CN114200525A - Self-adaptive multi-channel singular spectrum analysis seismic data denoising method - Google Patents

Self-adaptive multi-channel singular spectrum analysis seismic data denoising method Download PDF

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CN114200525A
CN114200525A CN202111508457.XA CN202111508457A CN114200525A CN 114200525 A CN114200525 A CN 114200525A CN 202111508457 A CN202111508457 A CN 202111508457A CN 114200525 A CN114200525 A CN 114200525A
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曹静杰
朱跃飞
魏亚杰
殷晗钧
杨贺龙
蔡志成
杨歧焱
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Abstract

The application discloses a self-adaptive multi-channel singular spectrum analysis seismic data denoising method, which comprises the following steps: step 1: presetting time domain seismic data, and converting the time domain seismic data into frequency domain seismic data through DFFT; step 2: generating a block Hankel matrix based on the frequency domain seismic data; and step 3: decomposing the Hankel matrix to obtain a singular value matrix, and combining singular values in the singular value matrix into a singular value sequence; and 4, step 4: based on Akaike information criterion, transforming the singular value sequence to obtain the number of the singular values; and calculating and denoising the number of singular values to obtain denoised seismic data. The method and the device automatically determine the number of the proper singular values based on the Akaike information criterion, and are beneficial to the industrial realization of multi-channel singular spectrum analysis.

Description

Self-adaptive multi-channel singular spectrum analysis seismic data denoising method
Technical Field
The invention belongs to the technical field of seismic data denoising processing, and particularly relates to a self-adaptive multi-channel singular spectrum analysis seismic data denoising method.
Background
The multi-channel singular spectrum analysis (MSSA) is a denoising method based on rank reduction, which decomposes original data into a signal subspace and a noise subspace through singular value decomposition, then sets the energy of the noise subspace to be zero (truncation), and achieves the purpose of denoising through inverse transformation. MSSA was developed from univariate Singular Spectral Analysis (SSA), which was widely used as an unconstrained model method for singular spectral analysis of one-dimensional time series trace matrices. Read (1993) rates the first extension of SSA to MSSA for the study of multivariate MSSA methods. The low-rank Hankel matrix is formed by the frequency spectrum similarity and predictability of adjacent seismic channels on the basis of the assumption of linear homodyne axes, the low-rank structure of the Hankel matrix of the data frequency slice is damaged by the existence of noise, and a truncated singular value decomposition method is commonly used for solving the low-rank approximation problem. Trickett (2008) applies the method to seismic data noise suppression and popularizes the method to f-x-y three-dimensional data to attenuate random noise. Oropeza and Sacchi (2011) use MSSA to achieve simultaneous denoising and reconstruction in prestack three-dimensional data. Many numerical experiments show that random noise cannot be completely eliminated by using the MSSA algorithm, and the denoising effect of the MSSA algorithm has a great space for improvement. Huang et al (2015) propose a damped multi-channel singular spectral analysis (DMSSA) algorithm by introducing a damping operator into the conventional MSSA. By introducing a soft threshold moving average operator into the damped rank reduction framework, Oboue et al (2020) use a method called robust damped rank reduction to fuse the advantages of the soft threshold moving average operator and the damping operator together, thereby improving the signal-to-noise ratio of the seismic data. The damping rank reduction method has become an effective method, and can recover effective signals from observation data containing noise and incompleteness.
The existing rank reduction method is based on the basic assumption of seismic linear homodyne axes, time domain signals are converted into frequency domain signals after discrete fast Fourier transform, and then the rank reduction processing is realized by truncating the same singular value numbers for all frequencies through a manual estimation method. For large-scale data, the method based on rank reduction needs to divide the seismic data into different blocks, but the number of singular values corresponding to each block is different, so that the proper number of singular values needs to be manually estimated for the data of each block at present, the calculation efficiency is low, and industrialization cannot be realized.
Disclosure of Invention
The application provides a self-adaptive multi-channel singular spectrum analysis seismic data denoising method, which is used for automatically determining the number of proper singular values based on an Akaike information criterion and is beneficial to the industrial realization of multi-channel singular spectrum analysis.
In order to achieve the above purpose, the present application provides the following solutions:
a self-adaptive multi-channel singular spectrum analysis seismic data denoising method comprises the following steps:
step 1: presetting time domain seismic data, and converting the time domain seismic data into frequency domain seismic data through DFFT;
step 2: generating a block Hankel matrix based on the frequency domain seismic data;
and step 3: decomposing the Hankel matrix to obtain a singular value matrix, and combining singular values in the singular value matrix into a singular value sequence;
and 4, step 4: based on Akaike information criterion, transforming the singular value sequence to obtain the number of the singular values; and calculating and denoising the number of singular values to obtain denoised seismic data.
Preferably, the method of step 2 comprises:
obtaining frequency slice data of the frequency domain seismic data for each frequency; generating a Hankel matrix based on each row of data of the frequency slice data; and arranging all the Hankel matrixes into one block Hankel matrix.
Preferably, the singular value matrix is
Figure BDA0003405054910000031
Wherein
Figure BDA0003405054910000032
Is composed of
Figure BDA0003405054910000033
The rank of (c) is determined,
Figure BDA00034050549100000310
is that
Figure BDA00034050549100000311
Of left singular value vector of (V)x×Lx)×(Vx×Lx) An orthogonal matrix of orders;
Figure BDA0003405054910000038
is that
Figure BDA0003405054910000039
Of right singular value vector of (H)x×Ly)×(Hx×Ly) An orthogonal matrix of orders;
Figure BDA0003405054910000034
is a diagonal matrix formed by singular values in descending order, the number of non-zero singular values is equal to the matrix
Figure BDA0003405054910000035
Is the ith frequency.
Preferably, the singular value sequence is
Figure BDA0003405054910000036
Preferably, the method for transforming the singular value sequence based on Akaike information criterion to obtain the number of singular values includes:
performing second-order derivation on a singular value sequence curve to obtain the change rate of the slope of the singular value sequence curve; calculating Akaike information criterion values of the change rates of the slope of the singular value sequence curves of all the frequencies at a preset point based on the Akaike information criterion; and calculating the minimum value of the Akaike information criterion values based on all the Akaike information criterion values, wherein the minimum value is the number of singular values of the frequency domain seismic data.
Preferably, the change rate of the slope of the curve of the singular value sequence is
Figure BDA0003405054910000037
Preferably, the Akaike information criterion value is
Figure BDA0003405054910000041
Preferably, the method for performing computational denoising on the number of singular values includes: and inversely transforming the singular value sequence to a frequency domain through the block Hankel matrix, and then inversely transforming to a time domain through Fourier transform to obtain the denoised seismic data.
The beneficial effect of this application does:
for the traditional MSSA denoising method, the determination of the number of effective singular values is the key of the method. The application provides a self-adaptive multi-channel singular spectrum analysis seismic data denoising method, which can automatically determine the number of reliable singular values for massive data based on an Akaike information criterion, and denoise by adopting a DMSSA method to obtain a denoising effect with a high signal-to-noise ratio. The validity and reliability of the automatic method provided by the application are proved by numerical verification, and the method has great potential in industrial application. In addition, in the new method provided by the application, the computer can automatically perform denoising processing only by determining the wavelet dominant frequency range.
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In order to more clearly illustrate the technical solution of the present application, the drawings needed to be used in the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a self-adaptive multi-channel singular spectrum analysis seismic data denoising method in an embodiment of the present application;
FIG. 2(a) is a three-dimensional view of simulated seismic data with five seismic event axes, as shown in FIG. 2;
FIG. 2(b) is a three-dimensional view of simulated seismic data according to the second embodiment of the present application, wherein 10% of random noise is added to the simulated seismic data;
FIG. 3 is a diagram illustrating the first 30 singular value curves of a frequency of seismic data three-dimensional view data simulated in the second embodiment of the present application;
FIG. 4(a) is a diagram illustrating the self-adaptive method for determining singular value quantity in the second embodiment of the present application
Figure BDA0003405054910000051
A sequence graph diagram;
FIG. 4(b) is a schematic diagram of a sequence curve in determining singular value quantity by the adaptive method according to the second embodiment of the present application;
fig. 5(a) is a schematic diagram of a denoising result in a simulation data denoising effect in a second embodiment of the present application;
FIG. 5(b) is a schematic diagram of noise removed in the simulation of data denoising effect according to the second embodiment of the present application;
FIG. 6 is a schematic diagram of an actual noisy two-dimensional seismic section in the third embodiment of the present application;
FIG. 7 is a schematic diagram illustrating a singular value estimation principle of two-dimensional seismic data according to a third embodiment of the present application;
fig. 8(a) is a schematic diagram of a noise suppression result of actual data applied to the denoising effect of actual seismic data in the third embodiment of the present application;
fig. 8(b) is a schematic diagram of noise removed in an actual seismic data denoising effect in the third embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. 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 application.
In order to make the aforementioned objects, features and advantages of the present application more comprehensible, the present application is described in further detail with reference to the accompanying drawings and the detailed description.
The first embodiment is as follows: as shown in fig. 1, assume that a three-dimensional seismic data containing noise is D (x, y, t), where x is (x ═ x1,…,xm)，y＝(y1,…,yn)，t＝t1,…tsSeismic data size of xm×yn×ts. According to the DMSSA theory, the data can be denoised using the following four steps.
In a first step, seismic data is transformed from the time domain to the frequency domain by DFFT to obtain data F (x, y, w), where w is (w)1,…,wj)。
Second, each frequency slice data is arranged into a block Hankel matrix within a given frequency. When the frequency is equal to wiThe data for the frequency slice is shown in equation (1):
Figure BDA0003405054910000061
the process of building a block Hankel matrix includes two steps. First, F (x, y, w)i) Each row of (a) is constructed as a Hankel matrix:
Figure BDA0003405054910000062
wherein R isKIs of size Vx×HxThe Hankel matrix of (1),
Figure BDA0003405054910000063
Hx＝yn-Vx+1, symbol
Figure BDA0003405054910000064
Representing a rounding operation. R in formula (2)KDenotes a group consisting of F (x, y, w)i) The K-th row of (1) of the Hankel matrix. Then, all R's are combinedK，K＝1,…,xmArranged into a block Hankel matrix
Figure BDA0003405054910000071
As shown in equation (3):
Figure BDA0003405054910000072
wherein
Figure BDA0003405054910000073
Is (V)x×Lx)×(Hx×Ly) The block Hankel matrix of the rank,
Figure BDA0003405054910000074
Ly＝xm-Lx+1。
the third step is to
Figure BDA0003405054910000075
Singular value decomposition is performed and singular values are selected and truncated, which is a key step of the multi-channel singular spectrum analysis-like method. If the number of the singular values corresponding to the effective signal is N, only the first N singular values are reserved in the singular value diagonal matrix, and the sizes of all other singular values are set to be zero. To pair
Figure BDA0003405054910000076
Singular value decomposition is performed to obtain formula (4):
Figure BDA0003405054910000077
wherein
Figure BDA0003405054910000078
Wherein d is
Figure BDA0003405054910000079
The rank of (c) is determined,
Figure BDA00034050549100000710
is that
Figure BDA00034050549100000711
Of left singular value vector of (V)x×Lx)×(Vx×Lx) An orthogonal matrix of orders;
Figure BDA00034050549100000712
is that
Figure BDA00034050549100000713
Of right singular value vector of (H)x×Ly)×(Hx×Ly) An orthogonal matrix of orders;
Figure BDA00034050549100000714
is a diagonal matrix formed by singular values in descending order, the number of non-zero singular values is equal to the matrix
Figure BDA00034050549100000715
Is determined by the size of the rank of (c).
Specifically, when the acquired seismic data does not contain noise, the diagonal matrix of equation (5) contains only non-zero singular values associated with the significant signal. If the data contains noise, the magnitude of all singular values will change and the number of non-zero singular values will increase. The original MSSA method only reserves the number of singular values, and has no influence on the size of the singular values, so that the denoising result has a great improvement space.
The DMSSA method is to attenuate the singular value increments caused by noise by adding a damping factor. Equations (6) and (7) represent this process:
Figure BDA0003405054910000081
Figure BDA0003405054910000082
wherein T represents a damping operator, I is an identity matrix, N is the number of predicted singular values, D represents a damping factor, the smaller the value of D is, the stronger the damping effect is, otherwise, the weaker the damping effect is, and the formulas (6) and (7) are the cores of the DMSSA. The essence of DMSSA denoising is that the numerical value of the (N + 1) th singular value is amplified or reduced by using a damping factor D, then the numerical values are subtracted by using the first N singular values, and the singular values after the (N + 1) th singular value are set to be zero, so that the purpose of suppressing noise is achieved.
Determining N is the most critical step in DMSSA denoising, which will affect the effect of noise suppression and the degree of corruption to the effective signal. If N is chosen too small, the valid signal will be corrupted; if N is selected too large, the noise suppression effect is reduced, and for MSSA methods, how to automatically determine the number of singular values is critical. The above derivation is performed under the assumption that N is known, which is a crucial parameter, and it is a considerable problem to be studied how to determine the number of singular values to be retained in a data block when complex and variable actual seismic data has no other sufficient geological data. The method automatically determines the number of proper singular values based on Akaike information criterion, and is favorable for industrialized realization of multi-channel singular spectrum analysis.
Specifically, singular values in the singular value matrix are combined into a singular value sequence
Figure BDA0003405054910000083
For singular value sequence
Figure BDA0003405054910000084
The number of effective singular values can be determined according to the huge difference between the Nth singular value and the (N + 1) th singular value and the severe bending phenomenon. In fact, the choice of the value of N is to detect the sequence of singular valuesThe location of the inflection point in the column. An Akaike information criterion is given below to automatically determine the number of retained singular values. Firstly, singular value vectors are transformed as follows:
Figure BDA0003405054910000091
equation (8) is actually the second derivative of the singular value sequence curve,
Figure BDA0003405054910000092
the rate of change of the slope of the singular value curve is described. Then at wiThe Akaike information criterion value for calculating the L-th point under the frequency is as follows:
Figure BDA0003405054910000093
where var is the variance of the data sequence and d is the vector
Figure BDA0003405054910000094
Length of (d).
Figure BDA0003405054910000095
Is a vector of length d.
Figure BDA0003405054910000096
The position corresponding to the global minimum in the sequence is the inflection point position, and then the minimum in all frequencies is solved according to the formula (9)
Figure BDA0003405054910000097
The global minimum value in equation (10) is the number N of singular values that need to be preserved in the entire data block.
After the singular value is determined by using the method, the frame of the DMSSA method is adopted in the denoising process. The newly proposed algorithm is called an adaptive damped multichannel singular spectrum analysis (admsas) method. In the proposed new algorithm, the computer can automatically perform denoising processing only by determining the dominant frequency range of the wavelet.
And fourthly, calculating a denoised result based on the truncated singular value. And performing inverse transformation on the frequency domain through a Hankel matrix, and performing inverse Fourier transformation on the frequency domain and the time-space domain to obtain the de-noised seismic data. The process can be expressed as
Figure BDA0003405054910000101
Figure BDA0003405054910000102
And performing the operation on all the frequencies to obtain the denoised seismic data.
Example two: to verify the validity and feasibility of the present application, a simulation data experiment was used to illustrate.
FIG. 2 is a simulated three dimensional seismic data having five seismic event axes of different dip angles, a data dimension of 300X 60, 300 samples over time, a sampling rate of 2ms, 60 samples in both the inline and crossline directions, FIG. 2(a) is data without noise, FIG. 2(b) is data with 10% random noise added, and a signal-to-noise ratio (SNR) of-1.322 dB. The wavelets used for the analog data are Rake wavelets with a dominant frequency of 40Hz, and the signal-to-noise ratio (SNR) is defined as:
Figure BDA0003405054910000103
where d is noise-free data, r is denoised data, the symbol | |2Representing the L2 norm.
Fig. 3 is a singular value of a block Hankel matrix corresponding to a certain frequency in the simulation data, a solid line in fig. 3 corresponds to a singular value of noiseless data, a dotted line corresponds to a singular value of data after noise is added, and a dot-dash line is a singular value of data after de-noising by the DMSSA method; the solid line in fig. 3 shows that the seismic data only has a few large singular values in the absence of noise, the number of the singular values is equal to N, and other singular values are all small, so that the singular value curve has a remarkable buckling phenomenon. Theoretically, in the absence of noise, the singular values after N should all be zero. After the noise is added to the data, the magnitude of the singular value is changed and a large number of non-zero singular values also appear, so that the curve of the singular value after the noise is added is relatively gentle in decline, but a huge drop still exists between the Nth item and the (N + 1) th item.
Fig. 4(a) and 4(b) are calculation results of analog data using Akaike information criterion. In FIG. 4(a), the solid line represents a singular value curve at a certain frequency, and the dotted line represents the corresponding AICwiCurve line. A minimum occurs at the dashed line N-8. Since the numerical result in the main frequency range is stable, and abnormal values often appear in other ranges, in order to improve the precision, the control frequency is within 10-90Hz, the number of the singular values determined in the frequency range is selected by the self-adaptive method in the step (b) in FIG. 4, and as can be seen from the step (b) in FIG. 4, the number of the singular values determined in the self-adaptive manner is 8, and the result close to the true value N can be automatically estimated when the noise-containing data is processed by the method based on the Akaike information criterion.
Fig. 5(a) and 5(b) show the processing results of fig. 2(b) using the admsas method, where the number of singular value reservations determined by the adaptive method is 8 and the damping factor D is 3, and the results are respectively shown in fig. 5(a) and the signal-to-noise ratio is 22.110 dB; fig. 5(b) shows the removed noise. The self-adaptive algorithm can obtain a result which is closer to an accurate N value, obtain higher signal-to-noise ratio data, have clear coherence of a same phase axis and retain local details.
Example three: in order to verify the effectiveness and feasibility of the application, an actual data experiment is used for illustration.
In order to prove the denoising effect of the algorithm provided by the application on the actual seismic data, a two-dimensional post-stack data seismic data is used for verifying the denoising effect of the self-adaptive method. The two-dimensional actual seismic data is shown in fig. 6, the data has 200 channels, each channel comprises 270 sampling points, the sampling rate is 2ms, the signal-to-noise ratio of the seismic data is low, the continuity of seismic event axes is poor, the random noise energy is strong, faults exist in the middle part and the lower part of the section, and particularly, a plurality of fracture structures exist in the same depth of the lower part.
FIG. 7 is a process for determining the number of event axes of two-dimensional actual seismic data in an adaptive manner. The horizontal axis indicates different frequencies, the vertical axis indicates the number of corresponding singular values, and the number of singular values determined by the adaptive method is 8 as seen from the solid line in fig. 7.
FIG. 8(a) is the result of denoising in an adaptive manner, and FIG. 8(b) is the removed noise; the damping factor D is 5, the edges of the earthquake homophase axes are clearly depicted and the noise is completely removed from the result. Although some signal energy loss exists between the bending and breaking coaxial regions, the protection on construction details is good, faults are still well represented, and experiments show that the method has a good effect in denoising two-dimensional actual seismic data.
The above-described embodiments are merely illustrative of the preferred embodiments of the present application, and do not limit the scope of the present application, and various modifications and improvements made to the technical solutions of the present application by those skilled in the art without departing from the spirit of the present application should fall within the protection scope defined by the claims of the present application.

Claims (8)

1. A self-adaptive multi-channel singular spectrum analysis seismic data denoising method is characterized by comprising the following steps:
step 1: presetting time domain seismic data, and converting the time domain seismic data into frequency domain seismic data through DFFT;
step 2: generating a block Hankel matrix based on the frequency domain seismic data;
and step 3: decomposing the Hankel matrix to obtain a singular value matrix, and combining singular values in the singular value matrix into a singular value sequence;
and 4, step 4: based on Akaike information criterion, transforming the singular value sequence to obtain the number of the singular values; and calculating and denoising the number of singular values to obtain denoised seismic data.
2. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 1, wherein the step 2 method comprises:
obtaining frequency slice data of the frequency domain seismic data for each frequency; generating a Hankel matrix based on each row of data of the frequency slice data; and arranging all the Hankel matrixes into one block Hankel matrix.
3. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 2, wherein the singular value matrix is
Figure FDA0003405054900000011
Wherein
Figure FDA0003405054900000012
Is composed of
Figure FDA0003405054900000013
The rank of (c) is determined,
Figure FDA0003405054900000014
is that
Figure FDA0003405054900000015
Of left singular value vector of (V)x×Lx)×(Vx×Lx) An orthogonal matrix of orders;
Figure FDA0003405054900000016
is that
Figure FDA0003405054900000017
Of right singular value vector of (H)x×Ly)×(Hx×Ly) An orthogonal matrix of orders;
Figure FDA0003405054900000018
is a diagonal matrix formed by singular values in descending order, the number of non-zero singular values is equal to the matrix
Figure FDA0003405054900000021
Of rank, wiIs the ith frequency.
4. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 3, wherein the sequence of singular values is
Figure FDA0003405054900000022
5. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 1, wherein the method of transforming the singular value sequence based on Akaike information criterion to obtain the number of singular values comprises:
performing second-order derivation on a singular value sequence curve to obtain the change rate of the slope of the singular value sequence curve; calculating Akaike information criterion values of the change rates of the slope of the singular value sequence curves of all the frequencies at a preset point based on the Akaike information criterion; and calculating the minimum value of the Akaike information criterion values based on all the Akaike information criterion values, wherein the minimum value is the number of singular values of the frequency domain seismic data.
6. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 5, wherein the rate of change of the curve slope of the sequence of singular values is
Figure FDA0003405054900000023
7. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 5, wherein the Akaike information criterion value is
Figure FDA0003405054900000024
8. The adaptive multi-channel singular spectral analysis seismic data denoising method of claim 1, wherein the method of computationally denoising the number of the singular values comprises: and inversely transforming the singular value sequence to a frequency domain through the block Hankel matrix, and then inversely transforming to a time domain through Fourier transform to obtain the denoised seismic data.
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