Self-adaptive noise reduction method and device for low-rank matrix analysis seismic data

Abstract

The invention provides a low-rank matrix analysis seismic data adaptive noise reduction method, which comprises the steps of collecting seismic data of a preset area, and establishing a three-dimensional seismic data volume according to the seismic data; the three-dimensional seismic data volume is a three-dimensional matrix of a space-time dimension; converting the three-dimensional matrix from a time domain to a matrix of a corresponding frequency domain; constructing Hankel matrixes line by line for the matrix of the frequency domain under a preset frequency to obtain the Hankel matrix of each line; building a block Hankel matrix by using each row of Hankel matrix; performing singular value decomposition on the block Hankel matrix to obtain a plurality of singular values; performing singular value truncation on the block Hankel matrix to obtain a frequency domain matrix after noise reduction; and converting the matrix of the frequency domain after noise reduction into a matrix of a time domain after noise reduction. According to the method, random noise in the seismic data can be effectively removed, and adaptive noise reduction of the seismic data is realized.

Description

Technical Field

[0001] The present invention relates to the field of geophysical exploration, and particularly to a method and device for adaptively denoising seismic data based on low-rank matrix analysis. Background Art

[0002] Seismic data denoising is an important means to improve the imaging resolution of underground media and data quality. In the field of artificial exploration seismology, due to factors such as the complexity of underground media structures, terrain obstacles, and economic costs, the collected raw data often contains a large amount of noise. The noisy and irregular seismic data will have a serious impact on subsequent processing and interpretation steps such as multiple attenuation, reverse time migration imaging, prestack seismic attribute analysis, and post-stack seismic inversion. Therefore, seismic data noise suppression is a very important research topic.

[0003] The current rank reduction methods are based on the basic assumption of seismic linear events. The time-domain signal is first converted into a frequency-domain signal through a discrete fast Fourier transform, and then the rank reduction process is achieved by artificially estimating the same number of singular values to be truncated for all frequencies. For large-scale data, the rank reduction-based methods need to divide the seismic data into different blocks. However, the number of singular values corresponding to each block is different. Currently, it is necessary to artificially estimate the appropriate number of singular values for the data of each block, resulting in low computational efficiency, and the numerical effect of large-scale industrial processing needs to be improved. Summary of the Invention

[0004] In view of the above problems, the present invention is proposed to provide a method and device for adaptively denoising seismic data based on low-rank matrix analysis that overcomes or at least partially solves the above problems.

[0005] In a first aspect, an embodiment of the present invention provides a method for adaptively denoising seismic data based on low-rank matrix analysis, including:

[0006] Collect seismic data in a preset area and establish a three-dimensional seismic data volume according to the seismic data; the three-dimensional seismic data volume is a three-dimensional matrix in the space-time dimension;

[0007] Convert the three-dimensional matrix from the time domain to a matrix in the corresponding frequency domain;

[0008] Construct a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency to obtain a Hankel matrix for each row;

[0009] Construct a block Hankel matrix using the Hankel matrices of each row;

[0010] Perform singular value decomposition on the block Hankel matrix to obtain a plurality of singular values;

[0011] Truncate the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after primary denoising;

[0012] Convert the matrix in the denoised frequency domain into a matrix in the denoised time domain.

[0013] In one embodiment, the truncating the singular values of the block Hankel matrix includes:

[0014] Based on the DFFITS criterion, calculate the multiple singular values to determine whether the singular values need to be truncated;

[0015] If it is determined that truncation is needed, truncate the singular values of the block Hankel matrix to obtain a matrix in the denoised frequency domain.

[0016] In one embodiment, between the truncating the singular values of the block Hankel matrix to obtain a matrix in the denoised frequency domain and converting the matrix in the denoised frequency domain into a matrix in the denoised time domain, it further includes:

[0017] Use a damping algorithm to denoise the matrix in the denoised frequency domain to obtain a matrix in the denoised frequency domain.

[0018] In one embodiment, the calculating the multiple singular values based on the DFFITS criterion to determine whether the singular values need to be truncated includes:

[0019] Arrange the multiple singular values in descending order to obtain a singular vector;

[0020] Establish a linear regression model according to the singular vector;

[0021] Perform the following calculations on the singular values in the singular vector in sequence:

[0022] Calculate the regression prediction value including the current singular value, the regression prediction value not including the current singular value, the standard error of the current singular value, and the leverage value of the current singular value according to the linear regression model;

[0023] Determine the difference between the regression prediction value including the current singular value and the regression prediction value not including the current singular value;

[0024] Calculate the square root of the product of the square of the standard error of the current singular value and the leverage value of the current singular value;

[0025] Calculate the quotient of the difference and the square root;

[0026] Compare the quotient of the difference and the square root with a preset quotient threshold. If the quotient is greater than the preset quotient threshold, determine that the singular value needs to be truncated.

[0027] In one embodiment, the singular vector is δ = [δ1, δ2,..., δ J-2 , δJ-1 , δ J ;

[0028] The expression of the linear regression model is as follows:

[0029] δ = Aβ + e;

[0030] Where: A is a preset full-rank constant matrix; β is a J×p unknown parameter vector; e is a J×1 random distribution error vector;

[0031] The preset quotient threshold is

[0032] In one embodiment, constructing a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency includes:

[0033] Starting from the first element in the first row of the matrix in the frequency domain, take out the first preset number of elements as the row vector of the first row of the Hankel matrix;

[0034] Repeat the above operation until the last element in the first row of the matrix in the frequency domain is taken out to obtain the first row of the Hankel matrix;

[0035] Repeat the above operation until the last element in the last row of the matrix in the frequency domain is taken out.

[0036] In one embodiment, constructing a block Hankel matrix using each row of the Hankel matrix includes:

[0037] Take each row of the Hankel matrix as a block matrix respectively;

[0038] Starting from the block matrix in the first row, take out the second preset number of block matrices as the elements of the first row of the block Hankel matrix;

[0039] Repeat the above operation until the block matrix in the last row of the matrix in the frequency domain is taken out.

[0040] In one embodiment, performing singular value decomposition on the block Hankel matrix to obtain multiple singular values, including:

[0041] Calculate the transpose matrix of the block Hankel matrix;

[0042] Calculate the product of the transpose matrix and the block Hankel matrix to obtain a product matrix;

[0043] Calculate multiple eigenvalues of the product matrix;

[0044] Calculate the square root of the multiple eigenvalues to obtain singular values.

[0045] In one embodiment, the dimension of the three-dimensional matrix is: Nx ×N y ×N t ; where N x and N y are the number of spatial coordinates, and N t is the number of temporal coordinates;

[0046] The first preset quantity is:

[0047] The second preset quantity is:

[0048] where represents rounding.

[0049] In a second aspect, an embodiment of the present invention provides a low-rank matrix analysis seismic data adaptive noise reduction device, including:

[0050] A data volume module, configured to collect seismic data in a preset area and establish a three-dimensional seismic data volume according to the seismic data; the three-dimensional seismic data volume is a three-dimensional matrix in the space-time dimension;

[0051] A conversion module, configured to convert the three-dimensional matrix from the time domain into a matrix in the corresponding frequency domain;

[0052] A Hankel module, configured to construct a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency to obtain a Hankel matrix for each row;

[0053] A block Hankel module, configured to construct a block Hankel matrix by using the Hankel matrices of each row;

[0054] A decomposition module, configured to perform singular value decomposition on the block Hankel matrix to obtain a plurality of singular values;

[0055] A truncation module, configured to truncate the singular values of the block Hankel matrix to obtain a matrix in the noise-reduced frequency domain;

[0056] An inverse conversion module, configured to convert the matrix in the noise-reduced frequency domain into a matrix in the noise-reduced time domain.

[0057] In a third aspect, an embodiment of the present invention provides a computing device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, where when the processor executes the program, the low-rank matrix analysis seismic data adaptive noise reduction method described above is implemented.

[0058] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the low-rank matrix analysis seismic data adaptive noise reduction method described above is implemented.

[0059] The beneficial effects of the above technical solutions provided by the embodiments of the present invention at least include:

[0060] The embodiments of the present invention provide a low-rank matrix analysis-based seismic data adaptive noise reduction method, including: The embodiments of the present invention utilize the low-rank property of linear coaxial lines in seismic data to construct a block Hankel matrix for the matrix in the frequency domain obtained by converting three-dimensional seismic data volumes at a preset frequency; perform singular value decomposition on the block Hankel matrix to obtain a plurality of singular values; truncate the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after noise reduction; convert the matrix in the frequency domain after noise reduction into a matrix in the time domain after noise reduction. By selecting an appropriate number of singular values for each data block, seismic data denoising can be better achieved.

[0061] The embodiments of the present invention decompose the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace through truncated singular value decomposition (TSVD). Among them, determining the number of effective singular values is the key to this method. The embodiments of the present invention use the DFFITS criterion to utilize the characteristics of least squares linear regression of singular values to screen out the number of truncated singular values, automatically determine appropriate singular values and corresponding singular vectors, avoid the uncertainty brought by manual estimation, effectively remove random noise in seismic data and retain the main characteristics of seismic data, optimize the seismic data denoising performance, realize seismic data adaptive noise reduction, save labor costs and time costs, and do not require human intervention. During implementation, automatic denoising processing can be realized, the calculation efficiency can be improved, and industrial application of seismic data denoising based on low-rank matrix analysis can be realized.

[0062] The embodiments of the present invention embed the DFFITS criterion in the damping algorithm to automatically distinguish the singular values corresponding to effective signals from the singular values related to noise, overcome the problem of manually selecting the number of singular values, facilitate the denoising of massive seismic data, can automatically determine a reliable number of singular values, and obtain a denoising result with a high signal-to-noise ratio.

[0063] Other features and advantages of the present invention will be described in the subsequent specification, and part of them will become obvious from the specification or be understood by implementing the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in the written specification, claims, and drawings.

[0064] The technical solutions of the present invention will be further described in detail below through the drawings and embodiments. Description of the Drawings

[0065] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0066] Figure 1 Flow chart of an adaptive seismic data denoising method for low-rank matrix analysis provided by an embodiment of the present invention;

[0067] Figure 2 Flow chart of the method of singular value decomposition provided by an embodiment of the present invention;

[0068] Figure 3 First group of simulated seismic data diagrams provided by an embodiment of the present invention;

[0069] Figure 4 Data diagram of the first group of simulated seismic data after adding random noise provided by an embodiment of the present invention;

[0070] Figure 5 Data diagram of the first group of simulated seismic data after denoising provided by an embodiment of the present invention;

[0071] Figure 6 Data diagram of the noise removed from the first group of simulated seismic data provided by an embodiment of the present invention;

[0072] Figure 7 First group of real seismic data diagrams provided by an embodiment of the present invention;

[0073] Figure 8 Data diagram of the first group of real seismic data after denoising provided by an embodiment of the present invention;

[0074] Figure 9 Data diagram of the noise removed from the first group of real seismic data provided by an embodiment of the present invention;

[0075] Figure 10 Second group of real seismic data diagrams provided by an embodiment of the present invention;

[0076] Figure 11 Data diagram of the second group of real seismic data after denoising provided by an embodiment of the present invention;

[0077] Figure 12 Data diagram of the noise removed from the second group of real seismic data provided by an embodiment of the present invention;

[0078] Figure 13 Structure block diagram of an adaptive seismic data denoising device for low-rank matrix analysis provided by an embodiment of the present invention. Detailed implementation manners

[0079] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0080] Generally speaking, in seismic data, compared with random noise, the energy of the effective signal is more concentrated and the correlation is better, and it can be represented by larger singular values and their related singular vectors. The number of linear event axes in the effective signal is the same as the number of ranks of the Hankel matrix of the effective signal block, that is, equal to the number of non-zero singular values in the matrix; therefore, introducing noise will not only increase the number of non-zero singular values in the Hankel matrix of the effective signal block, but also change the size of the corresponding singular values. Therefore, the denoising problem of seismic data can be transformed into the problem of restoring the number and size of the singular values of the Hankel matrix of the effective signal block.

[0081] Based on the above analysis, an embodiment of the present invention provides a low-rank matrix analysis seismic data adaptive denoising method, and its flowchart is as Figure 1 shown, including:

[0082] Step S11, collect seismic data in a preset area and establish a three-dimensional seismic data volume according to the seismic data; the three-dimensional seismic data volume is a three-dimensional matrix in the space-time dimension;

[0083] Step S12, convert the three-dimensional matrix from the time domain to a matrix in the corresponding frequency domain;

[0084] Step S13, construct a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency to obtain the Hankel matrix of each row;

[0085] Step S14, construct a block Hankel matrix using the Hankel matrices of each row;

[0086] Step S15, perform singular value decomposition on the block Hankel matrix to obtain a plurality of singular values;

[0087] Step S16, truncate the singular values of the block Hankel matrix to obtain a matrix in the denoised frequency domain;

[0088] Step S17, convert the matrix in the denoised frequency domain to a matrix in the denoised time domain.

[0089] The above three-dimensional data volume in the space-time dimension is D time (x, y, t), where x = 1,..., N x and y = 1,..., N y represent spatial coordinates, and t = 1,..., N t represents the time coordinate; the dimension of the three-dimensional matrix is: Nx ×N y ×N t ; where N x and N y is the number of spatial coordinates, and N t is the number of time coordinates;

[0090] In the above step S13, the preset frequency can be, for example, w0. Then, at the frequency w0, the matrix in the frequency domain corresponds to:

[0091]

[0092] where N x is the number of spatial coordinates in the x direction of the three-dimensional matrix.

[0093] A method for constructing a Hankel matrix row by row for the above matrix D(w0) can be, for example:

[0094] Starting from the first element in the first row of the matrix in the frequency domain, take out the first preset number of elements as the row vector of the first row of the Hankel matrix;

[0095] Repeat the above operation until the last element in the first row of the matrix in the frequency domain is taken out to obtain the Hankel matrix of the first row;

[0096] Repeat the above operation until the last element in the last row of the matrix in the frequency domain is taken out.

[0097] Then, according to the above method of constructing the Hankel matrix row by row, D(w0) is constructed, and the Hankel matrix of each row obtained is:

[0098]

[0099] where m is the first preset number. To make the calculation more concise and convenient and the dimension of the Hankel matrix approximate a square matrix, it is generally defaulted that where represents rounding.

[0100] In one embodiment, in the above step S14, a block Hankel matrix is constructed using the Hankel matrix of each row. For example, the following method can be adopted:

[0101] Respectively take each row Hankel matrix as a block matrix;

[0102] Starting from the block matrix in the first row, take out the second preset number of block matrices as the elements of the first row of the block Hankel matrix;

[0103] Repeat the above operation until the block matrix in the last row of the matrix in the frequency domain is taken out.

[0104] According to the above method of constructing the block Hankel matrix, for Ri Construct it, and the obtained block Hankel matrix can be represented in the following manner:

[0105]

[0106] where n is the second preset quantity. In the case of making the calculation more efficient and the dimension of the block Hankel matrix being approximately a square matrix, select where represents rounding down.

[0107] The size of the block Hankel matrix is I×J, where I = (N x - m + 1)(N y - n + 1), J = mn; m and n are positive integers.

[0108] In the above step S15, perform singular value decomposition on the block Hankel matrix. According to the singular value decomposition theorem, the steps are as follows:

[0109] Since the block M of the block Hankel matrix in the embodiment of the present invention can be expressed as the superposition of the block Hankel matrix S of the effective signal and the block Hankel matrix N of the noise, then:

[0110] M = S + N;

[0111] Assume that M and N are full-rank matrices, that is, rank(M) = rank(N) = J, while S is a low-rank matrix, that is, rank(S) = N < J. The singular value decomposition performed on the block Hankel matrix M can be expressed as:

[0112]

[0113] where the diagonal matrix has larger singular values, the diagonal matrix has smaller singular values, and the singular values in are arranged in descending order of magnitude.

[0114] represents the correlation matrix composed of singular vectors.

[0115] In the above step S15, perform singular value decomposition on the block Hankel matrix to obtain multiple singular values, which can be carried out in the following manner:

[0116] S21. Calculate the transpose matrix of the block Hankel matrix;

[0117] S22. Calculate the product of the transpose matrix and the block Hankel matrix to obtain a product matrix;

[0118] S23. Calculate multiple eigenvalues of the product matrix;

[0119] S24. Calculate the square roots of multiple eigenvalues to obtain singular values.

[0120] The calculated singular values can be referred to the following formula:

[0121] δ i (i = 1, 2,..., J)

[0122] δ i is the i-th singular value of M;

[0123] The aforementioned singular vectors are composed of δ i in descending order and can be expressed by the following formula:

[0124] δ = [δ1, δ2,..., δ J-2 , δ J-1 , δ J .

[0125] Between the aforementioned step S116 and the aforementioned step S17, it further includes:

[0126] Use the damping algorithm to perform noise reduction on the matrix in the frequency domain after noise reduction to obtain the matrix in the frequency domain after noise reduction.

[0127] To remove noise, assume is the singular value corresponding to the noise and make it 0, then a block Hankel matrix containing only the effective signal can be obtained.

[0128]

[0129] However, it is actually still contaminated by residual random noise. The embodiment of the present invention uses the damped multi-channel singular spectrum analysis (DMSSA) algorithm to attenuate the residual random noise that cannot be eliminated by the traditional MSSA algorithm. The damping matrix T is introduced into the MSSA algorithm in the following way.

[0130]

[0131]

[0132] where I is the identity matrix. represents the largest element in, and K represents the damping factor. It is worth mentioning that the larger K is, the weaker the damping. When K → ∞, Equation (2) degenerates into Equation (1).

[0133] If the number of singular values corresponding to the effective signal is N, then the singular value diagonal matrix Only the first N singular values ​​are retained, and the sizes of all other singular values ​​are set to zero. The number N of singular value cutoffs determines the effect of noise suppression and the degree of retention of effective signals. If N is selected too small, effective signals will be lost; if N is selected too large, noise will be retained. For multi-channel singular spectrum analysis methods, automatically determining the number of singular values ​​that are cut off is the key. The above derivation assumes that N is known, but for actual seismic data, how to determine the number of singular values ​​that should be retained in each data block is a vital issue that needs to be solved urgently. An embodiment of the present invention proposes a method based on the fitting difference (DFFITS) criterion to automatically determine the appropriate number of singular value cutoffs, thereby realizing the industrial application of multi-channel singular spectrum analysis methods.

[0134] In a full-rank linear regression model, the DFFITS criterion can be used to determine the contribution of each data point to the certainty of the least squares estimate of the parameter vector. The singular value distribution characteristics of seismic data (most singular values ​​are statistically linearly related) are very conducive to the application of the DFFITS criterion. Larger singular values ​​have a greater impact on the least squares fit of all singular values ​​and can therefore be regarded as strong influencing points. The DFFITS criterion can quantitatively describe this impact.

[0135] In the aforementioned step S16, truncating singular values ​​of the block Hankel matrix includes:

[0136] Based on the DFFITS criterion, the plurality of singular values ​​are calculated to determine whether the singular values ​​need to be truncated;

[0137] If it is determined that truncation is required, the singular values ​​of the block Hankel matrix are truncated to obtain a frequency domain matrix after noise reduction.

[0138] The aforementioned calculation of multiple singular values ​​based on the DFFITS criterion to determine whether the singular values ​​need to be truncated includes:

[0139] According to the singular vector δ, a linear regression model is established;

[0140] For the singular values ​​δ in the singular vector δ i Perform the following calculations in sequence:

[0141] Calculate the current singular value δ according to the linear regression model i The regression prediction value does not include the current singular value δ i The regression prediction value and the current singular value δ i The standard error and the current singular value δ i The leverage value;

[0142] Determine the value containing the current singular value δ i The regression prediction value and the current singular value δ are not included i The difference between the regression prediction values ​​of

[0143] Calculate the current singular value δ i The sum of the squares of the standard errors of δ and the current singular value δ i The square root of the product of the leverage values of δ;

[0144] Calculate the quotient of the difference and the square root;

[0145] Compare the quotient of the difference and the square root with a preset quotient threshold. If the quotient is greater than the preset quotient threshold, it is determined that the singular value needs to be truncated.

[0146] The expression of the above linear regression model is as follows:

[0147] δ = Aβ + e;

[0148] Where: A is a known full-rank constant matrix; β is an unknown parameter vector of J×p; e is a random distribution error vector of J×1, and E(e) = 0.

[0149] In regression analysis, the DFFITS criterion is used to detect strong influence points in the data and measure the influence of each data point on the predicted value. The DFFITS criterion is an elimination method that measures the influence of removing the i-th observation on the predicted value, that is, the fitted value, and is written in the following form

[0150]

[0151] In the formula, and refer to the regression predicted values with and without point i, that is is the y obtained when removing the i-th observation i The fitted value of S (i) is the standard error without point i, and h ii is the leverage value of this point. For simple linear regression analysis, if the DFFITS value of a certain data point is greater than then this point can be regarded as a strong influence point. The present invention uses this theory as the threshold for selecting singular values, that is, the threshold of the above preset quotient.

[0152] Finally, the frequency slice of the seismic data is restored from the block Hankel matrix of the effective signal and then the denoised seismic data in the time-space domain is obtained through the inverse discrete Fourier transform.

[0153] Use the above low-rank matrix analysis seismic data adaptive denoising method to denoise the simulated seismic data. The first group of simulated seismic data diagrams is as Figure 3 shown. The data dimension is 300×60, there are 300 sampling points in time, the sampling rate is 2 ms, and there are 60 sampling points in both the main survey line direction and the connecting survey line direction;Figure 3 is the data without noise, Figure 4 is the data after adding random noise, with a signal-to-noise ratio of -4.6590 dB. The result after denoising is as shown in Figure 5 , with a signal-to-noise ratio of 21.7780 dB. The removed noise is as shown in Figure 6 ; The number of singular values confirmed in the embodiment of the present invention is 3.

[0154] The first group of real seismic data diagram is as shown in Figure 7 , with a time sampling rate of 4 ms, 200 time sampling points, and 300 channels in space. The denoising result is as shown in Figure 8 , and the removed noise is as shown in Figure 9 ; The number of singular values confirmed in the embodiment of the present invention is 8.

[0155] The second group of real seismic data with noise data 2 is as shown in 10, with a time sampling rate of 4 ms, 100 time sampling points, and 300 channels in space. Figure 11 is the denoising result, Figure 12 is the diagram of the removed noise; The number of singular values confirmed in the embodiment of the present invention is 7.

[0156] Based on the same inventive concept, the embodiment of the present invention also provides an adaptive seismic data denoising device based on low-rank matrix analysis. Its structural block diagram is as shown in Figure 13 , and includes:

[0157] A data volume module 131, configured to collect seismic data in a preset area and establish a three-dimensional seismic data volume according to the seismic data; the three-dimensional seismic data volume is a three-dimensional matrix in the space-time dimension;

[0158] A conversion module 132, configured to convert the three-dimensional matrix from the time domain to a corresponding matrix in the frequency domain;

[0159] A Hankel module 133, configured to construct a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency to obtain a Hankel matrix for each row;

[0160] A block Hankel module 134, configured to construct a block Hankel matrix by using the Hankel matrices of each row;

[0161] A decomposition module 135, configured to perform singular value decomposition on the block Hankel matrix to obtain a plurality of singular values;

[0162] A truncation module 136, configured to truncate the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after denoising;

[0163] An inverse conversion module 137, configured to convert the matrix in the frequency domain after denoising to a matrix in the time domain after denoising.

[0164] Based on the same inventive concept, an embodiment of the present invention further provides a computing device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, a method for adaptively denoising seismic data by low-rank matrix analysis is implemented.

[0165] Based on the same inventive concept, an embodiment of the present invention further provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, a method for adaptively denoising seismic data by low-rank matrix analysis is implemented.

[0166] Since the principles of the problems solved by these devices are similar to those of the aforementioned method for adaptively denoising seismic data by low-rank matrix analysis, the implementation of these devices can refer to the implementation of the aforementioned method, and the repeated parts will not be elaborated.

[0167] An embodiment of the present invention provides a method for adaptively denoising seismic data by low-rank matrix analysis, including: The embodiment of the present invention utilizes the low-rank property of linear coaxial lines in seismic data to construct a block Hankel matrix for the matrix in the frequency domain obtained by converting the three-dimensional seismic data volume at a preset frequency; performs singular value decomposition on the block Hankel matrix to obtain a plurality of singular values; truncates the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after denoising; converts the matrix in the frequency domain after denoising into a matrix in the time domain after denoising. By selecting an appropriate number of singular values for each data block, seismic data denoising can be better realized.

[0168] The embodiment of the present invention decomposes the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace through truncated singular value decomposition (TSVD). Among them, determining the number of effective singular values is the key to this method. The embodiment of the present invention uses the DFFITS criterion to utilize the characteristics of the least squares linear regression of singular values to screen out the number of truncated singular values, automatically determine appropriate singular values and corresponding singular vectors, avoid the uncertainty brought by manual estimation, effectively remove the random noise in seismic data and retain the main characteristics of seismic data, optimize the seismic data denoising performance, realize the adaptive denoising of seismic data, save labor costs and time costs, and do not require human intervention. During implementation, automatic denoising processing can be realized, the calculation efficiency can be improved, and the industrial application of seismic data denoising based on low-rank matrix analysis can be realized.

[0169] The embodiment of the present invention embeds the DFFITS criterion in the damping algorithm to automatically distinguish the singular values corresponding to effective signals from the singular values related to noise, overcome the problem of manually selecting the number of singular values, is beneficial to the denoising of massive seismic data, can automatically determine a reliable number of singular values, and obtain a denoising result with a high signal-to-noise ratio.

[0170] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories and optical memories, etc.) that contain computer-usable program code.

[0171] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0172] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that realizes the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0173] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. An adaptive noise reduction method for seismic data based on low-rank matrix analysis, characterized in that, Including: Collect seismic data of a preset area and establish a three-dimensional seismic data volume according to the seismic data; The three-dimensional seismic data volume is a three-dimensional matrix in the space-time dimension; Convert the three-dimensional matrix from the time domain to a matrix in the corresponding frequency domain; Construct a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency to obtain a Hankel matrix for each row; Construct a block Hankel matrix using the Hankel matrices for each row; Perform singular value decomposition on the block Hankel matrix to obtain a plurality of singular values; Truncate the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after noise reduction; Convert the matrix in the frequency domain after noise reduction to a matrix in the time domain after noise reduction.

2. The method according to claim 1, wherein Between the step of truncating the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after noise reduction and the step of converting the matrix in the frequency domain after noise reduction to a matrix in the time domain after noise reduction, it further includes: Use a damping algorithm to perform noise reduction on the matrix in the frequency domain after noise reduction to obtain a matrix in the frequency domain after noise reduction.

3. The method according to claim 1, characterized in that, The step of truncating the singular values of the block Hankel matrix includes: Based on the DFFITS criterion, calculate the plurality of singular values to determine whether the singular values need to be truncated; If it is determined that truncation is required, truncate the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after noise reduction.

4. The method according to claim 3, characterized in that, The step of calculating the plurality of singular values based on the DFFITS criterion to determine whether the singular values need to be truncated includes: Arrange the plurality of singular values in descending order to obtain a singular vector; Establish a linear regression model according to the singular vector; Perform the following calculations on the singular values in the singular vector in sequence: Calculate the regression prediction value including the current singular value, the regression prediction value excluding the current singular value, the standard error of the current singular value, and the leverage value of the current singular value according to the linear regression model; Determine the difference between the regression prediction value including the current singular value and the regression prediction value excluding the current singular value; Calculate the square root of the product of the square of the standard error of the current singular value and the leverage value of the current singular value; Calculate the quotient of the difference and the square root; Compare the quotient of the difference and the square root with a preset quotient threshold. If the quotient is greater than the preset quotient threshold, it is determined that the singular value needs to be truncated.

5. The method according to claim 4, wherein The singular vector is δ = [δ1, δ2,..., δ J-2 , δ J-1 , δ J ; The expression of the linear regression model is as follows: δ = Aβ + e; Where: A is a preset full-rank constant matrix; β is an unknown parameter vector of J×p; e is a random distribution error vector of J×1; The preset quotient threshold value is 6. The method according to claim 1, wherein The step of constructing a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency includes: Starting from the first element of the first row of the matrix in the frequency domain, take out a first preset number of elements as the row vector of the first row of the Hankel matrix; Repeat the above operation until the last element of the first row of the matrix in the frequency domain is taken out to obtain the Hankel matrix of the first row; Repeat the above operation until the last element of the last row of the matrix in the frequency domain is taken out.

7. The method according to claim 1, characterized in that, The step of constructing a block Hankel matrix using the Hankel matrices for each row includes: Respectively regard the Hankel matrices for each row as a block matrix; Starting from the block matrix of the first row, take out a second preset number of block matrices as the elements of the first row of the block Hankel matrix; Repeat the above operations until the block matrix in the last row of the matrix in the frequency domain is taken out.

8. The method according to claim 1, characterized in that, The singular value decomposition of the block Hankel matrix is performed to obtain a plurality of singular values, including: Calculate the transpose matrix of the block Hankel matrix; Calculate the product of the transpose matrix and the block Hankel matrix to obtain a product matrix; Calculate the plurality of eigenvalues of the product matrix; Calculate the square roots of the plurality of eigenvalues to obtain singular values.

9. The method according to claim 6 or 7, wherein: The three-dimensional matrix has dimensions: N x × N y × N t ; where N x and N y are the number of spatial coordinates, and N t is the number of temporal coordinates; The first preset quantity is: The second preset quantity is as follows: wherein represents rounding.

10. An adaptive noise reduction device for seismic data based on low-rank matrix analysis, characterized in that, It includes: A data volume module for collecting seismic data in a preset area and establishing a three-dimensional seismic data volume according to the seismic data; The three-dimensional seismic data volume is a three-dimensional matrix in the space-time dimension; A conversion module for converting the three-dimensional matrix from the time domain into a matrix in the corresponding frequency domain; A Hankel module for constructing a Hankel matrix row by row for the matrix in the frequency domain at a preset frequency to obtain a Hankel matrix for each row; A block Hankel module for constructing a block Hankel matrix by using the Hankel matrices of each row; A decomposition module for performing singular value decomposition on the block Hankel matrix to obtain a plurality of singular values; A truncation module for truncating the singular values of the block Hankel matrix to obtain a matrix in the frequency domain after noise reduction; An inverse conversion module for converting the matrix in the frequency domain after noise reduction into a matrix in the time domain after noise reduction.

11. A computing device, characterized in that, It includes: A memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements a method for adaptively denoising seismic data by low-rank matrix analysis according to any one of claims 1-9.

12. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements a method for adaptively denoising seismic data by low-rank matrix analysis according to any one of claims 1-9.

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