各向异性介质弹性波多参数全波形反演
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摘要
各向异性介质弹性波方程全波形反演过程中多参数之间的相互耦合,使得弱参数在反演过程中难得到理想的结果.本文以VTI介质为例,在各参数辐射模式分析的基础上,基于改进的散射积分算法实现目标函数梯度的直接求取,进一步构建高斯牛顿方向,实现Hessian矩阵的有效利用,以考虑Hessian矩阵非主对角线元素包含的各参数间的耦合效应,在不使用任何反演策略的情况下实现高精度的VTI介质弹性波方程多参数同步反演.同时,该方法在计算过程中无需存储庞大的核函数矩阵,且无需传统截断牛顿法中额外的正演计算,因此内存占用小,计算效率高.本文数值试验验证了该方法的有效性,为各向异性多参数全波形反演提供了一种新的解决方案.
The trade-off effects between parameters in anisotropic media,which have been studied in radiation patterns analysis,makes it difficult to get acceptable weak parameter results during full-waveform inversion(FWI)based on an elastic wave equation.In this paper,to reduce the trade-off effects between parameters,we apply the truncated Gauss-Newton method to anisotropic FWI,taking VTI media for example.All parameters have been revealed simultaneously without using any strategy.Based on the improved scattering-integral(SI)algorithm,the steepestdescent direction can be directly calculated by vector operations,without storing the huge Fréchet kernels in memory beforehand.The Gauss-Newton descent direction iteration needs just two vector operations without any extra forward computations.Numerical experiments in the final part prove the effectiveness of the proposed method which opens a new approach on simultaneously constructing anisotropic parameters in FWI.
The trade-off effects between parameters in anisotropic media,which have been studied in radiation patterns analysis,makes it difficult to get acceptable weak parameter results during full-waveform inversion(FWI)based on an elastic wave equation.In this paper,to reduce the trade-off effects between parameters,we apply the truncated Gauss-Newton method to anisotropic FWI,taking VTI media for example.All parameters have been revealed simultaneously without using any strategy.Based on the improved scattering-integral(SI)algorithm,the steepestdescent direction can be directly calculated by vector operations,without storing the huge Fréchet kernels in memory beforehand.The Gauss-Newton descent direction iteration needs just two vector operations without any extra forward computations.Numerical experiments in the final part prove the effectiveness of the proposed method which opens a new approach on simultaneously constructing anisotropic parameters in FWI.
引文
Barnes C,Charara M,Tsuchiya T.2008.Feasibility study for an anisotropic full waveform inversion of cross-well seismic data.Geophysical Prospecting,56(6):897-906,doi:10.1111/j.1365-2478.2008.00702.x.
Choi Y,Shin C,Min D J.2007.Frequency domain elastic full waveform inversion using the new pseudo-Hessian matrix:elastic Marmousi-2synthetic test.∥2007SEG Annual Meeting.San Antonio,Texas:SEG.
Dahlen F A,Hung S H,Nolet G.2000.Fréchet kernels for finitefrequency traveltimes-I.Theory.Geophysical Journal International,141(1):157-174,doi:10.1046/j.1365-246X.2000.00070.x.
Djebbi R,Alkhalifah T.2017.Frequency domain multi-parameter full waveform inversion for acoustic VTI media.∥79th EAGEConference and Exhibition.EAGE.
Fichtner A,Trampert J.2011.Hessian kernels of seismic data functionals based upon adjoint techniques.Geophysical Journal International,185(2):775-798,doi:10.1111/j.1365-246X.2011.04966.x.
Lee H Y,Koo J M,Min D J,et al.2010.Frequency-domain elastic full waveform inversion for VTI media.Geophysical Journal International,183(2):884-904,doi:10.1111/j.1365-246X.2010.04767.x.
Liu Y Z,Dong L G,Wang Y W,et al.2009.Sensitivity kernels for seismic Fresnel volume tomography.Geophysics,74(5):U35-U46,doi:10.1190/1.3169600.
Liu Y Z,Wang G Y,Yang J Z,et al.2015.Multi-parameter fullwaveform inversion for VTI media based on Born sensitivity kernels.Chinese Journal of Geophysics(in Chinese),58(4):1305-1316,doi:10.6038/cjg20150418.
Liu Y Z,Yang J Z,Chi B X,et al.2015.An improved scatteringintegral approach for frequency-domain full waveform inversion.Geophysical Journal International,202(3):1827-1842,doi:10.1093/gji/ggv254.
Luo J R,Wu R S,Gao F C.2018.Time-domain full waveform inversion using instantaneous phase information with damping.Journal of Geophysics and Engineering,15(3):1032-1041,doi:10.1088/1742-2140/aaa984.
Métivier L,Brossier R,Virieux J,et al.2012.Toward gauss-newton and exact newton optimization for full waveform inversion.∥74th EAGE Conference and Exhibition.SPE,EAGE.
Operto S,Gholami Y,Prieux V,et al.2013.A guided tour of multiparameter full waveform inversion for multicomponent data:from theory to practice.The Leading Edge,32(9):1040-1054,doi:10.1190/tle32091040.1.
Pan W Y,Innanen K A,Margrave G F,et al.2016.Estimation of elastic constants for HTI media using Gauss-Newton and fullNewton multiparameter full-waveform inversion.Geophysics,81(5):R275-R291,doi:10.1190/geo2015-0594.1.
Plessix R é.2009.Three-dimensional frequency-domain full-waveform inversion with an iterative solver.Geophysics,74(6):WCC149-WCC157,doi:10.1190/1.3211198.
Pratt R G.1999.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model.Geophysics,64(3):888-901,doi:10.1190/1.1444597.
Prieux V,Brossier R,Operto S,et al.2013.Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field.Part 1:imaging compressional wave speed,density and attenuation.Geophysical Journal International,194(3):1640-1664,doi:10.1093/gji/ggt177.
Sheen D H,Tuncay K,Baag C E,et al.2006.Time domain GaussNewton seismic waveform inversion in elastic media.Geophysical Journal International,167(3):1373-1384,doi:10.1111/j.1365-246X.2006.03162.x.
Sirgue L,Barkved O I,van Gestel J P,et al.2009.3D waveform inversion on Valhall wide-azimuth OBC.∥71st EAGE Conference and Exhibition.SPE,EAGE.
Spetzler J,Snieder R.2004.The Fresnel volume and transmitted waves.Geophysics,69(3):653-663,doi:10.1190/1.1759451.
Sun M A,Yang J Z,Dong L G,et al.2017.Density reconstruction in multiparameter elastic full-waveform inversion.Journal of Geophysics and Engineering,14(6):1445-1462,doi:10.1088/1742-2140/aa93b0.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266,doi:10.1190/1.1441754.
Woodward M J.1992.Wave-equation tomography.Geophysics,57(1):15-26,doi:10.1190/1.1443179.
Yang J Z,Liu Y Z,Dong L G.2014.A multi-parameter full waveform inversion strategy for acoustic media with variable density.Chinese Journal of Geophysics(in Chinese),57(2):628-643,doi:10.6038/cjg20140226.
Zhou B,Greenhalgh S.2009.On the computation of the Fréchet derivatives for seismic waveform inversion in 3Dgeneral anisotropic,heterogeneous media.Geophysics,74(5):WB153-WB163,doi:10.1190/1.3123766.
刘玉柱,王光银,杨积忠等.2015.基于Born敏感核函数的VTI介质多参数全波形反演.地球物理学报,58(4):1305-1316,doi:10.6038/cjg20150418.
杨积忠,刘玉柱,董良国.2014.变密度声波方程多参数全波形反演策略.地球物理学报,57(2):628-643,doi:10.6038/cjg20140226.
Choi Y,Shin C,Min D J.2007.Frequency domain elastic full waveform inversion using the new pseudo-Hessian matrix:elastic Marmousi-2synthetic test.∥2007SEG Annual Meeting.San Antonio,Texas:SEG.
Dahlen F A,Hung S H,Nolet G.2000.Fréchet kernels for finitefrequency traveltimes-I.Theory.Geophysical Journal International,141(1):157-174,doi:10.1046/j.1365-246X.2000.00070.x.
Djebbi R,Alkhalifah T.2017.Frequency domain multi-parameter full waveform inversion for acoustic VTI media.∥79th EAGEConference and Exhibition.EAGE.
Fichtner A,Trampert J.2011.Hessian kernels of seismic data functionals based upon adjoint techniques.Geophysical Journal International,185(2):775-798,doi:10.1111/j.1365-246X.2011.04966.x.
Lee H Y,Koo J M,Min D J,et al.2010.Frequency-domain elastic full waveform inversion for VTI media.Geophysical Journal International,183(2):884-904,doi:10.1111/j.1365-246X.2010.04767.x.
Liu Y Z,Dong L G,Wang Y W,et al.2009.Sensitivity kernels for seismic Fresnel volume tomography.Geophysics,74(5):U35-U46,doi:10.1190/1.3169600.
Liu Y Z,Wang G Y,Yang J Z,et al.2015.Multi-parameter fullwaveform inversion for VTI media based on Born sensitivity kernels.Chinese Journal of Geophysics(in Chinese),58(4):1305-1316,doi:10.6038/cjg20150418.
Liu Y Z,Yang J Z,Chi B X,et al.2015.An improved scatteringintegral approach for frequency-domain full waveform inversion.Geophysical Journal International,202(3):1827-1842,doi:10.1093/gji/ggv254.
Luo J R,Wu R S,Gao F C.2018.Time-domain full waveform inversion using instantaneous phase information with damping.Journal of Geophysics and Engineering,15(3):1032-1041,doi:10.1088/1742-2140/aaa984.
Métivier L,Brossier R,Virieux J,et al.2012.Toward gauss-newton and exact newton optimization for full waveform inversion.∥74th EAGE Conference and Exhibition.SPE,EAGE.
Operto S,Gholami Y,Prieux V,et al.2013.A guided tour of multiparameter full waveform inversion for multicomponent data:from theory to practice.The Leading Edge,32(9):1040-1054,doi:10.1190/tle32091040.1.
Pan W Y,Innanen K A,Margrave G F,et al.2016.Estimation of elastic constants for HTI media using Gauss-Newton and fullNewton multiparameter full-waveform inversion.Geophysics,81(5):R275-R291,doi:10.1190/geo2015-0594.1.
Plessix R é.2009.Three-dimensional frequency-domain full-waveform inversion with an iterative solver.Geophysics,74(6):WCC149-WCC157,doi:10.1190/1.3211198.
Pratt R G.1999.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model.Geophysics,64(3):888-901,doi:10.1190/1.1444597.
Prieux V,Brossier R,Operto S,et al.2013.Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field.Part 1:imaging compressional wave speed,density and attenuation.Geophysical Journal International,194(3):1640-1664,doi:10.1093/gji/ggt177.
Sheen D H,Tuncay K,Baag C E,et al.2006.Time domain GaussNewton seismic waveform inversion in elastic media.Geophysical Journal International,167(3):1373-1384,doi:10.1111/j.1365-246X.2006.03162.x.
Sirgue L,Barkved O I,van Gestel J P,et al.2009.3D waveform inversion on Valhall wide-azimuth OBC.∥71st EAGE Conference and Exhibition.SPE,EAGE.
Spetzler J,Snieder R.2004.The Fresnel volume and transmitted waves.Geophysics,69(3):653-663,doi:10.1190/1.1759451.
Sun M A,Yang J Z,Dong L G,et al.2017.Density reconstruction in multiparameter elastic full-waveform inversion.Journal of Geophysics and Engineering,14(6):1445-1462,doi:10.1088/1742-2140/aa93b0.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266,doi:10.1190/1.1441754.
Woodward M J.1992.Wave-equation tomography.Geophysics,57(1):15-26,doi:10.1190/1.1443179.
Yang J Z,Liu Y Z,Dong L G.2014.A multi-parameter full waveform inversion strategy for acoustic media with variable density.Chinese Journal of Geophysics(in Chinese),57(2):628-643,doi:10.6038/cjg20140226.
Zhou B,Greenhalgh S.2009.On the computation of the Fréchet derivatives for seismic waveform inversion in 3Dgeneral anisotropic,heterogeneous media.Geophysics,74(5):WB153-WB163,doi:10.1190/1.3123766.
刘玉柱,王光银,杨积忠等.2015.基于Born敏感核函数的VTI介质多参数全波形反演.地球物理学报,58(4):1305-1316,doi:10.6038/cjg20150418.
杨积忠,刘玉柱,董良国.2014.变密度声波方程多参数全波形反演策略.地球物理学报,57(2):628-643,doi:10.6038/cjg20140226.
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