CN110531420A - The lossless separation method of industry disturbance noise in a kind of seismic data - Google Patents

Abstract

The invention discloses a method for non-destructive separation of industrial interference noise in seismic data. Continuous wavelet transform and discrete cosine transform are selected as dictionaries that sparsely represent effective signals and industrial interference noise in seismic data respectively, and form a pair of super-complete dictionaries; then read Take single-trace seismic data, and calculate the normalized amplitude spectrum kurtosis, set a threshold, greater than the threshold, it is considered that there is industrial interference noise in the seismic data; for the determined single-trace seismic data that needs to be separated from industrial interference noise, use block The coordinate relaxation algorithm separates the effective signal and the industrial interference noise, and achieves the purpose of non-destructive separation of the industrial interference noise in the seismic data; repeat the above steps until the processing of all trace data is completed. The invention can effectively separate the industrial interference noise in the seismic data, hardly cause damage to the effective signal, and has high calculation efficiency.

Description

A Non-destructive Separation Method of Industrial Interference Noise in Seismic Data

technical field

The invention belongs to the technical field of seismic exploration data processing, in particular to a method for non-destructive separation of industrial interference noise in seismic data.

Background technique

In the process of deep coal and oil and gas exploration using seismic technology, due to the dense distribution of transmission lines and acquisition equipment in the deep mining area, strong industrial electrical interference near 50 Hz and its frequency multiplier components can be generated, which seriously affects the recorded seismic data The signal-to-noise ratio cannot meet the current industrial requirements for high-fidelity seismic data. Therefore, it is necessary to separate the industrial interference noise in the seismic data to improve the signal-to-noise ratio and fidelity of the seismic data. Due to the large amount of seismic record data, the industrial interference noise separation method needs to have faster computing efficiency.

At present, the frequency domain notch method used will damage the effective signal and easily produce boundary effects; while the receiver point domain separation method needs to transform the seismic data from the shot domain to the receiver point domain, and then transform the seismic data from the shot domain to the common receiver point Domain, repeated channel extraction wastes a lot of time and disk space, and the efficiency is low.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for non-destructive separation of industrial interference noise in seismic data in view of the deficiencies in the prior art above. The super-complete dictionary can perform non-destructive separation of industrial interference noise for single-channel seismic data with industrial interference noise reaching a certain intensity, saving time and high efficiency.

The present invention adopts following technical scheme:

A method for non-destructive separation of industrial interference noise in seismic data, comprising the following steps:

S1. Select continuous wavelet transform and discrete cosine transform as dictionaries that sparsely represent effective signals and industrial interference noise in seismic data respectively, and form a pair of over-complete dictionaries;

S2. Read the single-trace seismic data and calculate the normalized amplitude spectrum kurtosis P, when it is greater than the set threshold It is considered that there is industrial interference noise in the seismic data;

S3. Using the block coordinate relaxation algorithm to separate the single-trace seismic data of the industrial interference noise to be separated determined in step S2, and separate the effective signals and industrial interference noise of all trace data, so as to realize the lossless separation of the industrial interference noise in the seismic data.

Specifically, in step S1, use the selected dictionary A1, which is continuous wavelet transform, and A2, which is global discrete cosine transform, to form _a set of over _- complete dictionaries, sparsely represent the signal s, and calculate the sparse representation coefficients:

s=s ₁ +s ₂

Among them, x ₁ is the part corresponding to A ₁ in the reconstruction coefficient; x ₂ is the part corresponding to A ₂ in the reconstruction coefficient; is the Lagrangian multiplier; s ₁ and s ₂ are the effective signal and industrial interference noise in the seismic data respectively;

The continuous wavelet transform is selected as the dictionary to sparsely represent the effective signals in the seismic data, and the continuous wavelet transform is:

Among them, WT _x (a,τ) is the continuous wavelet transform coefficient of the signal to be analyzed, a represents the scale factor, x(t) represents the signal to be analyzed, ψ(t) represents the Morlet mother wavelet, t is time, and τ is the translation amount , * means conjugation;

The inverse of the continuous wavelet transform is:

Among them, the constant C _Ψ < ∞ is its allowable condition;

Construct the global discrete cosine transform as a dictionary that sparsely represents the coupling noise of the optical cable, and the global discrete cosine transform is:

Wherein, DCT(u) represents the global discrete cosine transform coefficient of the signal to be analyzed, x[n] represents the signal to be analyzed, u=1,2,...,N-1, N is the data sampling point length;

The inverse of the global discrete cosine transform is:

Among them, n=0...N-1.

Specifically, in step S2, the normalized amplitude spectrum kurtosis P is:

Among them, V is the normalized amplitude spectrum variance, Y[k] is the normalized discrete sampling value in the frequency domain, is the mean value of Y[k], and N is the number of discrete sampling points in the frequency domain;

The discrete single-channel data sampling point value is recorded as x[n], X[k] is the discrete Fourier transform of x[n], and the single-channel seismic data is transformed from the time domain to the frequency domain, using fast Fourier transform to find discrete frequency values:

X[k]=DFT(x[n])

Suppose ω _k is the discrete frequency of the kth point of the spectrum:

Among them, dt is the sampling interval, then is the sampling frequency, the sampling frequency is recorded as f _N , and half of the sampling frequency is recorded as f _N/2 ;

The normalized discrete sampling value Y[k] in the frequency domain is:

Y[k]=X[k]/m

The maximum value m of the absolute value of the discrete sampling value of the amplitude spectrum is:

m=max(abs(X[k])

The normalized amplitude spectrum variance V is:

in, The mean of Y[k] is:

.

Specifically, in step S3, the block coordinate relaxation algorithm is specifically:

First initialize the number of iteration steps k=0, the initial solution Indicates that signal component 1 is the coefficient initial solution of the effective signal, Represents the initial solution of the coefficient of the signal component 2, namely the industrial interference noise;

Each iteration k increases by 1, and calculates and

when When it is less than the preset value, the impact of continuing iteration on the result is small enough, and the iteration terminates; output: is the transform coefficient of the separated signal component 1, is the transform coefficient of the separated signal component 2.

further, and Specifically:

Among them, T _λ is a hard threshold function; and A ₁ form a pair of positive and negative transformations, and A ₂ form a pair of positive and negative transformations.

Compared with the prior art, the present invention has at least the following beneficial effects:

The invention discloses a method for non-destructive separation of industrial interference noise in seismic data. The dictionary is sparsely selected to represent the effective signal and industrial interference noise, and the signal-noise separation can be directly performed through the block coordinate relaxation algorithm. The method is simple, and the algorithm program does not require additional attachment conditions; Fast Fourier transform has high calculation efficiency; and the disturbance of the frequency point of industrial interference noise will not affect the present invention, and lossless separation can still be realized; by first judging the intensity of industrial interference noise, the weaker single channel of industrial interference noise The data is not processed, which can save the running time of the algorithm.

Further, the fact that a signal can be sparsely represented means that the signal can be represented by as few transform coefficients as possible, that is, the signal can be represented by a linear combination of as few transform atoms as possible. According to the theory of morphological component analysis, select a dictionary that can sparsely represent each component in a complex signal, and form a set of over-complete dictionaries to achieve a more sparse representation of complex signals, and achieve signal-to-noise separation by solving the sparse optimization formula, which can be used for suppressing noise in seismic records. It is very important to select dictionaries that can sparsely represent the effective signal and industrial interference noise respectively, and the selection can be made according to the difference in morphological characteristics of the effective signal and industrial interference noise. Based on the differences in waveform morphological characteristics, continuous wavelet transform is selected to represent effective signals sparsely, and discrete cosine transform is selected to represent industrial interference noise sparsely.

Further, calculating the normalized amplitude spectrum kurtosis of the single-channel data can measure the strength of the industrial interference noise contained in the data. If the industrial interference noise is strong, proceed to step S3 for noise lossless separation. If the industrial noise Weaker, that is, it is considered that the noise does not constitute substantial interference to the effective signal, so step S3 does not need to be performed, which can save computing time. In step S2, a threshold value of normalized amplitude spectrum kurtosis is set, and when it is greater than this threshold value, it is considered that the industrial interference noise is strong, and step S3 needs to be performed for lossless separation.

Furthermore, the morphological component analysis based on signal sparse representation theory is a method to solve the problem of multi-component separation of image or seismic signal. The core idea of the Block Coordinate Relaxation (BCR) algorithm is to set a reasonable threshold strategy, and alternately update the sparse coefficients in each iteration until the iteration termination condition is reached, so as to separate the two kinds of signals from the mixed signal. The target of the signal component.

To sum up, the present invention can effectively separate the industrial interference noise in the seismic data, and at the same time hardly cause damage to the effective signal, and has high calculation efficiency.

The technical solutions of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

Description of drawings

Figure 1 is the seismic data containing industrial interference noise;

Fig. 2 is the data analysis diagram of the 30th trace in the seismic data in Fig. 1, where (a) is the waveform diagram of the 30th trace data, (b) is the normalized amplitude spectrum of the 30th trace data, and (c) is the 30th trace data The time spectrum of the channel data;

Fig. 3 is the data analysis diagram of the 64th trace in the seismic data in Fig. 1, where (a) is the waveform diagram of the 64th trace data, (b) is the normalized amplitude spectrum of the 64th trace data, and (c) is the 64th trace data The time spectrum of the channel data;

Fig. 4 is a schematic diagram of atoms, wherein (a) is a schematic diagram of continuous wavelet transform atoms, and (b) is a schematic diagram of discrete cosine transform atoms;

Fig. 5 is the normalized amplitude spectrum kurtosis of each record of seismic data shown in Fig. 1;

Figure 6 is the seismic data map of interference noise, where (a) is the seismic data containing industrial interference noise, (b) is the seismic data after using this method to separate industrial interference noise without loss, and (c) is the industrial interference separated by this method noise;

Fig. 7 is the waveform diagram of the 88th track data extracted from the seismic data in Fig. 6, wherein (a) is the seismic data containing industrial interference noise, (b) is the seismic data after using this method to non-destructively separate industrial interference noise, and (c) is Industrial interference noise separated by this method;

Fig. 8 is the normalized amplitude spectrum magnitude of the 88th track data extracted from the seismic data in Fig. 6, wherein (a) is the seismic data containing industrial interference noise, (b) is the seismic data after using this method to non-destructively separate the industrial interference noise, (c) It is the industrial interference noise separated by this method;

Fig. 9 is the time-frequency diagram of the 88th channel data extracted from the seismic data in Fig. 6, where (a) is the seismic data containing industrial interference noise, (b) is the seismic data after using this method to non-destructively separate industrial interference noise, (c) Industrial interference noise separated by this method;

Fig. 10 is a flowchart of the patented method.

Detailed ways

The invention provides a method for non-destructive separation of industrial interference noise in seismic data. A set of over-complete dictionaries is formed by selecting dictionaries that can sparsely represent effective signals and industrial interference noise respectively, and can be used for single-channel seismic data with industrial interference noise reaching a certain intensity. Block coordinate relaxation algorithm for lossless separation of industrial interference noise.

Please refer to Fig. 10, a method for non-destructive separation of industrial interference noise in seismic data of the present invention, comprising the following steps:

S1. Select continuous wavelet transform and discrete cosine transform as dictionaries that sparsely represent effective signals and industrial interference noise in seismic data respectively, and form a pair of over-complete dictionaries;

Specifically:

The object of morphological component analysis is to contain two components with different waveform morphological characteristics:

s=s ₁ +s ₂

Among them, s represents the signal to be analyzed, that is, seismic data, and s ₁ and s ₂ represent two components in the signal, which are the effective signal and industrial interference noise in the seismic data, respectively, and have different waveform characteristics. The goal of morphological component analysis is to extract two components, s ₁ and s ₂ , respectively. Assume that _s1 and _s2 can be efficiently and _sparsely represented by dictionaries A1 and A2 respectively, but the _sparse representation _{of s1} by A2 and the sparse representation _{of s2} by A1 are poor.

Figure 1 is the seismic data containing industrial interference noise, a total of 192 channels, the sampling length is 6s, and the sampling interval is 1ms. It can be seen that the seismic data is interfered by industrial interference noise, and part of the event is covered, which reduces the signal to noise of the data. ratio, which affects the imaging analysis of seismic data.

From the seismic data shown in Figure 1, the 30th track data that almost does not contain industrial interference noise is extracted, and its waveform diagram, normalized amplitude spectrum, and time spectrum are shown in Figure 2(a), Figure 2(b), and Figure 2(c ) is shown in Figure 1; the 64th channel data containing strong industrial interference noise is extracted from the seismic data shown in Figure 1, and its waveform diagram, normalized amplitude spectrum, and time spectrum are shown in Figure 3(a), Figure 3(b), Figure 3(c) shows. It can be seen that the industrial interference noise data shows a single peak shape on the amplitude spectrum, and a horizontal straight line on the time spectrum, and the frequency is concentrated around 50Hz, because the frequency of industrial AC is 50Hz. However, the industrial interference noise of seismic data is not limited to a frequency point of 50 Hz, and may also be concentrated in frequency points such as 100 Hz, 150 Hz, and 250 Hz. In addition, industrial interference noise may not be exactly 50Hz, and its frequency point is disturbed around 50Hz.

Figure 4(a) and Figure 4(b) are schematic diagrams of continuous wavelet transform and discrete cosine transform atoms respectively. Comparing Figure 2(a) and Figure 3(a), it can be seen that the effective signal waveform diagram and continuous wavelet transform atom Relatively similar, industrial interference noise waveforms are relatively similar to discrete cosine transform atoms. Therefore, the present invention selects continuous wavelet transform to sparsely represent effective signals, and discrete cosine transform to represent industrial interference noise sparsely.

The continuous wavelet transform is chosen as the dictionary to sparsely represent the valid signals in the seismic data, where the continuous wavelet transform is:

Among them, WT _x (a,τ) is the continuous wavelet transform coefficient of the signal to be analyzed, a represents the scale factor, x(t) represents the signal to be analyzed, ψ(t) represents the Morlet mother wavelet, t is time, and τ is the translation amount , * indicates conjugation.

The inverse of the continuous wavelet transform is:

Among them, the constant C _Ψ <∞ is its allowable condition.

Construct the global discrete cosine transform as a dictionary that sparsely represents the fiber optic coupling noise, where the global discrete cosine transform is:

Among them, DCT(u) represents the global discrete cosine transform coefficient of the signal to be analyzed, x[n] represents the signal to be analyzed, u=1,2,...,N-1, and N is the length of data sampling points.

The inverse of the global discrete cosine transform is:

Among them, n=0...N-1.

Using the selected dictionary A ₁ is the continuous wavelet transform and A ₂ is the global discrete cosine transform to form a set of over-complete dictionaries, sparsely represent the signal s, and calculate the sparse representation coefficients:

Among them, x ₁ is the part corresponding to A ₁ in the reconstruction coefficient; x ₂ is the part corresponding to A ₂ in the reconstruction coefficient; is the Lagrangian multiplier.

S2. Read the single-trace seismic data, and calculate the normalized amplitude spectrum kurtosis, set a threshold, greater than the threshold, it is considered that there is industrial interference noise in the seismic data;

Specifically:

The discrete single-channel data sampling point value is recorded as x[n], X[k] is the discrete Fourier transform of x[n], and the single-channel seismic data is transformed from the time domain to the frequency domain, using fast Fourier transform to find discrete frequency values:

X[k]=DFT(x[n])

Assuming that the number of sampling points of the single-trace seismic data x[n] is N, the number of discrete sampling points in the frequency domain obtained by the FFT algorithm is also N. Since the spectrum obtained by the FFT algorithm is symmetrical with the Nyquist frequency, the first N/2 sampling values in the frequency domain are considered, that is, the spectrum within the 0-Nyquist frequency range. Since the frequency band of the actual seismic signal is limited, the present invention only considers the frequency spectrum between 0 and half of the Nyquist frequency.

Assuming ω _k is the discrete frequency of the kth point of the spectrum, the following formula is given:

Among them, dt is the sampling interval, then is the sampling frequency, which is denoted as f _N , and half of the sampling frequency is denoted as f _N/2 .

The normalized discrete sampling value in the frequency domain is denoted as Y[k], then:

Y[k]=X[k]/m

Among them, m is the maximum value of the absolute value of the discrete sampling value of the amplitude spectrum, namely:

m=max(abs(X[k])

First calculate the normalized amplitude spectrum variance, denoted as V, that is, calculate the variance of discrete sampling values between 0-half of the Nyquist frequency:

in, is the mean of Y[k]:

Calculate the normalized amplitude spectrum kurtosis, denoted as P, that is, calculate the kurtosis of discrete sampling values between 0-half of the Nyquist frequency:

.

Fig. 5 is the normalized amplitude spectrum kurtosis of each trace of the seismic data shown in Fig. 1 . It can be seen that the normalized amplitude spectrum kurtosis is in good agreement with the distribution of industrial interference noise, that is, the area with strong industrial interference noise has a larger normalized amplitude spectrum kurtosis.

Therefore, in step S2, set a kurtosis threshold parameter When the normalized amplitude spectrum kurtosis is greater than the threshold parameter, it is considered that the industrial interference noise of the seismic data is strong, and the industrial interference noise needs to be separated without loss. If the normalized amplitude spectrum kurtosis is not greater than the threshold parameter, the seismic data is considered to be The industrial interference noise of channel data is relatively weak and will not be processed.

S3. For the single-channel seismic data that needs to be separated from the industrial interference noise determined in step S2, use the block coordinate relaxation algorithm to separate the effective signal and the industrial interference noise, so as to achieve the purpose of non-destructive separation of the industrial interference noise in the seismic data;

Specifically include:

Initialization: initial iteration step k=0, initial solution

in, Indicates that signal component 1 is the coefficient initial solution of the effective signal, Represents the initial solution of the coefficient of the signal component 2, namely the industrial interference noise;

Iteration: Each iteration k increases by 1, and calculates:

Among them, T _λ is a hard threshold function; and A ₁ form a pair of positive and negative transformations, Constitute a pair of positive and negative transformations with A ₂ ;

Termination condition: when When it is less than the preset value, the effect of continuing iteration on the result is small enough, and the iteration terminates;

output:

in, is the transform coefficient of the separated signal component 1, is the transform coefficient of the separated signal component 2.

S4. Steps S2-S3 are repeated until all data processing is completed.

The present invention will study the waveform features of effective signals and industrial interference noise in seismic data, select two suitable dictionaries respectively, and separate industrial interference noise through a block coordinate relaxation algorithm. At the same time, in order to improve the calculation efficiency, the strength of the noise is judged in advance, and the industrial interference noise is separated only for the single-channel data that needs to be processed. Not only can the cost be reduced, but also the efficiency can be improved. This study has strong theoretical significance and market application value.

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. The components of the embodiments of the invention generally described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations. Accordingly, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

Next, the non-destructive separation method of industrial interference noise in seismic data based on the present invention is applied to actual seismic records to separate effective signals and industrial interference noise. The application result shows that the invention can effectively separate the industrial interference noise, and at the same time hardly cause damage to the effective signal.

Figure 6(a) shows the seismic data containing industrial interference noise, Figure 6(b) shows the seismic data after non-destructive separation of industrial interference noise using the patented method, and Figure 6(c) shows the separated industrial interference noise data. It can be seen that the separation of industrial interference noise in the original seismic data is relatively thorough, and the event becomes clearer. At the same time, there is no effective signal component in the separated industrial interference noise profile, that is, there is no damage to the effective signal. In this data example, the normalized amplitude spectrum kurtosis threshold.

The 88th track data in Figure 6(a), Figure 6(b) and Figure 6(c) are extracted, and their waveforms are shown in the top, middle and bottom of Figure 7 respectively. It can be seen that after separating the industrial interference noise, the original The characteristics of sine waves in the signal waveform diagram are weakened, and the effective signal amplitude does not appear notch waves in the frequency components affected by industrial interference.

Extract the 88th track data in Figure 6(a), Figure 6(b), and Figure 6(c), and its normalized amplitude spectrum is shown in Figure 8A, Figure 8(b), and Figure 8(c) respectively, which can be It can be seen that the single peaks at the frequency points of 50Hz, 150Hz and 250Hz in the amplitude spectrum disappear, which also shows that the industrial interference noise has been effectively separated. In addition, it can be clearly seen that the noise amplitude spectrum only contains the characteristics of industrial interference noise, indicating that there is no damage to the effective signal.

Extract the 88th track data in Figure 6(a), Figure 6(b), and Figure 6(c), when the frequency spectrum is shown in Figure 9(a), Figure 9(b), and Figure 9(c), it can be It can be seen that several horizontal straight lines in the time spectrum disappear, indicating that industrial interference noise has been effectively and thoroughly separated. At the same time, other features in the time spectrum remain unchanged except for the straight line feature, indicating that the patented method does not cause damage to effective signals.

The above content is only to illustrate the technical ideas of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solutions according to the technical ideas proposed in the present invention shall fall within the scope of the claims of the present invention. within the scope of protection.

Claims (5)

1. A lossless separation method for industrial interference noise in seismic data is characterized by comprising the following steps:

s1, selecting continuous wavelet transform and discrete cosine transform as dictionaries for respectively representing effective signals and industrial interference noise in the seismic data in a sparse mode, and forming a pair of super-complete dictionaries;

s2, reading single-channel seismic data and calculating the peak degree P of the normalized amplitude spectrum, when the peak degree P is larger than a set thresholdValue ofConsidering that industrial interference noise exists in the seismic data;

and S3, performing data separation on the single-channel seismic data of the industrial interference noise to be separated determined in the step S2 by using a block coordinate relaxation algorithm, separating effective signals and industrial interference noise of all channel data, and realizing nondestructive separation of the industrial interference noise in the seismic data.

2. The method of claim 1, wherein in step S1, the selected dictionary A is used₁Namely the continuous wavelet transform sum a₂Namely, global discrete cosine transform, to form a group of overcomplete dictionaries, sparsely representing a signal s, and calculating a sparse representation coefficient:

s＝s₁+s₂

wherein x is₁Is the sum of reconstruction coefficients A₁A corresponding portion; x is the number of₂Is the sum of reconstruction coefficients A₂A corresponding portion;is a lagrange multiplier; s₁、s₂Respectively effective signals and industrial interference noise in the seismic data;

selecting continuous wavelet transform as a dictionary for sparsely representing effective signals in seismic data, the continuous wavelet transform:

wherein, WT_x(a, τ) are continuous wavelet transform coefficients of the signal to be analyzed, a represents a scale factor, x (t) represents the signal to be analyzed, ψ (t) represents a Morlet mother wavelet, t is time,tau is translation quantity and represents conjugation;

the inverse transform of the continuous wavelet transform is:

wherein, constant C_ΨWith the permissible condition being < ∞;

constructing a global discrete cosine transform as a dictionary for sparsely representing optical cable coupling noise, wherein the global discrete cosine forward transform is as follows:

dct (u) represents a global discrete cosine transform coefficient of a signal to be analyzed, x [ N ] represents the signal to be analyzed, and u is 1, 2.. multidot.n-1, where N is a data sampling point length;

the inverse of the global discrete cosine transform is:

n-1, wherein N is 0.

3. The method for lossless separation of industrial interference noise in seismic data according to claim 1, wherein in step S2, the normalized amplitude spectrum kurtosis P is:

where V is the normalized amplitude spectral variance, Y k]For the normalized frequency domain discrete sample values,is Y [ k ]]N is the number of discrete sampling points in the frequency domain;

the discrete single-channel data sampling point value is recorded as X [ n ], X [ k ] is discrete Fourier transform of X [ n ], the single-channel seismic data is transformed from a time domain to a frequency domain, and a discrete frequency value is obtained by using fast Fourier transform:

X[k]＝DFT(x[n])

let omega be_kThe discrete frequencies at the kth point of the spectrum are:

wherein dt is the sampling interval, thenFor the sampling frequency, the sampling frequency is denoted as f_NAnd half the sampling frequency is denoted as f_N2；

The normalized frequency domain discrete sampling value Y [ k ] is:

Y[k]＝X[k]/m

the maximum value m of the absolute values of the discrete sampling values of the amplitude spectrum is as follows:

m＝max(abs(X[k])

the normalized amplitude spectral variance V is:

wherein,is Y [ k ]]The mean value of (A) is:

。

4. the method for lossless separation of industrial interference noise in seismic data according to claim 1, wherein in step S3, the block coordinate relaxation algorithm specifically comprises:

firstly, initializing the iteration step number k to be 0, and initially solving Representing the initial solution of the coefficients of the signal component 1 i.e. the significant signal,an initial solution of coefficients representing signal component 2, i.e. the industrial interference noise;

increase k by 1 per iteration step and calculateAnd

when in useWhen the value is smaller than the preset value, the influence of continuous iteration on the result is small enough, and the iteration is terminated; and (3) outputting: for the transform coefficients of the separated signal component 1,is the transform coefficient of the separated signal component 2.

5. The method of claim 4, wherein the step of lossless separation of interference noise in the seismic data comprises,andthe method specifically comprises the following steps:

wherein, T_λIs a hard threshold function;and A₁A pair of positive and negative conversion is formed,and A₂A pair of positive and negative conversion is formed.