Method for Suppressing and Evaluating Magnetic Interference Induced by Ocean Waves Based on Time-Series Matrix

Abstract

The present invention provides a method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrixization, including: reading the time series of marine geomagnetic fields; using a combination of variational mode decomposition and band-pass filtering to estimate noise; constructing a time series matrix and a noise matrix based on the phase space reconstruction matrixization method; performing MNF transformation on the data matrix; selecting high-order MNF components to reconstruct the noise matrix and inverse matrixize it to obtain the noise time series; performing band-pass filtering on the noise time series to extract ocean wave-induced magnetic noise to achieve signal-noise separation; evaluating the noise suppression effect based on the autocorrelation function; determining whether the requirements are met; and outputting the time series of the suppressed noise. The proposed interference suppression method provides an effective solution for suppressing noise that is aliased with the effective signal in the time domain and frequency domain, and improves the data signal-to-noise ratio. The noise suppression effect evaluation method based on the autocorrelation function can be used for measured data, and has a wider application range and practicality compared with traditional methods.

Description

Technical Field

[0001] The present invention relates to the technical field of marine geophysical signal processing, and specifically relates to a method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrixization. Background Art

[0002] Marine magnetotelluric sounding (MT) obtains the electrical property distribution of the seabed medium by observing the induced electromagnetic field generated by natural field sources on the seabed. It is an important geophysical means for studying the electrical structure of the oceanic crust and upper mantle and deep geological processes. In shallow water environments, the frequency range of the induced electromagnetic field interference generated by ocean wave motion overlaps with the frequency of MT signals, and it is not easy to separate it from MT signals in both the time domain and the frequency domain; the ocean wave-induced electromagnetic interference has strong energy, greatly reducing the signal-to-noise ratio of MT data, resulting in serious distortion of apparent resistivity and phase, and it is the main interference of shallow water MT data. Therefore, it is necessary to suppress the ocean wave-induced electromagnetic field to improve the signal-to-noise ratio of MT data in shallow water areas.

[0003] Traditional processing methods include wavelet transform, SVD decomposition, etc. Since noise and effective signals overlap in the time domain and frequency, the above methods are likely to damage the effective signals, resulting in unsatisfactory denoising effects. Yu Caixia et al. (2010) and Zhang Baoqiang (2018) respectively used EMD and wavelet threshold denoising methods to suppress ocean wave-induced magnetic noise in MT data. Such signal decomposition algorithms can effectively improve the apparent resistivity curve, but the correction effect of the phase curve is still not ideal enough. Feng Changqing et al. (2022) used the K-SVD dictionary learning algorithm to extract ocean wave-induced magnetic noise, and the improvement effect of apparent resistivity distortion is obvious, but the phase distortion still needs to be corrected twice by means of the corrected apparent resistivity, and the processing effect still needs to be further improved. In terms of evaluating the denoising effect, existing methods usually calculate indexes such as signal-to-noise ratio (SNR), root-mean-square error (RMSE), and correlation coefficient (CORC) in the time domain to evaluate the denoising effect (Wang et al., 2017; Feng Changqing et al., 2022). Such indexes need to be obtained by operating on the noise-free signal and the denoised signal. However, the noise-free signal of the measured data is unknown, so such indexes cannot be used to evaluate the denoising effect of the measured data. How to evaluate the application effect of the noise suppression method in the measured data has always been a hot issue discussed by geophysicists. Summary of the Invention

[0004] The object of the present invention is to provide a method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrixization, which can realize the matrixization of single-channel time series data, improve the signal-to-noise ratio of marine magnetotelluric data, and the proposed noise suppression effect evaluation method based on the autocorrelation function can be used to evaluate the application effect of ocean wave magnetic noise processing methods in measured data.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] 1. A method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrixization, comprising:

[0007] S1. Read the evaluation requirements and the original time series x(N) of the marine magnetotelluric field, where N is the number of data points;

[0008] S2. Use a method combining variational mode decomposition and band-pass filtering to estimate the noise of the time series x(N) to obtain the noise time series x n ;

[0009] S3. Based on the phase space reconstruction matrixization method, extract samples from the original time series x(N) as one-dimensional phase space vectors, and construct the original time series matrix X S :

[0010]

[0011] In the above formula, the number of rows m, the number of columns n of the matrix, and the time delay τ satisfy N = (m - 1)τ + n with respect to the total number of data points N of the time series. For the time delay τ, its value range is denotes rounding down;

[0012] S4. Matrixize the estimated noise time series x n to obtain the noise matrix X N ;

[0013] S5. Based on the original time series matrix X S and the noise matrix X N perform MNF transformation to obtain the MNF component Z;

[0014] S6. Based on the noise characteristics, select appropriate high-order MNF components to reconstruct the noise matrix

[0015] S7. Based on the time delay τ, perform inverse matrixization on the reconstructed noise matrix to obtain the extracted noise time series;

[0016] S8. Estimate the sea wave frequency band, perform band-pass filtering on the extracted noise time series, extract the sea wave-induced magnetic noise, and subtract the extracted sea wave-induced magnetic noise from the original time series;

[0017] S9. Calculate the autocorrelation function based on the time series after noise suppression, and evaluate the suppression effect of the sea wave-induced magnetic noise based on the autocorrelation function. The calculation method of the autocorrelation function is as follows:

[0018]

[0019] In the above formula, y t is the observed value of the time series at time t, is the average value of all observed values of the time series, k is the lag time, and its value range is [0, N - 1]. The autocorrelation function ACF refers to the sequence composed of the autocorrelation coefficients r k ;

[0020] S10. Judge whether the evaluation requirements are met based on the autocorrelation function. If met, turn to S11; if not, turn to S3.

[0021] S11. Output the magnetotelluric time series with suppressed noise.

[0022] Preferably, the calculation method of the MNF component Z is as follows:

[0023] Z = R T X S

[0024] In the formula, X S is the original time series matrix, and R T is the constructed rotation matrix calculated based on the noise matrix X N ;

[0025] Preferably, the calculation method of the reconstructed signal is as follows:

[0026]

[0027] In the formula, B is an m-row and m-column angular truncation matrix, which is represented as 1 on the corresponding rows of the MNF components participating in the reconstruction, and all other parts are 0.

[0028] Preferably, the calculation method for inverse matrix transformation of the reconstructed noise matrix is based on the time delay τ. The repeated data points of each sample in the data matrix are eliminated in sequence and spliced into a single-channel time series in sequence. Preferably, the noise suppression effect evaluation method based on the autocorrelation function can be applied to evaluate the suppression effect of signals with specific frequency characteristics in non-stationary signals, and can also be applied to the evaluation of measured data.

[0029] Compared with the prior art, in some embodiments of the present invention, the beneficial effects of the provided method are as follows:

[0030] The present invention mainly aims at the problem of strong interference caused by wave motion to MT magnetic field signals in marine magnetotelluric sounding, which leads to low signal-to-noise ratio of magnetotelluric data. A method for suppressing wave-induced magnetic interference based on time series matrixization is proposed. This method provides an effective technical solution for improving the signal-to-noise ratio of marine MT data in complex shallow water environments and can correct phase distortion more effectively. Compared with traditional magnetotelluric noise suppression methods, this method is based on the matrixization method of phase space reconstruction to realize the matrixization of single-channel time series, separates signals and noise through the minimum noise separation method, selects appropriate high-order MNF components based on noise characteristics to reconstruct the noise matrix, and obtains the extracted noise time series through inverse matrixization. The proposed method for suppressing wave magnetic interference provides an effective solution for suppressing noise that is aliased with effective signals in the time domain and frequency domain, and improves the signal-to-noise ratio of magnetotelluric data.

[0031] Aiming at the problem that common indicators cannot be used to evaluate the denoising effect of measured data, a method for evaluating the noise suppression effect based on the autocorrelation function is proposed. This method combines the non-stationary characteristics of MT signals and the periodicity of wave-induced magnetic noise, and uses the periodicity difference between the two to judge the signal-to-noise separation effect. The proposed method for evaluating the noise suppression effect based on the autocorrelation function does not require the known noise-free signal, and judges the denoising effect through the oscillation form of the curve. Compared with traditional evaluation methods, such indicators can be used to evaluate the denoising effect of measured data, improving the application scope and practicability of the evaluation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the following drawings are only partial embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0033] Figure 1 It is the program flow block diagram of the method of the present invention;

[0034] Figure 2 It is the schematic diagram of the one-dimensional geoelectric model structure;

[0035] Figure 3 It is the time series and power spectral density diagram before and after adding noise to the simulated MT data;

[0036] Figure 4 It is the time series and power spectral density diagram before and after denoising the simulated MT data;

[0037] Figure 5 It is the autocorrelation function diagram of the denoising effect of the simulated MT data;

[0038] Figure 6 To suppress the apparent resistivity and phase curves for interference. Specific embodiments

[0039] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clear, the following further describes the present invention in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0040] Embodiment 1

[0041] See Figure 1 , a method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrixization, comprising the following steps:

[0042] S1. Read the original time series x(N) of the marine geoelectric and geomagnetic fields, where N is the number of data, and read the evaluation criteria, i.e., the periodic feature threshold based on the autocorrelation function;

[0043] S2. Estimate the noise of the time series x(N) by using a method combining variational mode decomposition and band-pass filtering to obtain the noise time series x n ;

[0044] S3. Based on the phase space reconstruction matrixization method, extract samples from the original time series x(N) as one-dimensional phase space vectors to construct the original time series matrix X S :

[0045]

[0046] In the above formula, the number of rows m, the number of columns n of the matrix, and the time delay τ satisfy N=(m - 1)τ + n with the total number of data points N of the time series. For the time delay τ, its value range is denotes rounding down;

[0047] S4. Matrixize the estimated noise time series x n to obtain the noise matrix X N ;

[0048] S5. Perform MNF transformation based on the original time series matrix X S and the noise matrix X N to obtain the MNF component Z;

[0049] S6. Select appropriate high-order MNF components based on the noise characteristics to reconstruct the noise matrix

[0050] S7. Based on the time delay τ for the reconstructed noise matrix Perform inverse matrix transformation to obtain the extracted noise time series;

[0051] S8. Estimate the ocean wave frequency band, perform band-pass filtering on the extracted noise time series to extract the ocean wave-induced magnetic noise, and subtract the extracted ocean wave-induced magnetic noise from the original time series;

[0052] S9. Calculate the autocorrelation function based on the time series after suppressing the noise, and evaluate the suppression effect of the ocean wave-induced magnetic noise based on the autocorrelation function. The calculation method of the autocorrelation function is:

[0053]

[0054] In the above formula, y t is the observed value of the time series at time t, is the average value of all observed values of the time series, k is the lag time, and its value range is [0, N - 1]. The autocorrelation function ACF refers to the sequence composed of the autocorrelation coefficients r k ; if there is an influence of ocean wave-induced magnetic noise, the ACF curve of the MT time series shows certain periodic fluctuations; if the ocean wave-induced magnetic noise is suppressed, the periodic fluctuations in the ACF curve are reduced, showing a relatively smooth curve. Based on the above characteristics, ACF can be used to evaluate the denoising effect of the measured MT data;

[0055] S10. Judge whether the evaluation requirements are met based on the autocorrelation function. If they are met, turn to S11; if not, turn to S3;

[0056] S11. Output the magnetotelluric time series with suppressed noise.

[0057] Embodiment 2

[0058] Reference Figure 2 , is a one-dimensional geoelectric model diagram. To verify the feasibility of the proposed method for suppressing the measured ocean wave-induced magnetic interference in the present invention, the magnetic field simulated by the one-dimensional marine geoelectric model shown in Figure 2 is used as the effective magnetic signal, and the synthesized ocean wave-induced magnetic field is used as the noise and mixed into the effective signal to achieve the aliasing of the effective signal and the noise in the frequency band affected by the ocean wave-induced magnetic interference. The ocean wave-induced magnetic noise is simulated using the two-dimensional random ocean wave-induced magnetic field formula. Assuming that the ocean wave spectrum is the PM spectrum, the geomagnetic field intensity is 48000 nT, the thickness of the seawater layer is 25 m, the magnetic declination is 60°, the magnetic inclination is 45°, the resistivity of seawater is 0.3 Ω·m, and the wind speed is 13 m / s. The ocean wave-induced horizontal magnetic field time series with a sampling rate of 10 Hz and a duration of 1 h is simulated. The simulated ocean wave-induced magnetic noise is added to the simulated marine magnetotelluric component to obtain the synthesized MT data. Figure 3MT time series and power spectral density before and after adding noise. As can be seen from the figure, a strong energy anomaly bulge appears in the power spectral density of the MT data near 0.1 Hz after adding noise, and this anomaly is the sea wave induced magnetic noise. Figure 4 This is the denoising result of the method described in the present invention. As can be seen from the figure, the time series after MNF denoising has a high degree of fitting with the noise-free MT signal. MNF can suppress the sea wave induced magnetic noise while better protecting the MT signal, showing strong signal-to-noise separation ability.

[0059] Figure 5 This is the autocorrelation function ACF diagram for evaluating the denoising effect of synthetic MT data. This diagram shows the ACF curves of MT data and simulated sea wave induced magnetic noise before and after denoising. The dotted line in the figure indicates the lag time k at the peak of the ACF curve of the synthetic MT data before denoising. Given that the sampling rate f of the synthetic MT data is 10 Hz, the time interval Δt between the two peaks is calculated as Δt = Δk / f. As can be seen from the figure, the ACF curve of the simulated sea wave induced magnetic noise shows obvious periodic fluctuation characteristics, which are more obvious at small lag times, while the ACF curve of the noise-free MT signal is a smooth curve that decreases gently. Under the influence of the sea wave induced magnetic noise, the ACF curve of the synthetic MT data shows corresponding periodic fluctuation characteristics, and the period at which the peak appears is within the period range (6 - 16 s) of the sea wave induced magnetic noise. The ACF curve of the MNF processing result almost completely coincides with the ACF curve of the noise-free MT signal, and the periodic fluctuation characteristics disappear, indicating that MNF has less damage to the MT signal while suppressing the sea wave induced magnetic noise.

[0060] Perform Robust impedance estimation on the synthetic MT data before and after suppressing the sea wave induced magnetic noise, and calculate the apparent resistivity curve and phase curve as Figure 6 shown. As can be seen from the figure, for the synthetic MT data with added sea wave induced magnetic noise, its apparent resistivity and phase curves are distorted within the 6 - 16 s period range, significantly deviating from the true values. The apparent resistivity curve and phase curve obtained after MNF processing are smoother and more continuous, and are closer to the true values numerically in the frequency band affected by sea wave interference. The processing results of the simulation data show that the algorithm proposed in the present invention can effectively suppress the measured sea wave induced magnetic field aliased in the magnetic field component, and obtain more reliable apparent resistivity and phase curves by estimating the impedance. This also shows that the algorithm proposed in the present invention is effective.

[0061] 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 in the protection scope of the present invention.

Claims

1. A method for suppressing and evaluating sea wave-induced magnetic interference based on time series matrixization, characterized in that Including: S1. Read the evaluation requirements and the original time series x(N) of marine magnetotelluric fields, where N is the number of data; S2. Use the method of combining variational mode decomposition and band-pass filtering to estimate the noise of the time series x(N), and obtain the noise time series x n ; S3. Based on the phase space reconstruction matrix method, samples are extracted from the original time series x(N) as one-dimensional phase space vectors, and the original time series matrix X is constructed S : In the above formula, the number of rows \(m\), the number of columns \(n\) of the matrix, and the time delay \(\tau\) satisfy \(N=(m - 1)\tau + n\) with respect to the total number of data points \(N\) of the time series. For the time delay \(\tau\), its value range is which represents rounding down; S4. Matrixize the estimated noise time series x n to obtain a noise matrix X N ; S5. Based on the original time series matrix X S and the noise matrix X N perform the MNF transformation to obtain the MNF component Z; S6. Select appropriate high-order MNF components based on noise characteristics to reconstruct the noise matrix S7. Inverse matrix operation is performed on the reconstructed noise matrix based on the time delay τ to obtain the extracted noise time series; S8. Estimate the sea wave frequency band, perform band-pass filtering on the extracted noise time series, extract the sea wave induced magnetic noise, and subtract the extracted sea wave induced magnetic noise from the original time series; S9. Calculate the autocorrelation function based on the time series after noise suppression, and evaluate the suppression effect of the sea wave induced magnetic noise based on the autocorrelation function. The calculation method of the autocorrelation function is: In the above formula, y t is the observed value of the time series at time t, is the average value of all observed values of the time series, k is the lag time, and its value range is [0, N - 1]. The autocorrelation function ACF refers to the sequence composed of the autocorrelation coefficients r k ; S10. Judge whether the evaluation requirements are met based on the autocorrelation function. If met, go to S11; if not, go to S3; S11. Output the magnetotelluric time series with suppressed noise.

2. The method for suppressing and evaluating the magnetic interference induced by ocean waves based on time series matrix as claimed in claim 1, wherein The calculation method of the MNF component Z is: Z = R T X S Where, X S is the original time series matrix, and R T is the constructed rotation matrix calculated based on the noise matrix X N ​ 3. The method for suppressing and evaluating the magnetic interference induced by ocean waves based on time series matrix as claimed in claim 1, wherein Reconstructed signal The calculation method is as follows: In the formula, B is a corner truncation matrix of m rows and m columns, which is represented as 1 on the corresponding rows of the MNF components participating in the reconstruction, and all other parts are 0.

4. The method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrix as claimed in claim 1, wherein For reconstructing the noise matrix The calculation method for inverse matrix transformation is based on the time delay τ. Each sample's repeated data points in the data matrix are eliminated in sequence and then concatenated into a single-channel time series in sequence.

5. The method for suppressing and evaluating ocean wave-induced magnetic interference based on time series matrix as claimed in claim 1, wherein The noise suppression effect evaluation method based on the autocorrelation function can be applied to evaluate the suppression effect of signals with specific frequency characteristics in non-stationary signals, and can also be applied to the evaluation of measured data.

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