压缩感知技术在地震数据重建中的应用
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摘要
地震资料室内处理过程要求野外采集的地震资料越多越好,而地震数据远距离快速传输又要求野外地震数据量越少越好.为解决这一矛盾,将基于曲波变换与压缩感知的数据重建技术引入到地震资料处理中,对实际的野外不完整数据进行压缩重建.结果表明,曲波变换相对于傅里叶变换在数据压缩采样方法中占有一定的优势.但是,在对实际资料进行处理时,首先要对资料中的面波进行处理,同时还要在一定曲波基元尺寸的情况下,考虑缺失道数量的影响.最终,得到的重建数据图像纹理清晰、连接自然,从而验证了该方法的实用性和有效性.
There is a contradiction between seismic data processing and remote transmission of field seismic data,which is their different requirements about the data volume.More precisely,the former requires that the data quantity be as large as possible,while the latter requires the opposite.In order to solve this problem,a new method,compressed sensing(CS) technology,based on curvelet transform,is introduced into seismic data processing to reconstruct the actual incomplete data.The results show the advantage of curvelet transform compared with FFT in CS method.However,when it is used to actual data processing,surface wave must be removed first and the effect of the number of missing traces should be considered simultaneously.Finally,a reasonable reconstructed result is achieved,with clear texture and natural connection,illustrating the applicability and validity of the CS method.
There is a contradiction between seismic data processing and remote transmission of field seismic data,which is their different requirements about the data volume.More precisely,the former requires that the data quantity be as large as possible,while the latter requires the opposite.In order to solve this problem,a new method,compressed sensing(CS) technology,based on curvelet transform,is introduced into seismic data processing to reconstruct the actual incomplete data.The results show the advantage of curvelet transform compared with FFT in CS method.However,when it is used to actual data processing,surface wave must be removed first and the effect of the number of missing traces should be considered simultaneously.Finally,a reasonable reconstructed result is achieved,with clear texture and natural connection,illustrating the applicability and validity of the CS method.
引文
刘保童.2009.一种基于傅里叶变换的去假频内插方法及应用[J].煤田地质与勘探,37(2):63--67.
唐刚.2010.基于压缩感知和稀疏表示的地震数据重建与去噪[D].北京:清华大学:3--24.
仝中飞.2009.Curvelet阈值迭代法在地震数据去噪和插值中的应用研究[D].长春:吉林大学:1--6.
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Donoho D L,Huo X.2001.Uncertainty principles and ideal atomic decomposition[J].IEEE T Inform Theory,47:2845--2862.
Donoho D L.2006.Compressed sensing[J].IEEE T Inform Theory,52:1289--1306.
Herrmann F J,Hennenfent G.2008.Non-parametric seismic data recovery with curvelet frames[J].Geophys J Int,173(1):233--248.
唐刚.2010.基于压缩感知和稀疏表示的地震数据重建与去噪[D].北京:清华大学:3--24.
仝中飞.2009.Curvelet阈值迭代法在地震数据去噪和插值中的应用研究[D].长春:吉林大学:1--6.
Candès E J,Romberg J K.2005.Practical signal recovery from random projections[C]∥Proceedings of SPIE Computational ImagingⅢ:76--86.
Candès E J,Romberg J K,Tao T.2005.Stable signal recovery from incomplete and inaccurate measurements[J].Commun Pur Appl Math,99:1207--1223.
Candès E J,Romberg J K.2006.Quantitative robust uncertainty principles and optimally sparse decompositions[J].Found Comput Math,6:227--254.
Candès E J,Romberg J K,Tao T.2006.Robust uncertainty principles:Exact signal reconstruction from highlyincomplete frequency information[J].IEEE T Inform Theory,52:489--509.
Candès E J,Wakin M B.2008.An introduction to compressive sampling[J].IEEE Signal Proc Mag,25(2):21--30.
Donoho D L,Huo X.2001.Uncertainty principles and ideal atomic decomposition[J].IEEE T Inform Theory,47:2845--2862.
Donoho D L.2006.Compressed sensing[J].IEEE T Inform Theory,52:1289--1306.
Herrmann F J,Hennenfent G.2008.Non-parametric seismic data recovery with curvelet frames[J].Geophys J Int,173(1):233--248.
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