CN-115980850-B - Green function reconstruction method combining S transformation and dictionary learning

CN115980850BCN 115980850 BCN115980850 BCN 115980850BCN-115980850-B

Abstract

The invention discloses a green function reconstruction method combining S transformation and dictionary learning. The method comprises the steps of S-transform denoising a background noise cross-correlation function containing noise, obtaining a time spectrum coefficient, extracting a real part coefficient matrix and an imaginary part coefficient matrix of the time spectrum coefficient, respectively performing dictionary learning on the real part coefficient matrix and the imaginary part coefficient matrix, obtaining a dictionary of the real part coefficient matrix and a dictionary of the imaginary part coefficient matrix, obtaining a real part coefficient after dictionary learning and an imaginary part coefficient after dictionary learning, obtaining a reconstructed spectrum coefficient, and performing S-inverse transform on the reconstructed spectrum coefficient to obtain a reconstructed green function. The method can eliminate the interference of the anisotropic distribution noise source in the seismic background noise cross-correlation function, can obtain better effect on background noise cross-correlation data with low signal-to-noise ratio, and has the advantages of low complexity, high timeliness and high reconstruction precision.

Inventors

YE FANG
ZHANG HAN
CAI JINHUI

Assignees

中国计量大学

Dates

Publication Date: 20260512
Application Date: 20221027

Claims (6)

1. A seismic background noise cross correlation function green function reconstruction method combining S transformation and dictionary learning is characterized by comprising the following steps: S1, S-transform denoising is carried out on an actually observed noisy seismic background noise cross-correlation function, a filtered time spectrum coefficient is obtained, and a real part coefficient matrix and an imaginary part coefficient matrix of the filtered time spectrum coefficient are extracted; s2, dictionary learning is carried out on the real coefficient matrix and the imaginary coefficient matrix respectively, and a dictionary of the real coefficient matrix and a dictionary of the imaginary coefficient matrix are obtained; S3, utilizing dictionaries of the real part coefficient matrix and the imaginary part coefficient matrix and the sparse matrix of the real part coefficient and the sparse matrix of the imaginary part coefficient to obtain the real part coefficient after dictionary learning and the imaginary part coefficient after dictionary learning; S4, combining the real part coefficient after dictionary learning and the imaginary part coefficient after dictionary learning to obtain a reconstructed spectrum coefficient, and then performing S inverse transformation on the reconstructed spectrum coefficient to obtain a reconstructed Green function.
2. The method for reconstructing the green' S function of the cross-correlation function of the background noise of the earthquake by combining S transformation and dictionary learning according to claim 1, wherein the dictionary learning is determined according to the following model: ; ; In the formula, Representing a real coefficient matrix; a dictionary representing a real coefficient matrix; A sparse matrix representing real coefficients; representing an imaginary coefficient matrix; a dictionary representing the imaginary coefficient matrix; a sparse matrix representing an imaginary coefficient; Sparse matrix representing real coefficients Is the column vector of the ith column; Sparse matrix representing imaginary coefficients Is the column vector of the ith column; Representing the Frobenius norm; A norm; s.t. represents a constraint; () Representing the minimum of the objective function.
3. The method for reconstructing the green' S function of the cross-correlation function of the background noise of the earthquake combined with the S transformation and the dictionary learning according to claim 1, wherein the step S1 is specifically as follows: S3.1, performing time window interception on the cross correlation function of the seismic background noise, and setting a group velocity window as And the amplitude of the signal outside the time window is set to 0, and the time window of the cross correlation function of the background noise of the earthquake is determined Specifically, the method is determined according to the following formula: ; ; wherein dist represents the station spacing; s3.2, performing S transformation on the cross correlation function of the seismic background noise intercepted in the step S3.1, and determining according to the following formula: ; In the formula, Representing the time-frequency spectrum coefficient; representing the center point of the window function, and controlling the position of the window function on the time axis; Representing the frequency; representing a cross correlation function of the background noise of the earthquake after the time window is intercepted; Representing imaginary units; Representing time; Representing an exponential function; S3.3. set threshold coefficient λ=0.08, determine spectral coefficient The element with the largest absolute value Spectral coefficients are combined The absolute value of (a) is smaller than the threshold value Is set to 0, resulting in a filtered time-frequency spectrum coefficient ; S3.4, determining the time-frequency spectrum coefficient after filtering The real coefficient matrix and the imaginary coefficient matrix of (2) are determined according to the following formula: ; ; In the formula, Representing a real coefficient matrix; representing an imaginary coefficient matrix; representing the real part of the complex number; an imaginary part representing a complex number; a dictionary representing a real coefficient matrix; a dictionary representing the imaginary coefficient matrix; A sparse matrix representing real coefficients; Representing a sparse matrix of imaginary coefficients.
4. The method for reconstructing the green' S function of the cross-correlation function of the background noise of the earthquake by combining S transformation and dictionary learning according to claim 3, wherein the step S2 is specifically as follows: Firstly, carrying out iterative updating on a dictionary learning algorithm, and then obtaining a dictionary of an updated real coefficient matrix and a dictionary of an updated imaginary coefficient matrix according to the dictionary learning algorithm after iterative updating, wherein the dictionary learning algorithm carries out iterative calculation according to the following specific formula: ; In the formula, A training sample matrix representing real coefficients; Representing the Frobenius norm; Indicating the number of samples that the training samples contain, Column vectors representing the j-th column of the real coefficient dictionary; a row vector representing the j-th row of the sparse matrix of real coefficients; column vectors representing the nth column of the real coefficient dictionary, A row vector representing the nth row of the sparse matrix of real coefficients; Representing the real part residual; a training sample matrix representing the imaginary coefficient; column vectors representing the j-th column of the imaginary coefficient dictionary, A row vector representing the j-th row of the sparse matrix of the imaginary coefficients, Representing the residual of the imaginary part, Column vectors representing the nth column of the imaginary coefficient dictionary, A row vector representing the nth row of the sparse matrix of the imaginary coefficient; The real part residual error Column vector of nth column of real coefficient dictionary Row vector of n-th row of sparse matrix of real coefficient Residual error of imaginary part Column vector of n-th column of imaginary coefficient dictionary And row vector of n-th row of imaginary coefficient sparse matrix The iterative determination is updated according to the following formula: ; ; column vector of nth column of iterative updated real part residual error and real part coefficient dictionary Row vector of n-th row of sparse matrix of real coefficient Column vector of n-th column of imaginary part residual and imaginary part coefficient dictionary And row vector of n-th row of imaginary coefficient sparse matrix Specifically, the method is determined according to the following formula: ; ; In the formula, The sparse real part residual is represented, Representing left singular matrix after real part residual decomposition, R Representing the unitary matrix after the decomposition of the real part residual; Right singular matrix after representing real part residual decomposition; the sparse imaginary residual is represented, Representing left singular matrix after imaginary residual decomposition, I Representing the unitary matrix after the decomposition of the imaginary residual; a right singular matrix after the imaginary part residual error decomposition is represented; Representation matrix Column vectors of the first column; Representation matrix Transposed row vectors of the first row; Representation matrix Column vectors of the first column; Representation of The row vectors of the first row after transposition.
5. The method for reconstructing the green' S function of the cross-correlation function of the background noise of the earthquake combined with the S transformation and the dictionary learning as set forth in claim 4, wherein the step S3 is specifically as follows: s5.1, combining the dictionary of the updated real coefficient matrix Reconstructing the real part coefficient, and determining the real part coefficient after dictionary learning Specifically, the method is determined according to the following formula: ; S5.2, combining the dictionary of the updated imaginary coefficient matrix Reconstructing the imaginary coefficient and determining the imaginary coefficient after dictionary learning Specifically, the method is determined according to the following formula: 。
6. The method for reconstructing a green' S function by combining S-transform and dictionary learning according to claim 5, wherein said step S4 is specifically: Real part coefficient after combining dictionary learning And dictionary learned imaginary coefficient Obtaining reconstructed spectral coefficients Specifically, the method is determined according to the following formula: ; And then performing S inverse transformation on the reconstructed spectral coefficients to obtain a reconstructed green function, wherein the reconstructed green function is determined according to the following formula: ; In the formula, Representing the reconstructed green's function.

Description

Green function reconstruction method combining S transformation and dictionary learning Technical Field The invention relates to a function reconstruction technology in the field of signal processing, in particular to a green function reconstruction method combining S transformation and dictionary learning. Background Seismic background noise is mainly generated by ocean tidal wave, ocean and ocean bottom friction collision, atmospheric disturbance and surface friction. With the development of theoretical research, green's function can be approximately obtained by cross-correlation calculation of long-time seismic background noise. In seismology, the green function can be understood as a unit of concentrated pulse force generated displacement field, which is valuable for many applications. Such as noise surface wave imaging, monitoring subsurface medium changes, subsurface attenuation structure monitoring, seismic localization, and the like. In actual observation data, the amplitude of the left and right half branches of the cross correlation function of the seismic background noise is asymmetric under the influence of uneven distribution of noise sources, namely, the cross correlation function of the seismic background noise is different from the amplitude factor of the theoretical green function, so that reconstruction of the green function is necessary. Currently, the green's function is obtained mainly by the following methods. The green's function can be obtained by long-time superposition of background noise cross-correlation functions, but the acquisition requirement on background noise data is higher because the needed time sequence data is very long, the green's function can be obtained approximately by the method of linear superposition or phase weighted superposition of background noise cross-correlation waveforms, but the method can be influenced by seasonal variation and cannot guarantee the accuracy of the reconstructed green's function, and because the high-order cross-correlation of the seismic background noise cross-correlation wake is symmetrical, the green's function with higher quality can be obtained by carrying out cross-correlation calculation on the background noise cross-correlation wake again, but the larger calculation amount becomes the main reason for limiting the application of the green's function. In view of the shortcomings of the above methods, methods for obtaining the green function by denoising the seismic background noise cross-correlation function, such as denoising the background noise cross-correlation function S transformation, sliding window weighted singular value decomposition filtering and the like, are derived, but the method has poor processing effect on the seismic background noise cross-correlation function with low signal-to-noise ratio. Disclosure of Invention In order to remedy the shortcomings of the above methods, the present invention provides a green function reconstruction method combining S-transform and dictionary learning, the present invention denoises the background noise cross-correlation function by S-transform, dictionary learning is respectively carried out on the real part coefficient and the imaginary part coefficient of the S pedigree after denoising, and finally, a reconstructed green function is obtained through S inverse transformation, so that the reconstruction of the green function in a time-frequency domain is realized. The technical scheme adopted by the invention is as follows: the method comprises the following steps: s1, S-transform denoising is carried out on a background noise cross-correlation function containing noise, a filtered time spectrum coefficient is obtained, and a real part coefficient matrix and an imaginary part coefficient matrix of the filtered time spectrum coefficient are extracted; s2, dictionary learning is carried out on the real coefficient matrix and the imaginary coefficient matrix respectively, and a dictionary of the real coefficient matrix and a dictionary of the imaginary coefficient matrix are obtained; S3, utilizing dictionaries of the real part coefficient matrix and the imaginary part coefficient matrix and the sparse matrix of the real part coefficient and the sparse matrix of the imaginary part coefficient to obtain the real part coefficient after dictionary learning and the imaginary part coefficient after dictionary learning; S4, combining the real part coefficient after dictionary learning and the imaginary part coefficient after dictionary learning to obtain a reconstructed spectrum coefficient, and then performing S inverse transformation on the reconstructed spectrum coefficient to obtain a reconstructed Green function. The dictionary learning is specifically determined according to the following model: In the formula, RFS represents a real coefficient matrix, RD represents a dictionary of the real coefficient matrix, RX represents a sparse matrix of the real coefficient, IFS represents