基于一致性稀疏表示的地震信号补全算法
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摘要
针对由于记录仪器的故障和保存媒介的缺陷导致的地震信号中一部分波形出现的缺失,提出一种基于一致性稀疏表示(CSR)的地震波补全算法。首先,通过稀疏表示(SR)模型表示每一帧地震信号;随后,采用主分量分析(PCA)的方法提取在频谱的分布上的帧间一致性信息;最后,利用地震信号的每帧的稀疏性和用帧与帧之间频谱分布的一致性,对缺损的信号进行恢复。在对历史地震信号进行的仿真实验中,当缺损的部分的跨度达到帧数据量的50%时,传统的稀疏表示恢复算法的误差已经很大,而一致性稀疏表示模型仍然能够得到很好的结果。仿真实验结果表明,一致性稀疏表示模型的补全效果要远好于传统稀疏表示模型的补全效果。
Focusing on the issue that some portions of seismic waveforms were lost due to the mechanical failure of recording devices and damage of seismograms,an inpainting method based on Consistent Sparse Representation( CSR) model was proposed. Firstly,each seismic frame was represented individually in Sparse Representation( SR) model. Secondly,the consistency between spectra of seismic frames was employed. Principal Component Analysis( PCA) method was introduced to extract this consistency between seismic frames. Finally,combining the sparseness of each seismic frame and the consistency between seismic frames,the proposed algorithm was used to inpaint the lost portion. The simulation experiments showed that when the missing duration interval was 50% of the frame length, the inpainting method based on traditional sparse representation model obtained incorrect results whereas the inpainting method based on consistent sparse representation model recovered the lost portion well. The simulation experiments indicate that the performance of the consistent sparse representation inpainting method is much better than the traditional sparse representation inpainting method.
Focusing on the issue that some portions of seismic waveforms were lost due to the mechanical failure of recording devices and damage of seismograms,an inpainting method based on Consistent Sparse Representation( CSR) model was proposed. Firstly,each seismic frame was represented individually in Sparse Representation( SR) model. Secondly,the consistency between spectra of seismic frames was employed. Principal Component Analysis( PCA) method was introduced to extract this consistency between seismic frames. Finally,combining the sparseness of each seismic frame and the consistency between seismic frames,the proposed algorithm was used to inpaint the lost portion. The simulation experiments showed that when the missing duration interval was 50% of the frame length, the inpainting method based on traditional sparse representation model obtained incorrect results whereas the inpainting method based on consistent sparse representation model recovered the lost portion well. The simulation experiments indicate that the performance of the consistent sparse representation inpainting method is much better than the traditional sparse representation inpainting method.
引文
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[2]PINO N,PALOMBO B,VENTURA G,et al.Waveform modeling of historical seismograms of the 1930 Irpinia earthquake provides insight on“blind”faulting in Southern Apennines(Italy)[J].Journal of Geophysical Research:Solid Earth,2008,113(B5).
[3]BATH M.Earthquake magnitude—recent research and current trends[J].Earth-Science Reviews,1981,17(4):315-398.
[4]PINON,GIARDINI D,BOSCHI E.The December 2 8,1 9 0 8,Messina Straits,southern Italy,earthquake:waveform modeling of regional seismograms[J].Journal of Geophysical Research:Solid Earth,2000,105(B11):25473-25492.
[5]KIKUCHI M,NAKAMURA M,YOSHIKAWA K.Source rupture processes of the 1944 Tonankai earthquake and the 1945 Mikawa earthquake derived from low-gain seismograms[J].Earth,Planets and Space,2003,55(4):159-172.
[6]HERRMANN F J,HENNENFENT G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[7]YANG Y,MA J,OSHER S.Seismic data reconstruction via matrix completion[J].Inverse Problem and Imaging,2013,7(4):1379-1392.
[8]WANG L F,SUN Y,CAI X G.Inpainting of historical seismograms using sparse representation method[J].Geophysical Journal International,2015,200(1):679-691.
[9]STEPHANE G M,ZHANG Z.Matching pursuits with time-frequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[10]TROOP J,GILBERT A.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666.
[11]DONOHO D,TSAIG Y,DRORI I,et al.Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2012,58(2):1094-1121.
[12]RISH I,GRABARNIK G.Sparse Modeling:Theory,Algorithms,and Applications[M].Boca Raton,USA:CRC Press,2014:71-91.
[13]PATEL V M,CHELLAPPA R.Sparse Representations and Compressive Sensing for Imaging and Vision[M].Berlin:Springer,2013:41-62.
[14]BAHMANI S.Algorithms for Sparsity-Constrained Optimization[M].Berlin:Springer,2013:11-36.
[15]RUBINSTEIN R,ZIBULEVSKY M,ELAD M.Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit[J].CS Technion,2008,40(8):1-15.