Very-low-frequency three-component coil calibration method based on frequency sweep excitation

Abstract

The invention belongs to the field of geophysical exploration, and particularly relates to a very-low-frequency three-component coil calibration method based on frequency sweep excitation, which comprises the following steps: acquiring an alternating-current excitation current and a time domain signal of a three-component coil, and performing frequency domain transformation on the time domain signal to obtain a plurality of frequency domain response vectors covering a frequency sweep range; constructing a linear equation set for describing a coil system error based on a plurality of frequency domain response vectors measured under each attitude and the calculated excitation magnetic field reference vector, and solving the linear equation set by using a least square method to obtain a calibration matrix for correcting measurement data; and the calibration matrix is adopted to correct the measurement data of the three-component coil in the use state, so that systematic errors of the very-low-frequency three-component coil can be accurately calibrated and calibrated, and the measurement precision and data reliability of a very-low-frequency electromagnetic method are effectively improved.

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 rotated to K postures under the driving of the non-magnetic turntable, and data is synchronously collected at each posture. The time-domain signal of the three-component coil is 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 the Helmholtz coil to generate a sweep frequency magnetic field changing with time. The time-domain signal is subjected to frequency domain transformation to obtain a complex frequency domain response vector covering the sweep 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 coil system error 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 the use state is corrected by using the calibration matrix.

[0008] 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 signals respectively, and performing integral operation in an integral number of signal periods to obtain a complex frequency domain response representing amplitude and phase information.

[0009] Further, the K postures comprise at least three linearly independent direction vectors.

[0010] Further, the linear equation set is: , 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 at the kth posture, , , , three-axis actually measured and demodulated complex voltage vector, is a complex voltage vector actually measured and demodulated by the three-component coil at the target frequency axis, is a complex voltage vector actually measured and demodulated by the three-component coil at the target frequency axis, is a complex voltage vector actually measured and demodulated by the three-component coil at the target frequency axis; is a calibration matrix, the diagonal elements respectively represent , , Scale factor errors between the three axes, off-diagonal elements represent , , Three-axis non-orthogonality errors is the excitation magnetic field reference vector, , represents the magnetic field induced in the three-axis sensor at the th attitude for the target frequency , the three-component coil , , The theoretically induced magnetic field component values for the three axes, is the theoretically induced magnetic field component value for the axis, is the theoretically induced magnetic field component value for the axis, is the theoretically induced magnetic field component value for the axis , , and are the bias errors for the three axes, , ,

[0011] Further, the excitation magnetic field reference vector is calculated as: , where, is the Helmholtz coil constant, is the excitation current complex vector, is the direction projection vector at the th attitude, , , are the Helmholtz coil and three-component coil , , cosine of the angle between the is the vacuum permeability, is the number of turns of the Helmholtz coil, is the radius of the Helmholtz coil.

[0012] Further, the bias errors are obtained by cutting off the Helmholtz coil current and collecting the output voltage of the three-component coil.

[0013] Further, the linear equations are solved using the least squares method, including: Constructing the least squares optimization problem as: , ​To optimize the instruction, find the calibration matrix through the optimization instruction , so as to minimize the sum value.

[0014] Further, the measurement data of the three-component coil in use is corrected by using the calibration matrix, including: removing the bias error from the product of the inverse of the calibration matrix and the measurement data to obtain corrected magnetic field data.

[0015] Compared with the prior art, the present application has at least the following beneficial effects: the present application can accurately calibrate and correct the systematic error of the very low frequency three-component coil, effectively improving the measurement accuracy and data reliability of the very low frequency electromagnetic method. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The structure schematic diagram of the device provided by the embodiment of the present application is shown in Figure 2 The calibration method flow chart of the very low frequency three-component coil provided by the embodiment of the present application is shown in Figure 3 The electromagnetic data space distribution schematic diagram before and after correction provided by the embodiment of the present application is shown in DETAILED DESCRIPTION

[0017] In order to make the purpose, technical scheme and advantages of the present application clearer, the present 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 present application and do not limit the present application.

[0018] Referring to Figure 1 , the device used in the method of the present application includes 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.

[0019] According to some embodiments of the present application, based on the device of Figure 1 , referring to Figure 2 , the present application provides a calibration method for a very low frequency three-component coil. The calibration method comprises: The time-domain signals of the three-component coil and the alternating excitation current are acquired, the time-domain signals of the three-component coil and the alternating excitation current are the alternating excitation current with a continuously changing frequency in a very low frequency range output by a programmable current source, and the Helmholtz coil 1 is driven to generate a sweep magnetic field changing with time; the very low frequency range refers to the alternating excitation current with a frequency range of 3 kHz to 30 kHz; Under the drive of the non-magnetic turntable 2, the three-component coil is sequentially rotated to K postures, and the time-domain signals of the three-component coil and the alternating excitation current are synchronously acquired while the three-component coil is kept stable at each posture, the time-domain signals including time-domain voltage signals and time-domain current signals; The time-domain signals are subjected to frequency domain transformation to obtain the frequency-domain signals covering the sweep range; Based on the complex frequency-domain response vectors measured at each posture and the excitation magnetic field reference vectors calculated, a linear equation set describing the error of the coil system 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 of the three-component coil in use; The measurement data of the three-component coil in use is corrected by using the calibration matrix.

[0020] In some embodiments, the plurality of postures includes at least three linearly independent direction vectors, linear independence refers to a set of direction vectors is 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: Posture one: the main direction of the axis of the three-component coil is parallel to the direction of the magnetic field generated by the Helmholtz coil; Posture two: the main direction of the axis of the three-component coil is parallel to the direction of the magnetic field generated by the Helmholtz coil; Posture three: the main direction of the axis of the three-component coil is parallel to the direction of the magnetic field generated by the Helmholtz coil; And an intermediate angle is added to the above orthogonal angles, a total of K (K is greater than or equal to 3) angles.

[0021] In some embodiments, the direction projection vector at the first posture is defined as : = , wherein , , are the cosine values of the included angles between the Helmholtz coil and the three-component coil , , axis.

[0022] In some implementations, in When remaining stationary in the sub-attitude state, two signals are simultaneously acquired via the data acquisition module: The first path is the alternating current excitation current flowing through the Helmholtz coil. ; The second path is the three-channel induced voltage signal output by the three-component coil, which is the time-domain signal of the three-component coil.

[0023] In some implementations, in order to obtain the target frequency point To obtain the amplitude and phase information, the acquired time-domain signal needs to undergo frequency-domain transformation. This includes generating in-phase and quadrature reference signals with the same frequency as the excitation frequency, multiplying them by the acquired time-domain signal, and integrating them over an integer number of signal periods to obtain the complex-form frequency-domain response representing the amplitude and phase information. Specifically, digital synchronous demodulation is used, and the specific method is as follows: For the target frequency Time-domain voltage signal acquired Multiply by the in-phase reference signal respectively Orthogonal reference signal and in an integer number of periods ( , It is a positive integer. Integrate within ) , , This yields the complex form of the frequency domain response representing the voltage amplitude and phase information. , The real part of the voltage frequency domain response, It is the imaginary part of the voltage frequency domain response.

[0024] 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 ) , , 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.

[0025] In some implementations, for a standard Helmholtz coil, the Helmholtz coil constant is... The calculation formula is as follows: , In the formula, The permeability of free space, The number of coil turns. Where is the radius of the coil.

[0026] In some implementations, in In this posture, targeting the target frequency Excitation magnetic field reference vector The calculation formula is as follows: , 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.

[0027] 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 Establish the following linear model to describe the relationship between the measured value and the true value: , 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.

[0028] 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.

[0029] 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.

[0030] In some implementations, in subsequent measurement experiments, 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. , , 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.

[0031] like Figure 3The 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.

[0032] 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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