子波相位不准对叠前波形反演的影响（英文）
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摘要
子波是影响反演结果的关键因素之一。不正确的子波相位会改变目标函数的形态,导致反演结果收敛不到真实的位置,最终引起解释结果发生偏差甚至错误。基于两个简单模型,在忽略所有其它影响因素前提下,本文研究了子波依赖于频率的相位变化对叠前波形反演的影响,并对反演误差进行量化分析。实验结果表明,即使给定子波与真实子波有较高的相似性,依赖于频率的子波相位误差仍可能导致反演结果严重偏离真解。对给定子波进行常相位旋转可以在一定程度上提高反演结果的精度,但却无法完全校正子波相位不准的影响。而且子波相位不准为反演引人的是系统误差而非随机误差,很难采用统计性方法予以消除,从根本上限制了叠前反演的精度。
Wavelets are critical to inversion methods. Incorrect phase estimation will affect the objective function and cause convergence to local minima, and thus produce biased or incorrect results. Based on two simple models and ignoring all other factors, we studied the variation of the wavelet phase as a function of frequency and its effect on the prestack waveform inversion. Numerical experiments show that an incorrect phase may result in large deviations from the real solution, even if there is a high similarity between the model and real wavelets. The precision of the inversion slightly improves by using the constant-phase rotation; however, the effect of phase inaccuracy is not eliminated, which limits the precision of prestack inversion.
Wavelets are critical to inversion methods. Incorrect phase estimation will affect the objective function and cause convergence to local minima, and thus produce biased or incorrect results. Based on two simple models and ignoring all other factors, we studied the variation of the wavelet phase as a function of frequency and its effect on the prestack waveform inversion. Numerical experiments show that an incorrect phase may result in large deviations from the real solution, even if there is a high similarity between the model and real wavelets. The precision of the inversion slightly improves by using the constant-phase rotation; however, the effect of phase inaccuracy is not eliminated, which limits the precision of prestack inversion.
引文
Aki,K.,and Richards,P.G.,2002,Quantitative seismology:Theory and methods.University Science Books.
Alemie,W.and Sacchi,M.D.,2011,High-resolution three term AVO inversion by means of a Trivariate Cauchy probability distribution:Geophysics,2011,76(3),43–55.
Asnaashari,A.,Brossier,R.,Garambois,S.,Audebert,F.,Thore,P.,and Virieux,J.,2013,Regularized seismicfull wave form inversion with prior model information:Geophysics,78(2),R25–R36.
Broadhead,M.,2008,The impact of random noise onseismic wavelet estimation:The Leading Edge,27(2),226–230.
Buland,A.,and Omre,H.,2003,Bayesian wavelet estimation from seismic and well data:Geophysics,68(6),2000–2009.
Delprat-Jannaud,F.,and Lailly,P.,2005,A fundamental limitation for the reconstruction of impedance profiles from seismic data:Geophysics,70(1),1–14.
Edgar J,and van der Baan M.,2011,How reliable isstatistical wavelet estimation?:Geophysics,2011,76(4),59–68.
Huang,X.,Kelkar,M.,Chopra,A.,and Yang,C.,1995,Wavelet sensitivity study on inversion using heuristic combinatorial algorithms:65th Annual International Metting,SEG,Expanded Abstracts,1088–1090.
Liang,G.,Cai,X.,and Li,Q.,2002,Using high-ordercumulants to extrapolate spatially variant seismic wavelets:Geophysics,67(6),1869–1876.
Lindsey,J.P.1988,Measuring wavelet phase from seismicdata:The Leading Edge,7(7),10–16.
Nowak,E.J.,Swan,H.W.,and Lane,D.,2008,Quantitative thickness estimates from the spectral response of AVO measurements:Geophysics,73(1),C1–C6.
Ostrander,W.,1984,Plane–wave reflection coefficients for gas sands at nonnormal angles of incidence:Geophysics,49(10),1637–1648.
Perez,D.O.,and Veils,D.R.,2011,Sparse-spike AVO/AVA attributes from prestack data:81st Annual International Metting,SEG,,Expanded Abstracts,340–344.
Perez,D.O.,Veils,D.R.,and Sacchi,M.,2013,High resolution prestack seismic inversion using a hybrid FISTA least-squares strategy:Geophysics,78(5),185–195.
Todoeschuck,J.P.,and Jensen,O.G.,1988,Joseph geology and seismic deconvolution:Geophysics,53(11),1410–1414.
vander Baan,M.,2008,Time-varying wavelet estimation and deconvolution by kurtosis maximization:Geophysics,73(2),V11–V18.
vander Baan,M.,and Pham,D.,2008,Robust wavelet estimation and blind deconvolution of noisy surface seismics:Geophysics,73(5),37–46.
vander Baan,M.,and S.Fomel,2009,Nonstationary phase estimation using regularized local kurtosis maximization:Geophysics,74(6),A75–A80.
Velis,D.R.,2008,Stochastic sparse-spike deconvolution:Geophysics,73(1),R1–R9.
Wood,W.,1999,Simultaneous deconvolution and wavelet inversion as a global optimization:Geophysics,64(4),1108–1115.
Yu,Y.C.,Wang,S.X.Yuan,S.Y.,and Qi,P.F.,2011,Phase estimation in bispectral domain based on conformal mapping and applications in seismic wavelet estimation:Applied Geophysics,8(1),36–47.
Yuan,S.Y.,and Wang,S.X.,2011,Influence of in accurate wavelet phase estimation on seismic inversion:Applied Geophysics,8(1),48–59.
Yuan,S.Y.,and Wang,S.X.,2013,Spectral sparse Bayesian learning reflectivity inversion:Geophysical Prospecting,61(4),735–746.
Yuan,S.Y.,Wang,S.X.and Tian,N.2009,Swarm intelligen ceoptimization and its application in geophysical data inversion:Applied Geophysics,6(2),166–174.
Alemie,W.and Sacchi,M.D.,2011,High-resolution three term AVO inversion by means of a Trivariate Cauchy probability distribution:Geophysics,2011,76(3),43–55.
Asnaashari,A.,Brossier,R.,Garambois,S.,Audebert,F.,Thore,P.,and Virieux,J.,2013,Regularized seismicfull wave form inversion with prior model information:Geophysics,78(2),R25–R36.
Broadhead,M.,2008,The impact of random noise onseismic wavelet estimation:The Leading Edge,27(2),226–230.
Buland,A.,and Omre,H.,2003,Bayesian wavelet estimation from seismic and well data:Geophysics,68(6),2000–2009.
Delprat-Jannaud,F.,and Lailly,P.,2005,A fundamental limitation for the reconstruction of impedance profiles from seismic data:Geophysics,70(1),1–14.
Edgar J,and van der Baan M.,2011,How reliable isstatistical wavelet estimation?:Geophysics,2011,76(4),59–68.
Huang,X.,Kelkar,M.,Chopra,A.,and Yang,C.,1995,Wavelet sensitivity study on inversion using heuristic combinatorial algorithms:65th Annual International Metting,SEG,Expanded Abstracts,1088–1090.
Liang,G.,Cai,X.,and Li,Q.,2002,Using high-ordercumulants to extrapolate spatially variant seismic wavelets:Geophysics,67(6),1869–1876.
Lindsey,J.P.1988,Measuring wavelet phase from seismicdata:The Leading Edge,7(7),10–16.
Nowak,E.J.,Swan,H.W.,and Lane,D.,2008,Quantitative thickness estimates from the spectral response of AVO measurements:Geophysics,73(1),C1–C6.
Ostrander,W.,1984,Plane–wave reflection coefficients for gas sands at nonnormal angles of incidence:Geophysics,49(10),1637–1648.
Perez,D.O.,and Veils,D.R.,2011,Sparse-spike AVO/AVA attributes from prestack data:81st Annual International Metting,SEG,,Expanded Abstracts,340–344.
Perez,D.O.,Veils,D.R.,and Sacchi,M.,2013,High resolution prestack seismic inversion using a hybrid FISTA least-squares strategy:Geophysics,78(5),185–195.
Todoeschuck,J.P.,and Jensen,O.G.,1988,Joseph geology and seismic deconvolution:Geophysics,53(11),1410–1414.
vander Baan,M.,2008,Time-varying wavelet estimation and deconvolution by kurtosis maximization:Geophysics,73(2),V11–V18.
vander Baan,M.,and Pham,D.,2008,Robust wavelet estimation and blind deconvolution of noisy surface seismics:Geophysics,73(5),37–46.
vander Baan,M.,and S.Fomel,2009,Nonstationary phase estimation using regularized local kurtosis maximization:Geophysics,74(6),A75–A80.
Velis,D.R.,2008,Stochastic sparse-spike deconvolution:Geophysics,73(1),R1–R9.
Wood,W.,1999,Simultaneous deconvolution and wavelet inversion as a global optimization:Geophysics,64(4),1108–1115.
Yu,Y.C.,Wang,S.X.Yuan,S.Y.,and Qi,P.F.,2011,Phase estimation in bispectral domain based on conformal mapping and applications in seismic wavelet estimation:Applied Geophysics,8(1),36–47.
Yuan,S.Y.,and Wang,S.X.,2011,Influence of in accurate wavelet phase estimation on seismic inversion:Applied Geophysics,8(1),48–59.
Yuan,S.Y.,and Wang,S.X.,2013,Spectral sparse Bayesian learning reflectivity inversion:Geophysical Prospecting,61(4),735–746.
Yuan,S.Y.,Wang,S.X.and Tian,N.2009,Swarm intelligen ceoptimization and its application in geophysical data inversion:Applied Geophysics,6(2),166–174.
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