CN110531420A - The lossless separation method of industry disturbance noise in a kind of seismic data - Google Patents
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Abstract
It the invention discloses the lossless separation method of industry disturbance noise in a kind of seismic data, selects continuous wavelet transform and discrete cosine transform as the dictionary of useful signal and industry disturbance noise in rarefaction representation seismic data respectively, and constitutes a pair of super complete dictionary；Then single-channel seismic data are read, and calculate normalized amplitude spectral peak degree, a threshold value is set, and thinking the road seismic data greater than the threshold value, there are industry disturbance noises；To the determining single-channel seismic data for needing to separate industry disturbance noise, useful signal and industry disturbance noise are separated using piecemeal coordinate relaxed algorithm, realizes the lossless isolated purpose of industry disturbance noise in seismic data；Above step is repeated until the processing of all track datas is completed.The present invention hardly can cause to damage, and computational efficiency is higher in efficiently separating seismic data while industry disturbance noise to useful signal.
Description
Technical Field
The invention belongs to the technical field of seismic exploration data processing, and particularly relates to a nondestructive separation method for industrial interference noise in seismic data.
Background
In the process of deep coal and oil gas exploration by using the seismic technology, the transmission lines and the acquisition equipment in a deep mining area are densely distributed, so that strong industrial electric interference of frequency doubling components near 50Hz can be generated, the signal-to-noise ratio of the recorded seismic data is seriously influenced, and the requirement of the current industry on high fidelity of the seismic data cannot be met. There is therefore a need to separate the industrial interference noise in seismic data to improve the signal-to-noise ratio and fidelity of the seismic data. Due to the large volume of seismic record data, the industrial interference noise separation method needs to have faster operation efficiency.
At present, the adopted frequency domain notch method can damage effective signals and easily generate boundary effect; the demodulation point domain separation method needs to transform seismic data from an explosive domain to a demodulation point domain and then transform the seismic data from the explosive domain to a common demodulation point domain, and repeated channel extraction wastes a large amount of time and disk space, so that the efficiency is low.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a nondestructive separation method for industrial interference noise in seismic data aiming at the defects in the prior art, and the method is characterized in that dictionaries capable of sparsely representing effective signals and industrial interference noise in the seismic data are respectively selected to form a group of over-complete dictionaries, so that the industrial interference noise is nondestructively separated from the single-channel seismic data with the industrial interference noise reaching a certain intensity, the time is saved, and the efficiency is high.
The invention adopts the following technical scheme:
a nondestructive separation method for industrial interference noise in seismic data comprises 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 threshold valueConsidering 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.
Specifically, 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, WTx(a, τ) is a continuous wavelet transform coefficient of a 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, τ is translation amount, and τ represents conjugation;
the inverse transform of the continuous wavelet transform is:
wherein, constant CΨWith 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.
Specifically, 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 bekThe 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 fNAnd half the sampling frequency is denoted as fN/2；
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:
。
specifically, in step S3, the block coordinate relaxation algorithm specifically includes:
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.
Further, in the above-mentioned case,andthe method specifically comprises the following steps:
wherein, TλIs a hard threshold function;and A1A pair of positive and negative conversion is formed,and A2A pair of positive and negative conversion is formed.
Compared with the prior art, the invention has at least the following beneficial effects:
according to the lossless separation method for the industrial interference noise in the seismic data, the dictionary is selected to sparsely represent the effective signal and the industrial interference noise, the signal and noise can be separated directly through the block coordinate relaxation algorithm, the method is simple, and the algorithm program does not need additional accessory conditions; the fast Fourier transform is used, so that the calculation efficiency is high; the disturbance of the industrial interference noise frequency point does not influence the invention, and the lossless separation can still be realized; the method can save the running time of the algorithm by judging the strength of the industrial interference noise firstly and not processing the single-channel data with weak industrial interference noise.
Furthermore, the fact that the signal can be sparsely represented means that the signal can be represented by as few transform coefficients as possible, i.e., the signal can be represented by as few linear combinations of transform atoms as possible. According to the theory of morphological component analysis, dictionaries capable of respectively representing components in the complex signals in a sparse mode are selected, a group of over-complete dictionaries are formed, the complex signals are represented in a sparse mode, signal-noise separation is achieved through solving a sparse optimization mode, and the method can be used for suppressing noise in seismic records. It is important to select dictionaries capable of sparsely representing effective signals and industrial interference noise, and the selection can be performed according to morphological feature differences of the effective signals and the industrial interference noise. Based on the waveform morphological characteristic difference, continuous wavelet transform sparse representation effective signals are selected, and discrete cosine transform sparse representation industrial interference noise is selected.
Further, the normalized amplitude spectrum kurtosis of the single channel data can be calculated to measure the intensity of the industrial interference noise contained in the channel data, if the industrial interference noise is strong, the step S3 is continuously executed to perform noise lossless separation, and if the industrial noise is weak, the noise is considered not to form substantial interference on the effective signal, so that the step S3 is not required to be executed, and the operation time can be saved. A threshold value of the normalized amplitude spectrum kurtosis is set in step S2, and when the normalized amplitude spectrum kurtosis is greater than the threshold value, i.e. the industrial interference noise is considered to be strong, step S3 needs to be performed for lossless separation.
Further, morphological component analysis based on signal sparse representation theory is a method for solving the problem of multi-component separation of image or seismic signals. The core idea of a Block Coordinate Relaxation (BCR) algorithm is to set a reasonable threshold strategy, and alternately update a sparse coefficient in each iteration until an iteration termination condition is reached, so that a target of separating two signal components from a mixed signal is realized.
In conclusion, the method and the device can effectively separate the industrial interference noise in the seismic data, hardly damage the effective signal and have high calculation efficiency.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is seismic data containing industrial interference noise;
FIG. 2 is a plot of an analysis of trace 30 of the seismic data of FIG. 1, wherein (a) is a waveform plot for trace 30, (b) is a normalized amplitude spectrum for trace 30, and (c) is a time spectrum for trace 30;
FIG. 3 is a plot of an analysis of the 64 th trace of seismic data from FIG. 1, wherein (a) is a waveform plot for the 64 th trace, (b) is a normalized amplitude spectrum for the 64 th trace, and (c) is a time-frequency spectrum for the 64 th trace;
FIG. 4 is an atomic diagram, in which (a) is an atomic diagram of continuous wavelet transform and (b) is an atomic diagram of discrete cosine transform;
FIG. 5 is a normalized amplitude spectral kurtosis for each trace of the seismic data shown in FIG. 1;
FIG. 6 is a graph of interference noise seismic data, wherein (a) is seismic data containing industrial interference noise, (b) is seismic data after lossless separation of industrial interference noise using the present method, and (c) is industrial interference noise separated using the present method;
FIG. 7 is a waveform of the 88 th trace of seismic data from the seismic data of FIG. 6, wherein (a) is seismic data containing industrial interference noise, (b) is seismic data after lossless separation of industrial interference noise using the method, and (c) is industrial interference noise separated using the method;
FIG. 8 is a graph of normalized amplitude spectrum amplitude of the 88 th trace of seismic data from the seismic data of FIG. 6, where (a) is seismic data containing industrial interference noise, (b) is seismic data after lossless separation of industrial interference noise using the present method, and (c) is industrial interference noise separated using the present method;
FIG. 9 is a time-frequency plot of the 88 th trace of seismic data of FIG. 6, where (a) is seismic data containing industrial interference noise, (b) is seismic data after lossless separation of industrial interference noise using the method, and (c) is industrial interference noise separated using the method;
FIG. 10 is a flow chart of the method of this patent.
Detailed Description
The invention provides a nondestructive separation method for industrial interference noise in seismic data, which is characterized in that dictionaries capable of respectively sparsely representing effective signals and industrial interference noise are selected to form a group of over-complete dictionaries, and a block coordinate relaxation algorithm is used for carrying out nondestructive separation on the industrial interference noise on single-channel seismic data with the industrial interference noise reaching a certain intensity.
Referring to fig. 10, the method for lossless separation of interference noise in seismic data of the present invention includes 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;
the method specifically comprises the following steps:
the object of morphological analysis is to contain two components with different morphological characteristics of the waveform:
s＝s1+s2
where s denotes the signal to be analyzed, i.e. seismic data, s1、s2The two components in the representation signal are respectively effective signals and industrial interference noise in the seismic data and have different waveform morphological characteristics. The objective of morphological analysis is to extract s separately1、s2Two components. Suppose s1And s2Can be respectively represented by dictionary A1And A2Efficient sparse representation, but with A2Sparse representation s1And with A1Sparse representation s2The temporal sparsity is poor.
FIG. 1 shows that the seismic data containing industrial interference noise has 192 traces, the sampling length is 6s, and the sampling interval is 1ms, and it can be seen that the seismic data is interfered by the industrial interference noise, and partial in-phase axes are covered, so that the signal-to-noise ratio of the data is reduced, and the imaging analysis of the seismic data is influenced.
Extracting the 30 th data which contains little industrial interference noise from the seismic data shown in FIG. 1, wherein the oscillogram, normalized amplitude spectrum and time-frequency spectrum are shown in FIG. 2(a), FIG. 2(b) and FIG. 2 (c); the waveform diagram, normalized amplitude spectrum and time frequency spectrum of the 64 th data containing strong industrial interference noise are extracted from the seismic data shown in fig. 1, and are shown in fig. 3(a), 3(b) and 3 (c). It can be seen that the industrial interference noise data appears as a single peak in the amplitude spectrum, as a horizontal straight line in the time-frequency spectrum, and the frequency is concentrated around 50Hz because the industrial alternating current frequency is 50 Hz. However, the industrial interference noise of the seismic data can be concentrated on more than one frequency point of 50Hz, and can also be concentrated on frequency points of 100Hz, 150Hz, 250Hz and the like. In addition, the industrial interference noise may not be exactly 50Hz, and the frequency point thereof is disturbed around 50 Hz.
Fig. 4(a) and 4(b) are schematic diagrams of atoms of continuous wavelet transform and discrete cosine transform, respectively, and comparing fig. 2(a) and 3(a), it can be seen that the waveform diagram of the effective signal is more similar to the atoms of continuous wavelet transform, and the waveform diagram of the industrial interference noise is more similar to the atoms of discrete cosine transform. Therefore, the invention selects continuous wavelet transform to sparsely represent effective signals, and discrete cosine transform to sparsely represent industrial interference noise.
Selecting a continuous wavelet transform as a dictionary for sparsely representing significant signals in the seismic data, wherein the continuous wavelet transform:
wherein, WTx(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, τ is the translation amount, and τ represents the conjugate.
The inverse transform of the continuous wavelet transform is:
wherein, constant CΨAnd < ∞ is a permissible condition thereof.
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.
The inverse of the global discrete cosine transform is:
n-1, wherein N is 0.
With selected dictionary A1Namely 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:
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.
S2, reading single-channel seismic data, calculating the peak degree of the normalized amplitude spectrum, and setting a threshold value, wherein the fact that industrial interference noise exists in the single-channel seismic data if the peak degree of the normalized amplitude spectrum is larger than the threshold value is considered;
the method specifically comprises the following steps:
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])
and assuming that the number of sampling points of the single-channel seismic data x [ N ] is N, the number of frequency domain discrete sampling points obtained through the FFT algorithm is also N. Since the spectrum obtained by the FFT algorithm is symmetric about the Nyquist frequency, the first N/2 frequency domain sample values, i.e. the spectrum in the 0-Nyquist frequency range, are considered. Since the frequency band of actual seismic signals is limited, the present invention only considers the spectrum between 0 and half the Nyquist frequency.
Let omega bekFor the discrete frequency at the kth point of the spectrum, then there is the following equation:
wherein dt is the sampling interval, thenFor the sampling frequency, the sampling frequency is denoted as fNAnd half the sampling frequency is denoted as fN/2。
And the normalized frequency domain discrete sampling value is marked as Y [ k ], and then:
Y[k]＝X[k]/m
wherein m is the maximum value of the absolute value of the discrete sampling value of the amplitude spectrum, namely:
m＝max(abs(X[k])
the normalized amplitude spectral variance, denoted V, is first calculated, i.e. the variance of discrete sample values between 0 and half of the Nyquist frequency is calculated:
wherein,is Y [ k ]]Average value of (d):
calculating the normalized amplitude spectrum kurtosis, denoted as P, i.e. calculating the kurtosis of discrete sample values between 0 and half of the Nyquist frequency:
。
FIG. 5 is a normalized amplitude spectral kurtosis for each trace of the seismic data shown in FIG. 1. It can be seen that the normalized amplitude spectrum kurtosis is well consistent with the distribution of the industrial interference noise, i.e. in the region where the industrial interference noise is strong, the larger the normalized amplitude spectrum kurtosis is.
Therefore, in step S2, a kurtosis threshold parameter is setWhen the kurtosis of the normalized amplitude spectrum is larger than the threshold parameter, the industrial interference noise of the seismic data is considered to be strong, the nondestructive separation of the industrial interference noise is needed, and if the kurtosis of the normalized amplitude spectrum is not larger than the threshold parameter, the industrial interference noise of the seismic data is considered to be weak, and the processing is not carried out.
S3, separating the single-channel seismic data which are determined in the step S2 and need to be separated from the industrial interference noise by using a block coordinate relaxation algorithm, and achieving the purpose of lossless separation of the industrial interference noise in the seismic data;
the method specifically comprises the following steps:
initialization: initial iteration step number k is 0, initial solution
Wherein,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;
iteration: each iteration k is incremented by 1 and:
wherein, TλIs a hard threshold function;and A1A pair of positive and negative conversion is formed,and A2A pair of positive and negative conversion is formed;
termination conditions were as follows: 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:
wherein,for the transform coefficients of the separated signal component 1,is the transform coefficient of the separated signal component 2.
S4, repeating the steps S2-S3 until the data processing of all tracks is completed.
The method is characterized in that waveform morphological characteristics of effective signals and industrial interference noise in seismic data are researched, two proper dictionaries are respectively selected, and industrial interference noise separation is carried out through a block coordinate relaxation algorithm. Meanwhile, in order to improve the calculation efficiency, the noise strength is judged in advance, and the industrial interference noise separation is carried out on the single-channel data to be processed. Not only can reduce the cost, but also can improve the efficiency. The research has stronger theoretical significance and market application value.
In order to make the objects, 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 with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The nondestructive separation method of the industrial interference noise in the seismic data based on the invention is applied to the actual seismic record to separate the effective signal from the industrial interference noise. Application results show that the method can effectively separate the industrial interference noise, and hardly causes damage to effective signals.
Fig. 6(a) shows seismic data containing industrial interference noise, fig. 6(b) shows seismic data obtained by lossless separation of industrial interference noise using the method of the present invention, and fig. 6(c) shows separated industrial interference noise data. It can be seen that the industrial interference noise in the original seismic data is separated thoroughly, the in-phase axis becomes clearer, and meanwhile, no component of the effective signal exists in the separated industrial interference noise section, namely, no damage is caused to the effective signal. In this data example, the amplitude spectrum kurtosis threshold is normalized.
As shown in fig. 7, upper, middle and lower parts, the 88 th data in fig. 6(a), 6(b) and 6(c) are extracted, and the waveform diagrams thereof are respectively shown, it can be seen that after the industrial interference noise is separated, the characteristics of the sine wave in the original signal waveform diagram are weakened, and the effective signal amplitude does not appear to be trapped in the frequency components affected by the industrial interference.
Data of trace 88 in fig. 6(a), 6(b) and 6(c) are extracted, normalized amplitude spectra are respectively shown in fig. 8A, 8(b) and 8(c), and it can be seen that single peaks at frequency points of 50Hz, 150Hz and 250Hz in the amplitude spectra disappear, which also indicates that the industrial interference noise is effectively separated. Furthermore, it is clear that the noise amplitude spectrum contains only the characteristics of the industrial interference noise, indicating that no impairment is caused to the useful signal.
The 88 th data in fig. 6(a), 6(b), and 6(c) is extracted, and the time frequency spectrums are respectively shown in fig. 9(a), 9(b), and 9(c), it can be seen that several horizontal straight lines in the time frequency spectrums disappear, which indicates that the industrial interference noise is effectively and completely separated, and meanwhile, other features except for the straight line feature in the time frequency spectrums remain unchanged, which indicates that the method of the present invention does not damage the effective signal.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
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, WTx(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 CΨWith 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 bekThe 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 fNAnd half the sampling frequency is denoted as fN2；
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, TλIs a hard threshold function;and A1A pair of positive and negative conversion is formed,and A2A pair of positive and negative conversion is formed.
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