The full waveform inversion method can be regarded as a large nonlinear minimization problem.In this method,Hessian operator exerts significant influence on the inversion result.Nevertheless,traditional optimization methods can only express the Hessian operator approximately,which will lead to low inversion accuracy,slow convergence speed,and the result that the parameter cannot be focused,especially for deep inversion region target with poor illumination.In contrast,the truncated Newton method,a new optimization method,can obtain the information of Hessian operator more accurately by the computation of the product of Hessian matrix and a known vector,and thus can solve the problem mentioned above.Therefore,this paper achieves full waveform inversion in the frequency domain based on truncated Newton method.And the model test shows that the truncated Newton method has more precise inversion results and improves the efficiency of inversion,especially for deep area with insufficient illumination compared with the limited memory BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno,L-BFGS) method.
周斯琛, 李振春, 张敏, 张凯. 基于截断牛顿法的频率域全波形反演方法[J]. 物探与化探, 2017, 41(1): 147-152.
ZHOU Si-Chen, LI Zhen-Chun, ZHANG Min, ZHANG Kai. Full waveform inversion in frequency domain using the truncated Newton method. Geophysical and Geochemical Exploration, 2017, 41(1): 147-152.
[1] Virieux J,Operto S.An overview of full-waveform inversion in exploration geophysics[J].Geophysics,2009,74(6):WCC1-WCC26.
[2] 高凤霞.频率域波动方程多参数全波形反演方法研究[D].长春:吉林大学,2014.
[3] Plessix R E,Perkins C.Thematic Set:Full waveform inversion of a deep water ocean bottom seismometer dataset[J].First Break,2010,28(4):71-78.
[4] Xue Z,Zhu H.Full waveform inversion with sparsity constraint in seislet domain[C]//85th Annual International Meeting,SEG,Expanded Abstracts,2015.
[5] Prieux V,Brossier R,Operto S,et al.Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field,Part 1:imaging compressional wave speed,density and attenuation[J].Geophysical Journal International,2013,194(3):1640-1664.
[6] 李媛媛,李振春,张凯.频率域多尺度弹性波全波形反演[J].石油物探,2015,54(3):317-323.
[7] Lailly P.The seismic inverse problem as a sequence of before stack migrations[C]//Philadelphia:Conference on inverse scattering:theory and application,Society for Industrial and Applied Mathematics,1983:206-220.
[8] Tarantola A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,49(8):1259-1266.
[9] Pratt R G,Worthington M H.Inverse theory applied to multi-source cross-hole tomography,Part 1:acoustic wave-equation method[J].Geophysical Prospecting,1990,38(3):287-310.
[10] Vigh D,Starr E W.Comparisons for waveform inversion, time domain or frequency domain?[C]//78th Annual International Meeting,SEG,Expanded Abstracts,2008.
[11] Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model[J].Geophysics,1999,64(3):888-901.
[12] Pratt R G,Shipp R M.Seismic waveform inversion in the frequency domain,Part 2:Fault delineation in sediments using crosshole data[J].Geophysics,1999,64(3):902-914.
[13] Operto S,Ravaut C,Improta L,et al.Quantitative imaging of complex structures from dense wide-aperture seismic data by multiscale traveltime and waveform inversions:a case study[J].Geophysical prospecting,2004,52(6):625-651.
[14] Operto S,Gholami Y,Prieux V,et al.A guided tour of multiparameter full-waveform inversion with multicomponent data:From theory to practice[J].The Leading Edge,2013,32(9):1040-1054.
[15] 刘璐,刘洪,张衡,等.基于修正拟牛顿公式的全波形反演[J].地球物理学报,2013,56(7):2447-2451.
[16] Brossier R,Operto S,Virieux J.Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion[J].Geophysics,2009,74(6):WCC105-WCC118.
[17] Nash S G.A survey of truncated-Newton methods[J].Journal of Computational and Applied Mathematics,2000,124(1):45-59.
[18] 王义,董良国.基于截断牛顿法的VTI介质声波多参数全波形反演[J].地球物理学报,2015,58(8):2873-2885.
[19] Eisenstat S C,Walker H F.Choosing the forcing terms in an inexact Newton method[J].SIAM Journal on Scientific Computing,1996,17(1):16-32.