基于POCS方法指数阈值模型的不规则地震数据重建(英文)
|
摘要
不规则地震数据会对地震多道处理技术的正确运行造成不良影响,降低地震资料的处理质量。本文将广泛用于图形图像重建的凸集投影方法应用到地震数据重建领域,实现规则样不规则道缺失数据的插值重建。对于整道缺失地震数据,将POCS迭代重建过程由时间域转移到频率域实现,避免每次迭代都对时间做正反Fourier变换,节约了计算量。在迭代过程中,阈值参数的选择方式对重建效率有重要影响。本文设计了两种阈值集合模型进行重建试验,试验结果表明:在相同重建效果下,指数型阈值集合模型可以有效减少迭代次数,提高重建效率。此外,分析了POCS重建方法的抗噪性能和抗假频性能。最后,理论模型和实际资料处理效果验证了本文重建方法的正确性和有效性。
Irregular seismic data causes problems with multi-trace processing algorithms and degrades processing quality. We introduce the Projection onto Convex Sets (POCS) based image restoration method into the seismic data reconstruction field to interpolate irregularly missing traces. For entire dead traces, we transfer the POCS iteration reconstruction process from the time to frequency domain to save computational cost because forward and reverse Fourier time transforms are not needed. In each iteration, the selection threshold parameter is important for reconstruction efficiency. In this paper, we designed two types of threshold models to reconstruct irregularly missing seismic data. The experimental results show that an exponential threshold can greatly reduce iterations and improve reconstruction efficiency compared to a linear threshold for the same reconstruction result. We also analyze the anti- noise and anti-alias ability of the POCS reconstruction method. Finally, theoretical model tests and real data examples indicate that the proposed method is efficient and applicable.
Irregular seismic data causes problems with multi-trace processing algorithms and degrades processing quality. We introduce the Projection onto Convex Sets (POCS) based image restoration method into the seismic data reconstruction field to interpolate irregularly missing traces. For entire dead traces, we transfer the POCS iteration reconstruction process from the time to frequency domain to save computational cost because forward and reverse Fourier time transforms are not needed. In each iteration, the selection threshold parameter is important for reconstruction efficiency. In this paper, we designed two types of threshold models to reconstruct irregularly missing seismic data. The experimental results show that an exponential threshold can greatly reduce iterations and improve reconstruction efficiency compared to a linear threshold for the same reconstruction result. We also analyze the anti- noise and anti-alias ability of the POCS reconstruction method. Finally, theoretical model tests and real data examples indicate that the proposed method is efficient and applicable.
引文
Abma,R.,2005,Issues in multi-dimensional interpolation:75th Ann.Internal.Mtg.,Soc.Explor.Geophys.,Expanded Abstracts,2150–2154.
Abma,R.,and Kabir,N.,2006,3D interpolation of irregulardata with a POCS algorithm:Geophysics,71(6),E91–E97.
Bregman,L.,1965,The method of successive projection forfinding a common point of convex sets:Soviet Math,6(3),688–692.
Chemingui,N.,and Biondi,B.,2002,Seismic datareconstruction by inversion to common offset:Geophysics,67(5),1575–1585.
Duijndam¤,A.J.W.,Schonewille¤,M.A.,and Hindriks,C.O.H.1999,Reconstruction of band-limited signals,irregularly sampled along one spatial direction:Geophysics,64(2),524–538.
Fomel,S.,2003,Seismic reflection data interpolation withdifferential offset and shot continuation:Geophysics,68(2),733–744.
Galloway,E.,and Sacchi,M.,2007,POCS method forseismic data reconstruction of irregularly sampled data:In Abstract of2007-CSPG CSEG Conference,Calgary,Canada,555.
Gao,J.J.,Chen,X.H.,Li,J.Y.,Liu,Z.P.,and Zhang,N.N.,2009,Study on reconstruction of seismic data based onnon-uniform Fourier transform:Progress in Geophys.(inChinese),24(5),1741–1747.
Guo,J.Y.,Zhou,X.Y.,and Yu,S.P.,1996,Iso-intervaltrace interpolation in F-X domain:OGP,31(1),28–34.
Hindriks,H.,and Duijndam,W.,2000,Reconstructionof3D seismic signals irregularly sampled along twocoordinates:Geophysics,65(1),253–263.
Liu,B.,and Sacchi,M.,2004,Minimum weighted norminterpolation of seismic records:Geophysics,69(6),1560–1568.
Meng,X.H.,Guo,L.H.,Zhang,Z.F.,Li,S.L.,andZhou,J.J.,2008,Reconstruction of seismic data withleast squares inversion based on non-uniform fast Fouriertransform:Chinese J.Geophys.(in Chinese),51(1),235–241.
Naghizadeh,M.,and Sacchi,M.,2007,Multi-step auto-regressive reconstruction of seismic records:Geophysics,72(6),V111–V118.
Naghizadeh,M.,and Sacchi,M.,2009,F‐x adaptiveseismic‐trace interpolation:Geophysics,74(1),V9–V16.
Ozkan,M.,Tekalp,M.,and Sezan,M.,1994,POCS-based restoration of space-varying blurred images:IEEETransactions on Image Processing,3(4),450–454.
Patti,A.,Sezan,M.,and Tekalp,A.,1997,Superresolutionvideo reconstruction with arbitrary sampling lattices andnonzereo aperture time:IEEE Transactions on ImageProcessing,6(8),1064–1076.
Porsani,M.,1999,Seismic trace interpolation using half-step prediction filters:Geophysics,64(5),1461–1467.
Ronen,J.,1987,Wave equation trace interpolation:Geophysics,52(7),973–984.
Spitz,S.,1991,Seismic trace interpolation in the f-xdomain:Geophysics,56(6),785–794.
Stark,H.,and Oskoui,P.,1989,High resolution imagerecovery from image plane arrays using ConvexProjections:Journal of the Optical Society of American,6(11),1715–1726.
Tekalp,A.,Ozkan,M.,and Sezan,M.,1992,High-resolution image reconstruction from lower-resolutionimage sequences and space-varying image restoration:IEEE International Conference on Acoustics,Speech,and Signal Processing,ICASSP-92,3,169–172.
Xu,S.,Zhang,Y.,Pham,D.,and Lambare,G.,2005,Anti-leakage Fourier transform for seismic data regularization:Geophysics,70(4),V87–V95.
Youla,C.,and Webb,H.,1982,Image restoration by themethod of convex projections:part1theory:IEEE TransMed Imaging,1(2),81–94.
Yu,Y.L.,Xie,S.L.,and Cai,H.T.,2004,Introduction ofnew method of signal processing:Tinghua UniversityPress,China,79–81.
Zhou,X.Y.,1997,Seismic trace interpolation in F-Xdomain:Oil and Geophysical Prospecting,32(2),154–162.
Zwartjes,M.,and Gisolf,A.,2007,Fourier reconstructionwith sparse inversion:Geophys.Prosp.,55(2),199–221.
Abma,R.,and Kabir,N.,2006,3D interpolation of irregulardata with a POCS algorithm:Geophysics,71(6),E91–E97.
Bregman,L.,1965,The method of successive projection forfinding a common point of convex sets:Soviet Math,6(3),688–692.
Chemingui,N.,and Biondi,B.,2002,Seismic datareconstruction by inversion to common offset:Geophysics,67(5),1575–1585.
Duijndam¤,A.J.W.,Schonewille¤,M.A.,and Hindriks,C.O.H.1999,Reconstruction of band-limited signals,irregularly sampled along one spatial direction:Geophysics,64(2),524–538.
Fomel,S.,2003,Seismic reflection data interpolation withdifferential offset and shot continuation:Geophysics,68(2),733–744.
Galloway,E.,and Sacchi,M.,2007,POCS method forseismic data reconstruction of irregularly sampled data:In Abstract of2007-CSPG CSEG Conference,Calgary,Canada,555.
Gao,J.J.,Chen,X.H.,Li,J.Y.,Liu,Z.P.,and Zhang,N.N.,2009,Study on reconstruction of seismic data based onnon-uniform Fourier transform:Progress in Geophys.(inChinese),24(5),1741–1747.
Guo,J.Y.,Zhou,X.Y.,and Yu,S.P.,1996,Iso-intervaltrace interpolation in F-X domain:OGP,31(1),28–34.
Hindriks,H.,and Duijndam,W.,2000,Reconstructionof3D seismic signals irregularly sampled along twocoordinates:Geophysics,65(1),253–263.
Liu,B.,and Sacchi,M.,2004,Minimum weighted norminterpolation of seismic records:Geophysics,69(6),1560–1568.
Meng,X.H.,Guo,L.H.,Zhang,Z.F.,Li,S.L.,andZhou,J.J.,2008,Reconstruction of seismic data withleast squares inversion based on non-uniform fast Fouriertransform:Chinese J.Geophys.(in Chinese),51(1),235–241.
Naghizadeh,M.,and Sacchi,M.,2007,Multi-step auto-regressive reconstruction of seismic records:Geophysics,72(6),V111–V118.
Naghizadeh,M.,and Sacchi,M.,2009,F‐x adaptiveseismic‐trace interpolation:Geophysics,74(1),V9–V16.
Ozkan,M.,Tekalp,M.,and Sezan,M.,1994,POCS-based restoration of space-varying blurred images:IEEETransactions on Image Processing,3(4),450–454.
Patti,A.,Sezan,M.,and Tekalp,A.,1997,Superresolutionvideo reconstruction with arbitrary sampling lattices andnonzereo aperture time:IEEE Transactions on ImageProcessing,6(8),1064–1076.
Porsani,M.,1999,Seismic trace interpolation using half-step prediction filters:Geophysics,64(5),1461–1467.
Ronen,J.,1987,Wave equation trace interpolation:Geophysics,52(7),973–984.
Spitz,S.,1991,Seismic trace interpolation in the f-xdomain:Geophysics,56(6),785–794.
Stark,H.,and Oskoui,P.,1989,High resolution imagerecovery from image plane arrays using ConvexProjections:Journal of the Optical Society of American,6(11),1715–1726.
Tekalp,A.,Ozkan,M.,and Sezan,M.,1992,High-resolution image reconstruction from lower-resolutionimage sequences and space-varying image restoration:IEEE International Conference on Acoustics,Speech,and Signal Processing,ICASSP-92,3,169–172.
Xu,S.,Zhang,Y.,Pham,D.,and Lambare,G.,2005,Anti-leakage Fourier transform for seismic data regularization:Geophysics,70(4),V87–V95.
Youla,C.,and Webb,H.,1982,Image restoration by themethod of convex projections:part1theory:IEEE TransMed Imaging,1(2),81–94.
Yu,Y.L.,Xie,S.L.,and Cai,H.T.,2004,Introduction ofnew method of signal processing:Tinghua UniversityPress,China,79–81.
Zhou,X.Y.,1997,Seismic trace interpolation in F-Xdomain:Oil and Geophysical Prospecting,32(2),154–162.
Zwartjes,M.,and Gisolf,A.,2007,Fourier reconstructionwith sparse inversion:Geophys.Prosp.,55(2),199–221.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心