随钻地震参考信号稀疏分解去噪
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摘要
针对随钻地震资料信噪比较低的难题,将稀疏表示理论引入随钻地震参考信号的处理。根据希尔伯特变换求取实际随钻地震参考信号的瞬时属性,使用Morlet子波,构建合适的过完备原子字典,对随钻地震参考信号进行稀疏分解,采用L1范数谱投影梯度算法实现基追踪降噪。利用该方法实现了对实际随钻地震参考信号的稀疏分解降噪,改善了资料的信噪比,恢复了钻头震源信号。
To solve the problem of drilling seismic data with low signal to noise ratio,sparse representation theory is introduced into the reference signal processing for seismic while drilling(SWD).According to the Hilbert transform,the instantaneous attributes of the actual seismic reference signal are obtained,the over-complete dictionary of atoms was built using the Morlet wavelet,the reference signal for SWD was sparsely decomposed.Then the algorithm of spectral projection gradient for L1minimizition(SPGL1)was used to realize basis pursuit denoising.The result shows the sparse decomposition denoising of the actual drilling seismic reference signal is realized,the signal to noise ratio of the data is improved,and the source signal of the drill bit is recovered by this method.
To solve the problem of drilling seismic data with low signal to noise ratio,sparse representation theory is introduced into the reference signal processing for seismic while drilling(SWD).According to the Hilbert transform,the instantaneous attributes of the actual seismic reference signal are obtained,the over-complete dictionary of atoms was built using the Morlet wavelet,the reference signal for SWD was sparsely decomposed.Then the algorithm of spectral projection gradient for L1minimizition(SPGL1)was used to realize basis pursuit denoising.The result shows the sparse decomposition denoising of the actual drilling seismic reference signal is realized,the signal to noise ratio of the data is improved,and the source signal of the drill bit is recovered by this method.
引文
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[23]DONOHO D L,JOHNSTONE J M.Ideal spatial adaptation by wavelet shrinkage[J].Biometrika,1998,81(3):425-455.
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[25]孙万元,张会星,杜艺可.匹配追踪时频分析及其在油气检测中的应用[J].山东科技大学学报(自然科学版),2011,30(4):51-57.SUN Wanyuan,ZHANG Huixing,DU Yike.Matching trace time-frequency analysis and its application in oil gas detection[J].Journal of Shandong University of Science and Technology(Nature Science),2011,30(4):51-57.(in Chinese)
[26]邱娜.地震子波分解与重构技术研究[D].青岛:中国海洋大学,2012.QIU Na.Research on seismic wavelet decomposition and reconstruction technology[D].Qingdao:Ocean U-niversity of China,2012.(in Chinese)
[27]范兴利,成谷.基于Morlet小波尺度参数寻优的匹配追踪时频分析[J].中山大学学报(自然科学版),2014,53(6):85-92.FAN Xingli,CHENG Gu.Matching pursuit time-frequency analysis based on Morlet wavelet scale parameter optimization[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(6):85-92.(in Chinese)
[28]黄跃,许多,文雪康.多子波分解与重构中子波的优选[J].石油物探,2013,52(1):17-22.HUANG Yue,XU Duo,WEN Xuekang.Optimization of wavelets in multi-wavelet decomposition and reconstruction method[J].Geophysical Prospecting For Petroleum,2013,52(1):17-22.(in Chinese)
[2]李海山.基于稀疏表示理论的地震信号处理方法研究[D].青岛:中国石油大学(华东),2013.LI Haishan.Seismic signal processing methods based on sparse representation theory[D].Qingdao:China University of Petroleum,2013.(in Chinese)
[3]李立超.基于稀疏分解算法的地震信号去噪研究[D].大庆:东北石油大学,2014.LI Lichao.Research of seismic signal denoising based on sparse decomposition algorithm[D].Daqing:Northeast Petroleum University,2014.(in Chinese)
[4]程文波,王华军.信号稀疏表示的研究及应用[J].西南石油大学学报(自然科学版),2008,30(5):148-151.CHENG Wenbo,WANG Huajun.The research and application of sparse signal representation[J].Journal of Southwest Petroleum University(Science&Technology Edition),2008,30(5):148-151.(in Chinese)
[5]MALLAT S G,ZHANG Z F.Matching pursuits with time-frequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[6]赵天资,宋炜,王尚旭.基于匹配追踪算法的时频滤波去噪方法[J].石油物探,2008,47(4):367-371.ZHAO Tianzi,SONG Wei,WANG Shangxu.Timefrequency filtering de-noise method based on matching pursuit algorithm[J].Geophysical Prospecting for Prtroleum,2008,47(4):367-371.(in Chinese)
[7]王纯伟.MP算法在地震信号去噪中的应用研究[D].成都:西南交通大学,2010.WANG Chunwei.The application research of matching pursuit in seismic signal denoising[D].Chengdu:Southwest Jiaotong University,2010.(in Chinese)
[8]叶兰兰,付丽华,赵浩岚.地震信号稀疏分解的快速方法[J].地球物理学进展,2014,29(1):375-381.YE Lanlan,FU Lihua,ZHAO Haolan.The rapid method of seismic signal sparse decomposition[J].Progress in Geophysics,2014,29(1):375-381.(in Chinese)
[9]邓武兵,韩立国,李翔,等.L-BFGS和SPGL1在全波形反演中的联合应用[C]//中国地球物理学会.中国地球物理.合肥:中国科学技术大学出版社,2011:714.DENG Wubing,HAN Liguo,LI Xiang,et al.Apply the combination of L-BFGS and SPGLl to full waveform inversion[C]//Chinese Geophysical Society.The Chinese Geophsics.Hefei:Press of University of Science and Technology of China,2011:714.(in Chinese)
[10]BERG E V D,FRIEDLANDER M P,BERG E V D,et al.In pursuit of a root[D].Vancouver,Canada:U-niversity of British Columbia,2007.
[11]BERG E V D,FRIEDLANDER M P.Probing the pareto frontier for basis pursuit solutions[J].SIAMJournal on Scientific Computing,2008,31(2):890-912.
[12]BERG E V D,SCHMIDT M,FRIEDLANDER M P,et al.Group sparsity via linear-time projection[D].Vancouver,Canada:University of British Columbia,2008.
[13]杜小勇.稀疏成分分析及在雷达成像处理中的应用[D].长沙:国防科学技术大学,2005.DU Xiaoyong.Sparse component analysis and its applications in radar imaging processing[D].Changsha:National University of Defense Technology,2005.(in Chinese)
[14]OLSHAUSEN B,FIELD D J.Sparse coding with an overcomplete basis set:a strategy employed by V1?[J].Vision Research,1997,37(23):3311-3325.
[15]CHEN S S,DONOHO D L,SAUNDERS M A.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1999,20(1):33-61.
[16]CANDES E J,ROMBERG J K,TAO T.Stable signal recovery from incomplete and inaccurate measurements[J].Communications on Pure and Applied Mathematics,2006,59(8):1207-1223.
[17]TIBSHIRANI R.Regression shrinkage and selection via the Lasso[J].Journal of the Royal Statistical Society:Series B(Methodological),1996,58(1):267-288.
[18]邹欣.基于稀疏观测的雷达目标三维成像方法研究[D].长沙:国防科学技术大学,2011.ZHOU Xin.3Dradar imaging based on sparse measurement[D].Changsha:National University of Defense Technology,2011.(in Chinese)
[19]BIRGIN E G,MARTINEZ J M,RAYDAN M.Nonmonotone spectral projected gradient methods on convex sets[J].SIAM Journal on Optimization,2000,10(4):1196-1211.
[20]BIRGIN E G,MARTINEZ J M,RAYDAN M.Algorithm 813:SPG-software for convex constrained optimization[J].ACM Transactions on Mathematical Software,2001,27(3):340-349.
[21]DONOHO D L.De-noising by soft-thresholding[J].IEEE Transactions on Information Theory,1995,41(3):613-627.
[22]胡海平,莫玉龙.基于贝叶斯估计的小波阈值图像降噪方法[J].红外与毫米波学报,2002,21(1):74-76.HU Haiping,MO Yulong.Method of wavelet threshold denoising based on Bayesian estimation[J].Journal of Infrared Millimeter Waves,2002,21(1):74-76.(in Chinese)
[23]DONOHO D L,JOHNSTONE J M.Ideal spatial adaptation by wavelet shrinkage[J].Biometrika,1998,81(3):425-455.
[24]耿春,尹成,张白林,等.Morlet复小波用于地震瞬时属性提取的研究[J].天然气工业,2007,27(增刊A):448-450.GENG Chun,YIN Cheng,ZHANG Bailin,et al.Research on the Morlet wavelet apply to extract seismic instantaneous properties[J].Natural Gas Industry,2007,27(S A):448-450.(in Chinese)
[25]孙万元,张会星,杜艺可.匹配追踪时频分析及其在油气检测中的应用[J].山东科技大学学报(自然科学版),2011,30(4):51-57.SUN Wanyuan,ZHANG Huixing,DU Yike.Matching trace time-frequency analysis and its application in oil gas detection[J].Journal of Shandong University of Science and Technology(Nature Science),2011,30(4):51-57.(in Chinese)
[26]邱娜.地震子波分解与重构技术研究[D].青岛:中国海洋大学,2012.QIU Na.Research on seismic wavelet decomposition and reconstruction technology[D].Qingdao:Ocean U-niversity of China,2012.(in Chinese)
[27]范兴利,成谷.基于Morlet小波尺度参数寻优的匹配追踪时频分析[J].中山大学学报(自然科学版),2014,53(6):85-92.FAN Xingli,CHENG Gu.Matching pursuit time-frequency analysis based on Morlet wavelet scale parameter optimization[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(6):85-92.(in Chinese)
[28]黄跃,许多,文雪康.多子波分解与重构中子波的优选[J].石油物探,2013,52(1):17-22.HUANG Yue,XU Duo,WEN Xuekang.Optimization of wavelets in multi-wavelet decomposition and reconstruction method[J].Geophysical Prospecting For Petroleum,2013,52(1):17-22.(in Chinese)