector of the y-axis, is the actual measured and demodulated complex voltage vector of the z-axis, is the actual measured and demodulated complex voltage vector of the x-axis; is the actual measured and demodulated complex voltage vector of the y-axis; is the actual measured and demodulated complex voltage vector of the z-axis; is the calibration matrix, , diagonal elements respectively represent the scale factor errors between the three axes, , , non-diagonal elements represent the non-orthogonal errors between the three axes; , , ; is the reference vector of the excitation magnetic field, represents the theoretically induced magnetic field component value of the three-axis at the target frequency , , , , , is the theoretically induced magnetic field component value of the x-axis, is the theoretically induced magnetic field component value of the y-axis, is the theoretically induced magnetic field component value of the z-axis, is the theoretically induced magnetic field component value of the x-axis; is the theoretically induced magnetic field component value of the y-axis; is the theoretically induced magnetic field component value of the z-axis; , , and are the bias errors of the three-axis respectively. , ,

[0066] ​In some implementations, the bias error is obtained by cutting off the Helmholtz coil current and acquiring the output voltage of the three-component coil. That is, before applying the excitation magnetic field, the Helmholtz coil current is cut off, the output voltage of the three-component coil is acquired, and the bias vector is directly measured.

[0067] In some implementations, in order to obtain the optimal calibration matrix The objective function is constructed using the least squares method: , To optimize the instructions, the calibration matrix is ​​found through the optimization instructions. This minimizes the total sum.

[0068] In some implementations, in subsequent measurement experiments,

[0069] Measurement data obtained from three-component coil measurements By using the calibration model obtained from the solution, the corrected magnetic field data can be obtained. ,

[0070] ,

[0071] The corrected magnetic field data is obtained by removing the bias error from the product of the inverse of the calibration matrix and the measurement data.

[0072] like Figure 3 The figure shows a comparison of the distribution of magnetic field data before and after correction obtained using the method of this application. Figure 3 The original data is used to represent the magnetic field data before correction, and the calibration data is used to represent the magnetic field data after correction. It can be seen that the magnetic field data after correction is concentrated and relatively uniform, thus eliminating the interference of systematic errors.

[0073] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for calibrating a very low frequency three-component coil based on a frequency-sweep excitation, characterized in that, The method comprises the following steps: Obtaining time-domain signals of an alternating excitation current and a three-component coil, wherein the time-domain signals of the alternating excitation current and the three-component coil are obtained by using a programmable current source to output an alternating excitation current with a continuously changing frequency in a very low frequency range, and driving a Helmholtz coil to generate a time-varying swept-frequency magnetic field; under the driving of a magnetic turntable, the three-component coil is rotated to K postures in turn, and data collected synchronously at each posture is obtained; Performing frequency domain transformation on the time-domain signals to obtain a complex frequency domain response vector covering the swept-frequency range; Based on the complex frequency domain response vector measured at each posture and the calculated excitation magnetic field reference vector, a linear equation set describing the error of the coil system is constructed, and the linear equation set is solved by using a least square method to obtain a calibration matrix for correcting the measurement data. The measurement data of the three-component coil in a use state is corrected by using the calibration matrix.

2. The method of claim 1, wherein, The frequency domain transformation on the time-domain signals comprises the following steps: generating in-phase reference signals and quadrature reference signals with the same frequency as the excitation frequency, multiplying the collected time-domain signals respectively, and performing integral operation in an integral number of signal periods to obtain complex frequency domain responses representing amplitude and phase information.

3. The method of claim 1, wherein, The K postures comprise at least three linearly independent direction vectors.

4. The swept-frequency excitation-based very low frequency three-component coil calibration method according to claim 1, characterized in that The linear equation set is as follows: ， In the formula, For the observed values, , representing in Under the next attitude, targeting the target frequency Three-component coil , , The complex voltage vector obtained by actual measurement and demodulation along the three axes. for The complex voltage vector obtained by actual measurement and demodulation of the shaft. for The complex voltage vector obtained by actual measurement and demodulation of the shaft. for The complex voltage vector obtained by actual measurement and demodulation of the shaft; For calibration matrix, diagonal elements Represent , , Scale factor error between the three axes, off-diagonal elements represent , , Three-axis non-orthogonality error; To excite the magnetic field reference vector, , representing in Under the next attitude, targeting the target frequency Three-component coil , , The theoretically induced magnetic field components of the three axes. for Theoretically, the magnetic field components that the shaft should induce. for Theoretically, the magnetic field components that the shaft should induce. for The theoretically induced magnetic field component value of the shaft; , , and They are respectively , , Offset error of the three axes.

5. The method of claim 1, wherein, The calculation formula of the excitation magnetic field reference vector is as follows: ， wherein is the constant of the Helmholtz coil, is the complex vector of the excitation current, is the direction projection vector at the next attitude, , , are the constants of the Helmholtz coil and of the three-component coil, , , is the cosine of the angle between the axes, is the vacuum permeability, is the number of turns of the Helmholtz coil, is the radius of the Helmholtz coil.

6. The method of claim 4, wherein the method is a method of calibrating a very low frequency three-component coil based on a swept excitation, and wherein the method further comprises: The bias error is obtained by cutting off the Helmholtz coil current and collecting the output voltage of the three-component coil.

7. The method of claim 4, wherein the method is a method of calibrating a very low frequency three-component coil based on a swept excitation, and wherein the method further comprises: The least square method is used to solve the linear equation set, which comprises the following steps: The objective function is constructed by using the least square method, which is as follows: ， To optimize the instructions, the calibration matrix is found by optimizing the instructions to minimize the sum value.

8. The method of claim 1, wherein, The measurement data of the three-component coil in a use state is corrected by using the calibration matrix, which comprises the following steps: removing the bias error from the product of the inverse of the calibration matrix and the measurement data to obtain corrected magnetic field data.

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