A weighted nuclear norm minimization algorithm based on enhanced block matching accuracy and a method and application for suppressing low-frequency noise in desert earthquakes

Abstract

The present invention discloses a weighted nuclear norm minimization algorithm based on enhanced block matching accuracy, including: The present invention discloses a method for suppressing low-frequency noise in desert earthquakes based on a weighted nuclear norm minimization algorithm, including the following steps: Step 1, collecting desert earthquake low-frequency noise, determining the original reference data block and multiple ordinary data blocks, and obtaining a filtered reference data block and multiple ordinary data blocks; Step 2, calculating the similarity between the filtered reference data block and each ordinary data block, selecting the first m filtered ordinary data blocks as blocks similar to the filtered reference data block and merging them into a data matrix; Step 3, obtaining an approximate similar block data matrix of an ideal pure similar block data matrix from the data matrix; Step 4, obtaining approximate pure earthquake low-frequency noise data after noise suppression; The present invention also discloses an application of the method for suppressing low-frequency noise in desert earthquakes in suppressing low-frequency noise in desert earthquakes.

Description

Technical Field

[0001] The present invention relates to the field of suppressing desert noise, and in particular to a weighted nuclear norm minimization algorithm based on enhancing block matching accuracy and a method and application for suppressing low-frequency noise in desert earthquakes. Background Art

[0002] In the process of seismic signal acquisition, seismic signals are always contaminated by various random noises, which will greatly reduce the signal-to-noise ratio of seismic signals and make them less visible. The existence of random noise will lead to invalid recognition of reflected signals, which will affect the subsequent analysis of geological structures. Therefore, noise suppression plays a vital role in seismic signal processing. The low-frequency, non-stationary, and non-Gaussian characteristics of noise in desert areas make some traditional methods that have good effects in processing Gaussian white noise unable to suppress noise in desert areas well, which adds difficulty to the processing of seismic signals in desert areas. Based on the problems existing in current technology, it is necessary to focus on the suppression method of low-frequency noise in desert areas.

[0003] In recent years, the low-rank matrix approximation method has been widely used in seismic noise suppression due to its superior performance in noise suppression. According to the low-rank prior of seismic signals, seismic signals can be considered to be low-rank after a certain data transformation. The Hankel matrix composed of pure signals is decomposed into the product of two low-dimensional factor matrices using the iterative reweighted least squares (IRLS) method, and then a robust metric is obtained using the biquad function to approximate the Hankel matrix to a low-rank matrix. Non-low-rank seismic images containing multiple tilt events can be decomposed by EMD to obtain multiple low-rank signals (ELR) with only one tilt event. HLR simultaneously utilizes the Hankel structure and low-rank properties of useful seismic signals to better recover useful seismic signals from noisy seismic signals. Summary of the invention

[0004] The invention designs and develops a weighted nuclear norm minimization algorithm based on enhancing block matching accuracy. The invention aims to solve the problem that random noise cannot be effectively suppressed, which leads to inaccurate testing of desert noise for seismic low-frequency noise.

[0005] The present invention also discloses a method for suppressing low-frequency noise in desert earthquakes based on a weighted nuclear norm minimization algorithm. The purpose of the present invention is to utilize the non-local self-similarity of seismic records to construct a matrix with a low-rank prior through block matching, and then use the low-rank matrix approximation method to suppress random noise and thereby obtain a method for suppressing low-frequency noise in desert earthquakes.

[0006] The invention also discloses the application of the method for suppressing low-frequency noise in desert earthquakes in suppressing low-frequency noise in desert earthquakes. The purpose of the invention is to effectively suppress low-frequency random noise of desert earthquakes in practical applications.

[0007] The technical solution provided by the present invention is:

[0008] A weighted nuclear norm minimization algorithm based on enhancing block matching accuracy includes:

[0009]

[0010] In the formula, For Obtained The approximately similar block data matrix of is the noisy similar block data matrix, is an ideal pure similar block data matrix, w=[w1,w2,…,w n ] is the weight threshold vector, is the weighted nuclear norm;

[0011] in,

[0012] In the formula, c is a constant and c>0, and m is a matrix The number of similar blocks in For a pure matrix The singular value of , σ is the standard deviation of noise, and ε is a constant;

[0013] Among them, block matching is performed in the noisy data signal, a reference data block is selected, the similarity between multiple common data blocks around and the reference data block is calculated in the search range, and after arranging them in descending order, the first m common data blocks are selected as blocks similar to the reference data block and merged into a data matrix And the ideal pure similar block data matrix is of low rank.

[0014] Preferably, The calculation process is:

[0015] Preferably, ε=10 -16 .

[0016] Preferably, the similarity is the Euclidean distance between the reference data block and the common data block.

[0017] Preferably, the originally collected reference data blocks and common data blocks are processed by a bandpass filter to obtain the filtered reference data blocks and the common data blocks.

[0018] A method for suppressing low-frequency noise in desert earthquakes based on a weighted nuclear norm minimization algorithm comprises the following steps:

[0019] Step 1: Collect low-frequency noise from desert earthquakes and determine the original reference data block and multiple normal data blocks After that, the filtered data block is obtained by filtering through a bandpass filter. and multiple normal data blocks

[0020] Step 2: Calculate the filtered reference data block With each normal data block The similarity between them is calculated, and they are sorted in descending order, and the first m filtered common data blocks are selected. As the reference data block after filtering Similar blocks are merged into a data matrix

[0021] Step 3: Using the weighted nuclear norm minimization algorithm, from the data matrix Get the ideal pure similar block data matrix The approximately similar block data matrix

[0022] Step 4: the approximately similar block data matrix Perform the reverse operation of stacking data into a data matrix to obtain approximately pure seismic low-frequency noise data after noise suppression.

[0023] Preferably, in step 2, the similarity is the reference data block after filtering. With each normal data block The Euclidean distance between .

[0024] Preferably, in step 3, the weighted nuclear norm minimization algorithm is:

[0025]

[0026] In the formula, For Obtained The approximately similar block data matrix of is the noisy similar block data matrix, is an ideal pure similar block data matrix, w=[w1,w2,…,w n ] is the weight threshold vector, is the weighted nuclear norm;

[0027] in,

[0028] In the formula, c is a constant and c>0, and m is a matrix The number of similar blocks in For a pure matrix is the singular value of , σ is the noise standard deviation, and ε is a constant.

[0029] Preferably, The calculation process is: as well as

[0030] ε=10 -16 .

[0031] The invention discloses an application of a method for suppressing low-frequency noise in desert earthquakes to suppressing low-frequency noise in desert earthquakes, and uses the method for suppressing low-frequency noise in desert earthquakes.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The WNNM algorithm can use the non-local self-similarity of seismic records to construct a matrix with a low-rank prior through block matching, and then use the low-rank matrix approximation method to suppress random noise. However, the presence of random noise will greatly affect the accuracy of block matching, and it cannot be guaranteed that the constructed matrix has a low-rank prior. The low-rank matrix approximation method cannot effectively suppress random noise. Therefore, the present invention proposes to add a bandpass filter that has a certain suppression effect on low-frequency noise in desert areas during block matching. When calculating the similarity of two noisy data blocks, the two noisy data blocks are first roughly filtered with a bandpass filter, and then the similarity of the two filtered data blocks is calculated. This similarity is used to represent the similarity between the noisy data blocks. The original WNNM algorithm and the bandpass + WNNM comparison verify the feasibility and effectiveness of the method of the present invention.

[0034] 2. The present invention adds a bandpass filter suitable for low-frequency noise during block matching. When processing other noises, the bandpass filter can be replaced with a method that has a certain suppression effect on the noise type. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] FIG. 1( a ) is an ideal signal of the synthetic seismic recording according to the present invention.

[0036] FIG1( b ) is a noisy signal of the synthetic seismic record described in the present invention.

[0037] FIG1( c ) is a bandpass filter denoising result of the synthetic seismic record described in the present invention.

[0038] FIG1( d ) is the original WNNM algorithm denoising result of the synthetic seismic record described in the present invention.

[0039] FIG1(e) is a bandpass+WNNM denoising result of the synthetic seismic record described in the present invention.

[0040] FIG1( f ) is a denoising result of the synthetic seismic record according to the present invention based on the weighted nuclear norm minimization algorithm.

[0041] FIG. 2( a ) is the difference between the synthetic seismic record before and after pure noise removal according to the present invention.

[0042] FIG. 2( b ) is the difference between the synthetic seismic record before and after the bandpass filter denoising according to the present invention.

[0043] FIG. 2( c ) is the difference between the original WNNM algorithm denoising of the synthetic seismic record described in the present invention.

[0044] FIG. 2( d ) is the difference between the synthetic seismic record before and after bandpass+WNNM denoising according to the present invention.

[0045] FIG. 2( e ) is the difference between the synthetic seismic record before and after denoising based on the weighted nuclear norm minimization algorithm described in the present invention.

[0046] FIG3(a) is a composite record of a single channel randomly selected from the record of FIG1(a).

[0047] FIG3( b ) is a synthetic record of a single channel randomly selected from the record of FIG1( b ).

[0048] FIG3(c) is a synthetic record of a single channel randomly selected from the record of FIG1(c).

[0049] FIG3( d ) is a composite record of a single channel randomly selected from the record in FIG1( d ).

[0050] FIG3( e ) is a synthetic record of a single channel randomly selected from the record of FIG1( e ).

[0051] FIG3( f ) is a composite record of a single channel randomly selected from the record in FIG1( f ).

[0052] Figure 4(a) is the corresponding FK spectrum recorded in Figure 1(a).

[0053] Figure 4(b) is the corresponding FK spectrum recorded in Figure 1(b).

[0054] Figure 4(c) is the corresponding FK spectrum recorded in Figure 1(c).

[0055] Figure 4(d) is the corresponding FK spectrum recorded in Figure 1(d).

[0056] Figure 4(e) is the corresponding FK spectrum recorded in Figure 1(e).

[0057] Figure 4(f) is the corresponding FK spectrum recorded in Figure 1(f).

[0058] Figure 5(a) is the corresponding FK spectrum recorded in Figure 2(a).

[0059] Figure 5(b) is the corresponding FK spectrum recorded in Figure 2(b).

[0060] Figure 5(c) is the corresponding FK spectrum recorded in Figure 2(c).

[0061] Figure 5(d) is the corresponding FK spectrum recorded in Figure 2(d).

[0062] Figure 5(e) is the corresponding FK spectrum recorded in Figure 2(e).

[0063] FIG. 6( a ) is an original record of an actual earthquake record according to the present invention.

[0064] FIG6( b ) is a bandpass filter denoising result of an actual earthquake record according to the present invention.

[0065] FIG6( c ) is the original WNNM algorithm denoising result of the actual earthquake record described in the present invention.

[0066] FIG6( d ) is the bandpass+WNNM denoising result of the actual earthquake record described in the present invention.

[0067] FIG6(e) is a denoising result of an actual seismic record according to the present invention based on a weighted nuclear norm minimization algorithm. DETAILED DESCRIPTION

[0068] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0069] Non-local self-similarity is an important prior information of desert earthquake signals, that is, several data blocks similar to a data block of a specific size can be found near this block in the desert earthquake signal. The matrix stacked by these similar blocks has the characteristics of low rank, so the low rank matrix approximation method can be used to recover the effective signal; at the same time, weighted nuclear norm minimization (WNNM) is a method with the most significant noise suppression effect among the low rank matrix approximation methods. It uses the non-local self-similarity of pure seismic signals to process the matrix stacked by similar data blocks in the seismic signal. In WNNM, the method of finding similar blocks is to calculate the Euclidean distance between two data blocks. The smaller this value is, the more similar the two data blocks are. The process of finding similar blocks is also called block matching, which is carried out in a noisy seismic signal. Only when the potential pure similar block matrix corresponding to the noisy similar block matrix stacked by block matching meets the low rank standard, WNNM can show excellent denoising effect, that is, the higher the block matching accuracy, the better the denoising effect; but since block matching is carried out in a noisy seismic signal, Therefore, this can only ensure that these noisy data blocks are similar, but cannot ensure that the pure data blocks corresponding to these noisy data blocks are similar, because the existence of noise will greatly affect the accuracy of block matching. The higher the noise level, the greater the impact on block matching. Therefore, the present invention provides a method for suppressing low-frequency noise in desert earthquakes based on a weighted nuclear norm minimization algorithm, comprising the following steps:

[0070] Step 1: Collect low-frequency noise from desert earthquakes and determine the original reference data block and multiple normal data blocks After that, the filtered data block is obtained by filtering through a bandpass filter. and multiple normal data blocks

[0071] Step 2: Calculate the filtered reference data block With each normal data block The similarity between them is calculated, and they are sorted in descending order, and the first m filtered common data blocks are selected. As the reference data block after filtering Similar blocks are merged into a data matrix

[0072] Step 3: Using the weighted nuclear norm minimization algorithm, the data matrix Get the ideal pure similar block data matrix The approximately similar block data matrix

[0073] Step 4: the approximately similar block data matrix Perform the reverse operation of stacking data into a data matrix to obtain approximately pure seismic low-frequency noise data after noise suppression.

[0074] In step 3, the weighted nuclear norm minimization algorithm calculation process in this embodiment includes:

[0075] This application models the noisy desert earthquake signal as:

[0076] Y=X+N; (1)

[0077] Where Y is noisy seismic data, X is ideal pure seismic data, and N is random noise in the desert area. In this embodiment, random noise N has the characteristics of low frequency, non-stationary, and non-Gaussian. The purpose of denoising is to recover from Y a data that is as close to X as possible. In general, X itself is not low-rank, but in order to obtain a matrix that satisfies the low-rank property, block matching is required in Y, that is, first select a reference data block Then, within a search window of a specific size, we search for several data blocks that are most similar to the reference data block and stack them into a matrix. Formula (1) can be expressed as:

[0078]

[0079] in, and They represent the corresponding ideal pure similar block matrix and random noise similar block matrix respectively; without considering the influence of noise on block matching, it is considered that Satisfies the low-rank standard, so we can use the low-rank matrix approximation method to get Obtained Approximation All According to the reverse operation of the original stack, we can get By using the nuclear norm minimization (NNM) method, Obtained Right now

[0080]

[0081] Among them, ||·|| F represents the Frobenius norm, λ is a constant and λ>0, ||·|| * represents the nuclear norm of the matrix,

[0082] Among them, σ i(·) represents the i-th singular value of the matrix; the low-rank matrix approximation problem based on NNM can be easily solved by soft thresholding the singular values ​​of the observation matrix, that is, the solution of (3) can be obtained by the following formula

[0083]

[0084] in, yes The singular value decomposition of S λ (Σ) means that the diagonal matrix Σ is processed by soft threshold function, and the threshold is λ, that is, for each diagonal element Σ in Σ ii ,have

[0085] S λ (Σ) ii =max(Σ ii -λ,0);) (6)

[0086] Although NNM is widely used in low-rank matrix approximation, it still has some problems. In order to ensure convexity, the standard NNM performs the same threshold processing on each singular value, that is, the soft threshold operation in (6) reduces each singular value by λ. NNM ignores the prior information of the singular values ​​of the matrix. In general, the row (column) vectors of the matrix are usually located in a low-dimensional subspace, and the larger singular values ​​are usually related to the main projection direction; therefore, it is best to perform a smaller threshold processing on the larger singular values ​​to retain the main data components. Although (3) is convex and has a global optimal solution, it does not take this prior information into account when dealing with practical problems and cannot achieve good results.

[0087] In order to consider the importance of singular values ​​according to their size, a weighted nuclear norm minimization (WNNM) algorithm is proposed, which assigns different thresholds to singular values ​​of different sizes, as defined below:

[0088]

[0089] Where w=[w1,w2,…,w n ] is the weight threshold vector, is the weighted nuclear norm, w i Defined as

[0090]

[0091] Where c is a constant and c>0, m is a matrix The number of similar blocks in the equation, ε is a very small number. In order to avoid the denominator being 0, in this embodiment, ε=10 -16 , Represents a pure matrix The singular values ​​of is unknown, so It needs to be estimated by the following formula

[0092]

[0093] Here, σ represents the standard deviation of the noise.

[0094] From formula (8), we can see that the matrix The larger the singular value of i The smaller it is, the better WNNM can utilize the prior information of the matrix singular values. Although when the weight vector w is arranged in non-descending order, equation (7) is non-convex and cannot guarantee that it has a global optimal solution, it is proved that its local minimum optimal solution can be obtained through iteration. The method for solving equation (7) is similar to equation (3), that is,

[0095]

[0096] S w (Σ) ii =max(Σ ii -w i ,0); (11)

[0097] In step 2, the block matching strategy process in this embodiment includes:

[0098] WNNM uses the non-local self-similarity of the records to be processed to search for several blocks that are most similar to the reference block within a search window of a specific size and synthesize these blocks into a data matrix. WNNM uses a simple and effective grouping technique called matching, which is achieved by calculating the similarity between the reference block and blocks located at different spatial positions in pairs.

[0099] The similarity between two data blocks can be expressed by the distance between them. The smaller the distance, the more similar they are. WNNM uses the Euclidean distance, that is, a common block and reference blocks The similarity between them can be expressed as:

[0100]

[0101] WNNM sorts all blocks in descending order according to the similarity between common blocks and reference blocks, and then selects the first m blocks as blocks similar to the reference blocks and merges them into a data matrix WNNM will be integrated with the matrix The corresponding clean data matrix By default, it is low rank, so we can use formula (7) according to the low rank property. Recover from Approximation

[0102] In step 1, the process of enhancing the block matching accuracy by using a bandpass filter in this embodiment includes:

[0103] There is a problem in WNNM when matching blocks. WNNM should use the non-local self-similarity of pure seismic signals, but when searching for similar blocks, it is done in noisy seismic signals. There is no doubt that the presence of noise will greatly affect the accuracy of the calculated similarity. Therefore, and Expressed as

[0104]

[0105]

[0106] in, and and Respectively and The corresponding pure data block and pure noise data block in (12) can be expressed as

[0107]

[0108] In fact, what should be used is the similarity of the pure data blocks, that is, to make the similarity of the two noisy data blocks as close as possible to the similarity of the two corresponding pure data blocks.

[0109]

[0110] From equations (15) and (16), we can see that noise is an important factor affecting the calculation of similarity. The higher the noise level, the greater the impact, and the worse the noise suppression effect of the WNNM algorithm. Therefore, how to reduce the impact of noise when calculating similarity in block matching is a key issue in the WNNM algorithm.

[0111] When the WNNM algorithm is used in desert earthquake noise suppression, in order to reduce the influence of desert low-frequency noise on WNNM block matching, the present invention uses a bandpass filter to filter the reference block during block matching. and normal blocks Simply filter the wave and obtain the filtered data blocks respectively and Then when calculating the similarity, use and The similarity between and The similarity between

[0112]

[0113] Because the bandpass filter has a certain inhibitory effect on the low-frequency noise of the desert, the bandpass filter can be used to suppress part of the noise during block matching, so that the calculated similarity Closer This is more in line with the non-local self-similarity of the pure seismic signal. The noisy data matrix stacked in this way The corresponding clean data matrix It better satisfies the low-rank property, so it has a better effect in subsequent denoising.

[0114] For each reference data block, the method of the present invention searches for m data blocks that are most similar to it, and then merges them into a matrix for denoising.

[0115] Example 1

[0116] Synthetic Seismic Recording Experiment

[0117] In order to verify the effectiveness of the method of the present invention, the present invention first tests the synthetic seismic record. The present invention obtains the synthetic record shown in Figure 1(a) through simulation. There are a total of 7 valid events in the record, including hyperbolic reflection events, horizontal events, bending events, cross events and interruption events. These events are generated by Ricker wavelets with a main frequency of 25HZ or 30HZ. In order to obtain synthetic data close to the truth, the present invention adds random noise in the actual desert area, so that the signal-to-noise ratio of the synthetic record is -13.0462dB. As shown in Figure 1(b), it can be seen that the valid events have been basically submerged by random noise;

[0118] In this embodiment, the present invention sets c to , m is 71, the size of the seismic data block is 4×4, and the length of the search window is 50; when processing records with different noise levels, the seismic data block size and search window length that achieve the best effect are different, and they should be debugged according to the actual situation.

[0119] In order to demonstrate the superiority of the method of the present invention, the present invention uses a bandpass filter, the original WNNM algorithm and a bandpass + WNNM (i.e., first preprocessing the noisy record with a bandpass filter, and then processing the preprocessed record with the WNNM algorithm) to compare with the method of the present invention, and their processing results for the record in Figure 1(b) correspond to Figures 1(c)-(f) respectively. Figure 2(a) is a pure noise record added to the record in Figure 1(b), and the parts filtered out by these four methods correspond to Figures 2(b)-(e) respectively. Figures 3(a)-(f) are respectively a single-channel synthetic record (channel 3) randomly selected from the records in Figures 1(a)-(f). It can be seen intuitively from the processing result diagram that a lot of noise still remains in the records processed by the bandpass filter, and the signal is not completely restored; no effective signal can be seen in the records processed by the original WNNM algorithm, and the signal can be clearly seen in the filtered records; although the bandpass + WNNM has a significant suppression effect on desert noise, some noise still remains, and the signal produces artifacts; the method of the present invention suppresses desert noise more thoroughly, and the effective signal is also clearly restored, and basically no effective signal can be seen in the filtered records. In comparison, the processing effect of the method of the present invention is the best.

[0120] In order to more comprehensively compare the processing results of these four methods, the present invention analyzes the denoising results of these four methods in the frequency domain. Figure 4 (a)-(f) are the corresponding FK spectra recorded in Figure 1 (a)-(f), and Figure 5 (a)-(e) are the corresponding FK spectra recorded in Figure 2 (a)-(e). It can be clearly seen that the bandpass filter filters out both low-frequency and high-frequency signals and noise, and the noise in the same frequency band as the signal is not filtered out; There is no obvious signal frequency in the result of the original WNNM algorithm processing, only part of the noise frequency, and it can be seen from Figure 5 (c) that the effective signal is filtered out; Bandpass + WNNM is just based on the processing result of the bandpass filter and then processed by WNNM. It can be seen that the low-frequency and high-frequency signals filtered by the bandpass are still not restored, but only part of the noise in the same frequency band as the signal is filtered out, which enhances the effective signal of this frequency band; The method of the present invention can well restore the effective signal and has a strong suppression effect on low-frequency noise.

[0121] In order to evaluate the processing performance of the method of the present invention on records with different noise levels, the method is used to process synthetic seismic records with signal-to-noise ratios ranging from 2.0027dB to -13.0462dB, and the bandpass filter, the original WNNM algorithm and the bandpass + WNNM are used for comparison. The denoising results are quantitatively analyzed by calculating the signal-to-noise ratio and mean square error of the processed records. The calculation formulas for the signal-to-noise ratio and mean square error are as follows:

[0122]

[0123]

[0124] Where X is an ideal pure signal, is the processed signal, N represents X and The number of elements in .

[0125] As described in Table 1 and Table 2, the signal-to-noise ratios of the processing results of the four methods are listed in Table 1, and the mean square errors are listed in Table 2; the higher the signal-to-noise ratio and the lower the mean square error, the better the denoising result. It can be seen from Table 1 and Table 2 that the signal-to-noise ratio after processing by the method of the present invention is always significantly higher than that of other methods, and the mean square error suppression is significantly lower than that of other methods. This can indicate that the performance of the method of the present invention in processing records with different noise levels is better than that of several other methods.

[0126] Table 1. Comparison of signal-to-noise ratio (dB) of processing results of different methods

[0127]

[0128] Table 2. MSE comparison of processing results of different methods

[0129]

[0130]

[0131] Example 2

[0132] Actual earthquake recording experiment

[0133] In order to further test the feasibility and effectiveness of the method of the present invention in processing actual data, the present invention uses it to process a 109-channel actual common shot point record collected in a desert area in Figure 6 (a), and the sampling frequency of the record is 500Hz. It can be seen from Figure 6 (a) that the existence of random noise and surface waves conceals the effective reflection events, and the continuity of effective seismic events is seriously damaged. In order to reflect the superiority of the method of the present invention in suppressing random noise in desert areas, the present invention also uses a bandpass filter, the original WNNM algorithm and the bandpass + WNNM processing results to compare with the method of the present invention. The processing results of these four methods correspond to Figures 6 (b)-(e) respectively. It can be seen from Figure 6(b) that the bandpass filter has a certain suppression effect on low-frequency noise and surface roll, and can also restore some effective reflection events, but there is still some residual random noise, which is particularly obvious in the area circled by the box; it can be seen from Figure 6(c) that the original WNNM algorithm basically does not suppress the low-frequency noise before the first arrival, and the suppression of the surface roll is not thorough enough, and the effective seismic events are not well restored; it can be seen from Figure 6(d) that the bandpass + WNNM can further suppress the noise on the basis of the bandpass filter processing, but it can be seen from the box part that there is still obvious noise residue; it can be seen from Figure 6(e) that the method of the present invention has a significant suppression effect on the random noise of the record, and can also filter out the surface roll to restore the effective reflection events, and the processing result is better than several other methods.

[0134] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for suppressing low-frequency noise in desert earthquakes based on a weighted nuclear norm minimization algorithm, characterized in that: The steps include: Step 1: Collect low-frequency noise from desert earthquakes and determine the original reference data block and multiple normal data blocks After that, the filtered data block is obtained by filtering through a bandpass filter. and multiple normal data blocks Step 2: Calculate the filtered reference data block With each normal data block The similarity between them is calculated, and they are sorted in descending order, and the first m filtered common data blocks are selected. As the reference data block after filtering Similar blocks are merged into a data matrix Step 3: Using the weighted nuclear norm minimization algorithm, from the data matrix Get the ideal pure similar block data matrix The approximately similar block data matrix Step 4: the approximately similar block data matrix Perform the reverse operation of stacking data into a data matrix to obtain approximately pure seismic low-frequency noise data after noise suppression. In the step 2, the similarity is the reference data block after filtering With each normal data block The Euclidean distance between In step 3, the weighted nuclear norm minimization algorithm is: In the formula, For Obtained The approximately similar block data matrix of is the noisy similar block data matrix, is an ideal pure similar block data matrix, w=[w1,w2,…,w n ] is the weight threshold vector, is the weighted nuclear norm; in, In the formula, c is a constant and c>0, and m is a matrix The number of similar blocks in For a pure matrix The singular value of , σ is the standard deviation of noise, and ε is a constant; The calculation process is: as well as e=10 -16 ; The denoising results are quantitatively analyzed by the signal-to-noise ratio and mean square error. The calculation formulas of the signal-to-noise ratio and mean square error are as follows: Where X is an ideal pure signal, is the processed signal, and N represents the number of elements in X and .

2. An application of a method for suppressing low-frequency noise in desert earthquakes in suppressing low-frequency noise in desert earthquakes, characterized in that: Use the method for suppressing low-frequency noise in desert earthquakes as described in claim 1.

Images