CN110221349B - A Noise Reduction Method for Transient Electromagnetic Signals Based on Wavelet Transform and Sine Wave Estimation - Google Patents

Abstract

The invention discloses a transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation. Perform wavelet denoising processing to obtain the signal after wavelet denoising; (3) Invert the signal after wavelet denoising, intercept the front part of the inverted signal as a part of the sine wave interference signal, and apply zero padding or zero-filling to this part of the signal. The interpolation technique is extended, and then FFT transform is performed; (4) Estimate the amplitude, phase and frequency of the sine wave signal; (5) Calculate the entire estimated sine wave interference signal; (6) Use the inverted signal to subtract the estimate The sine wave interference signal, and then invert the subtracted signal to obtain a transient electromagnetic signal. The present invention can effectively improve the signal-to-noise ratio of transient electromagnetic signals in a complex environment including white noise and power frequency interference.

Description

A Noise Reduction Method for Transient Electromagnetic Signals Based on Wavelet Transform and Sine Wave Estimation

technical field

The invention relates to the technical field of transient electromagnetic signal processing, in particular to a transient electromagnetic noise reduction method based on wavelet transform and sine wave estimation.

Background technique

As a powerful means of underground exploration, transient electromagnetic signals are easily interfered by the internal noise and power frequency noise from the acquisition instruments during the acquisition process, which often lead to the weak transient electromagnetic signals being severely interfered in the middle and late stages and cannot be used. Therefore, it is very necessary to find a suitable denoising method to improve the signal-to-noise ratio of transient electromagnetic signals under complex background noise.

Commonly used methods to remove transient electromagnetic signal noise include superposition average method, notch method, wavelet denoising method, etc. Among these methods, superposition average method and wavelet method can effectively eliminate the interference of white noise, but for power frequency interference and Sine wave interference has no effect; the notch method has a suppressing effect on power frequency noise, which is equivalent to a very narrow narrowband filter, but the signal near the specified frequency point will be suppressed, which inevitably introduces distortion.

SUMMARY OF THE INVENTION

In view of the deficiencies of the prior art, the technical problem solved by the present invention is how to remove the white noise and sinusoidal interference contained in the transient electromagnetic signal (set the noise components as white noise and sinusoidal interference signals).

In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is a method for noise reduction of transient electromagnetic signals based on wavelet transform and sine wave estimation, comprising the following steps:

(1) Select the wavelet basis function to perform wavelet transform on the noisy transient electromagnetic signal. The specific process is as follows:

Set the noise components as white noise and sinusoidal interference signal, and the frequency of sinusoidal interference signal is 50Hz, then:

The decomposition formula of Mallat orthogonal wavelet transform of sampling discrete signal x _n , 0≤n≤N-1 can be expressed as:

where c _{j, k} are called scale coefficients, d _jk are called wavelet coefficients, h(n) is a finite-length low-pass filter, g(n) is a finite-length high-pass filter, n=0,...,N-1, The two are mutually orthogonal mirror filter banks, j (j=1, . . . , 5) is the number of decomposition layers, and N is the number of sampling points.

(2) Set an appropriate threshold for the wavelet coefficients and perform wavelet denoising processing to obtain the signal after wavelet denoising. The specific process is as follows:

(1) Select the soft threshold function to process the signal;

(2) Adaptive threshold selection heuristic threshold;

(3) The threshold value selected by each layer does not need to be readjusted;

(4) Perform inverse wavelet transform on the threshold quantized signal and reconstruct the inversely transformed coefficients.

(3) Invert the signal after wavelet denoising, intercept the front part of the inverted signal as a part of the sine wave interference signal, apply zero-filling technology to this part of the signal to extend, and perform FFT transformation on it; the specific process is as follows:

Invert the transient electromagnetic signal after wavelet transform denoising, the first half of the inverted signal corresponds to the late data of the transient electromagnetic signal, the late signal is completely submerged by noise, and it is regarded as the noise estimation of the sine wave interference signal part, denoted as d(k)(k=0,1,...,M-1), the length is M; considering to improve the frequency resolution, apply zero-filling technology to this part of the signal to extend, that is, after d(k) Fill with zeros, let the length of d(k) reach K (K≥M, K=M is the case without extension), and perform K-point FFT transformation to obtain: D(l), l=0,1,...,K -1.

(4) According to the result of FFT transformation, the amplitude, phase and frequency of the sine wave signal are estimated. The specific process is as follows:

According to the obtained D(l) signal, in the first K/2 points, find the maximum amplitude point _l0 in the frequency domain as the corresponding sine wave interference frequency point, and estimate the amplitude of the sine wave interference to be 2|D( l ₀ )|/K, the phase is estimated as arg[D(l ₀ )], and the frequency is estimated as l ₀ f _s /K, where f _s is the sampling frequency of the TEM signal.

(5) Calculate the estimated sine wave interference signal according to the amplitude, phase and frequency of the estimated sine wave interference signal. The specific process is as follows:

表示为：

The estimated interfering signal is based on the estimated amplitude, phase and frequency of the sinusoidal interfering signal

Expressed as:

(6) Subtract the estimated interference signal from the inverted signal, and then invert the signal to obtain the noise-removed transient electromagnetic signal. The specific process is as follows:

并将其反转，就得到去除白噪声和正弦波干扰后的瞬变电磁信号。Subtract the estimated interference signal from the inverted signal

And invert it to get the transient electromagnetic signal after removing white noise and sine wave interference.

Compared with the prior art, the present invention can effectively improve the signal-to-noise ratio of transient electromagnetic signals in a complex environment including power frequency interference and white noise.

Description of drawings

Fig. 1 is the schematic flow chart of the present invention;

Figure 2 is a noisy transient electromagnetic signal with power frequency interference and white noise added;

Fig. 3 is the transient electromagnetic signal that eliminates white noise by wavelet transform;

Fig. 4 is used to estimate the signal of power frequency noise;

Figure 5 is a comparison diagram of the estimated sine wave interference signal and the actual noise signal;

Figure 6 is a comparison diagram of the final noise reduction signal and the pure signal.

Detailed ways

The specific embodiments of the present invention are further described below with reference to the accompanying drawings, but the present invention is not limited.

Figure 1 shows a transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation, which includes the following steps:

(1) Select the wavelet basis function to perform wavelet transform on the noisy transient electromagnetic signal. The specific process is as follows: Set the noise components as white noise and 50Hz sinusoidal interference, as shown in Figure 2, then:

The decomposition formula of Mallat orthogonal wavelet transform of sampling discrete signal x _n , 0≤n≤N-1 can be expressed as:

where c _{j, k} are called scale coefficients, d _jk are called wavelet coefficients, h(n) is a finite-length low-pass filter, g(n) is a finite-length high-pass filter, n=0,...,N-1, The two are mutually orthogonal mirror filter banks, j (j=1, . . . , 5) is the number of decomposition layers, and N is the number of sampling points.

(2) Set an appropriate threshold for the wavelet coefficients, perform threshold denoising, and obtain the signal after wavelet denoising. The specific process is as follows:

(1) Select the soft threshold function to process the signal;

The variance of the wavelet coefficients in the interval [-3*sigma, 3*sigma] is mostly noise variance, and the variance beyond this range is a useful signal variance. The processing method of hard threshold is to set all variances in the interval to 0, that is, The part whose modulus is less than 3*sigma is cut off, and the processing method of soft threshold is to set the value in the interval to 0, and the part whose modulus value is greater than 3*sigma is uniformly subtracted by 3*sigma, and the part less than -3*sigma is uniformly added. on 3*sigma. Compared with the hard threshold, the soft threshold processing method makes the wavelet coefficients smoother in the wavelet domain;

(2) Adaptive threshold selection heuristic threshold;

(3) The threshold value selected by each layer does not need to be readjusted;

(4) Perform wavelet inverse transformation on the coefficients after threshold denoising and reconstruct the inversely transformed coefficients, as shown in FIG. 3 .

(3) Invert the signal after wavelet denoising, intercept the front part of the inverted signal as a part of the sine wave interference signal, as shown in Figure 4, apply zero-filling technology to this part of the signal to extend, and perform FFT transformation, The specific process is as follows:

Invert the transient electromagnetic signal after wavelet transform denoising, the first half of the inverted signal corresponds to the late data of the transient electromagnetic signal, the late signal is completely submerged by noise, and it is regarded as the noise estimation of the sine wave interference signal part, denoted as d(k), and the length is M; considering to improve the frequency resolution, apply zero-padding technique to this part of the signal to extend, that is, pad d(k) with zeros, so that the length of d(k) reaches K(K ≥M, K=M is the case of no extension), and K-point FFT transformation is performed to obtain: D(l), l=0, 1, ..., K-1.

(4) According to the result of FFT transformation, the amplitude, phase and frequency of the sinusoidal signal are estimated. The specific process is as follows:

According to the obtained D(l) signal, in the first K/2 points, find the maximum amplitude point _l0 in the frequency domain as the corresponding 50Hz frequency point, and estimate the amplitude of the sine wave interference to be 2|D( _l0 )|/K, the phase is estimated as arg[D(l ₀ )], and the frequency is estimated as l ₀ f _s /K, where f _s is the sampling frequency of the TEM signal.

(5) Calculate the estimated sine wave interference signal according to the estimated amplitude, phase and frequency of the sine wave signal, as shown in Figure 5. The specific process is as follows:

表示为：

k＝0,1,…,N-1，其中N为含噪瞬变电磁信号的长度。Calculate the entire estimated sine wave interference signal according to the amplitude, phase and frequency of the estimated sine wave signal

Expressed as:

k=0,1,...,N-1, where N is the length of the noisy transient electromagnetic signal.

(6) Subtract the estimated interference signal from the inverted signal, and invert it to obtain the transient electromagnetic signal with sinusoidal interference removed, as shown in Figure 6. The specific process is as follows:

并将其反转，就得到去除白噪声和正弦波干扰后的瞬变电磁信号。Subtract the estimated interference signal from the inverted signal

And invert it to get the transient electromagnetic signal after removing white noise and sine wave interference.

The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principle and spirit of the present invention, various changes, modifications, substitutions and alterations to these embodiments still fall within the protection scope of the present invention.

Claims (7)

1. a transient electromagnetic signal noise reduction method based on wavelet transformation and sine wave estimation, is characterized in that, comprises the following steps: (1) Selecting the wavelet basis function to perform wavelet transform on the noisy transient electromagnetic signal; (2) Setting appropriate thresholds for the wavelet coefficients, and performing wavelet denoising processing to obtain the signal after wavelet denoising; (3) Invert the signal after wavelet denoising, intercept the front part of the inverted signal as a part of the sine wave interference signal, apply zero-filling technology to this part of the signal to extend, and perform FFT transformation on it; (4) Estimate the amplitude, phase and frequency of the sine wave signal according to the result of the FFT transformation; (5) Calculate the entire estimated sine wave interference signal according to the estimated amplitude, phase and frequency of the sine wave signal; (6) Subtract the estimated sine wave interference signal from the inversion signal, and then invert the subtracted signal to obtain the transient electromagnetic signal after reducing the influence of white noise and sine wave interference. 2. the transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation according to claim 1, is characterized in that, the concrete process of described step (1) is as follows: Set the noise components as white noise and sine wave interference, then: The decomposition formula of Mallat orthogonal wavelet transform of sampling discrete signal x _n , 0≤n≤N-1 can be expressed as:

where c _{j, k} are called scale coefficients, d _jk are called wavelet coefficients, h(n) is a finite-length low-pass filter, g(n) is a finite-length high-pass filter, n=0,...,N-1, The two are mutually orthogonal mirror filter banks, j is the number of decomposition layers, j=1,...,5, N is the number of sampling points. 3. the transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation according to claim 1, is characterized in that, the concrete process of described step (2) is as follows: (1) Select a soft threshold function to process the wavelet coefficients; (2) Adaptive threshold selection heuristic threshold; (3) The threshold value selected by each layer does not need to be readjusted; (4) Perform inverse wavelet transform on the threshold quantized wavelet coefficients and reconstruct the inversely transformed coefficients. 4. the transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation according to claim 1, is characterized in that, the concrete process of described step (3) is as follows: Invert the transient electromagnetic signal after wavelet transform denoising, the front part of the inverted signal corresponds to the late data of the transient electromagnetic signal, the late signal is completely submerged by noise, and it is regarded as the noise estimation of the sine wave interference signal part, denoted as d(k), where k=0,1,...,M-1, and the length is M; considering to improve the frequency resolution, apply zero-filling technology to this part of the signal to extend, that is, after d(k) Fill with zeros to make the length of d(k) reach K, where K≥M, K=M is the case of no extension, and perform K-point FFT transformation to obtain: D(l), l=0,1,...,K -1. 5. the transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation according to claim 4, is characterized in that, the concrete process of described step (four) is as follows: According to the obtained frequency domain signal D(l), l=0,1,...,K-1, K is the length of the frequency domain signal D(l), in the first K/2 points, find out the frequency domain amplitude The maximum point l ₀ is used as the corresponding sine wave interference frequency point, and the estimated amplitude of the sine wave interference is 2|D(l ₀ )|/K, the phase is estimated as arg[D(l ₀ )], and the frequency is estimated as l ₀ f _s /K, where f _s is the sampling frequency of the TEM signal. 6. The transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation according to claim 5, is characterized in that, the concrete process of described step (5) is as follows: According to the estimated amplitude, phase and frequency of the sine wave signal, the estimated sine wave interference signal is obtained

Expressed as:

where N is the length of the noisy transient electromagnetic signal. 7. The transient electromagnetic signal noise reduction method based on wavelet transform and sine wave estimation according to claim 1, is characterized in that, the concrete process of described step (six) is as follows: Subtract the estimated sine wave interference signal from the inverted signal

And invert it to get the transient electromagnetic signal after removing white noise and sine wave interference.

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