基于稀疏变换的地震数据重构方法
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摘要
缺失地震数据重构恢复是后期地震资料处理取得良好效果的前提。笔者通过研究稀疏变换(F-K变换、Cur-velet变换)与最近流行的压缩感知理论,将两者结合起来,建立基于稀疏变换的地震数据重构模型。F-K变换是将地震数据由时间—空间域变换到稀疏域频率—波数域,Curvelet变换由于其良好的方向性、局部性以及各向异性,能够将地震数据进行更优的稀疏表达。基于重构模型,分别采用这两种稀疏变换对地震数据进行重构,并且比较两者的重构效果,证实Curvelet变换重构效果优于F-K变换。最终通过Marmousi 2模型以及实际地震资料处理分析,证明该重构模型的正确性和有效性。
The seismic data recovery from data with missing traces plays an important role in the later stage seismic processing.The authors studied the sparse transform(F-K transform and Curvelet transform) and popular compressed sensing theory,and then combined the two methods together to build the seismic data recovery model which is based on sparse transform.The F-K transform changes the seismic data from the t-x(time-space) domain into the f-k(frequency-wavenumber) domain.Because of the favorable directionality and locality and multidimensionality,the curvelet transform can represent the seismic data in a more compressible way.On the basis of the recovery model,the missed seismic data are recovered by the two sparse transforms and the recovery results are compared and analyzed.The recovery results prove that the Curvelet transform recovery can get the better reconstruction effect than the F-K transform.Finally the Marmousi2 model and practical seismic data are processed,and the result shows that the seismic data recovery model is correct and effective.
The seismic data recovery from data with missing traces plays an important role in the later stage seismic processing.The authors studied the sparse transform(F-K transform and Curvelet transform) and popular compressed sensing theory,and then combined the two methods together to build the seismic data recovery model which is based on sparse transform.The F-K transform changes the seismic data from the t-x(time-space) domain into the f-k(frequency-wavenumber) domain.Because of the favorable directionality and locality and multidimensionality,the curvelet transform can represent the seismic data in a more compressible way.On the basis of the recovery model,the missed seismic data are recovered by the two sparse transforms and the recovery results are compared and analyzed.The recovery results prove that the Curvelet transform recovery can get the better reconstruction effect than the F-K transform.Finally the Marmousi2 model and practical seismic data are processed,and the result shows that the seismic data recovery model is correct and effective.
引文
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[2]Gulunay N,Chambers R E.Unaliased f-k domain trace interpola-tion(UFKI)[C]//66th Ann.Internat.Mtg.,Soc Expl.Geo-phys,Expanded Abstracts,1996:1461.
[3]Ronen J.Wave equation trace interpolation[J].Geophysics,1987,52(7):973-984.
[4]高建军,陈小宏,李景叶,等.基于非均匀Fourier变换的地震数据重建方法研究[J].地球物理学进展,2009,24(5):1741-1747.
[5]Naghizadeh M,Sacchi M.Beyond alias hierarchical scale curveletinterpolation of regularly and irregularly sampled seismic data[J].Geophysics,2010,75(6):189-202.
[6]Naghizadeh M,Sacchi M.Hierarchical scale curvelet interpolationof aliased seismic data[J].SEG International Exposition and 80thAnnual Meeting,2010.
[7]Herrmann J,Hennenfent G.Non-parametric seismic data recoverywith curvelet frames[J].Geophysical Journal International,2008,173(1):A1-A5.
[8]Donoho D.Compressed sensing[J].IEEE Trans.On InformationTheory,2006,52(4):1289-1306.
[9]Donoho D,Tsaig Y.Extensions of compressed sensing[J].SignalProcessing,2006,86(3):533-548.
[10]Berg E D,Friedlander M P.Probing the Pareto frontier for basispursuit solutions[J].SIAM J.On Scientific Computing,2008,31(2):890-912.
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