Reflection waveform inversion based on cross-correlation misfit function
LI Qingyang1,2, WU Guochen1,2, DUAN Peiran1, LIANG Zhanyuan1,2
1. School of Geosciences, China University of Petroleum(East China), Qingdao, Shandong 266580, China; 2. Evaluation and Detection Technology Laboratory of Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong 266071, China
Abstract：On a velocity and density model,the density from conventional FWI (Full Waveform Inversion) is seriously migrated,namely low wavenumber information in the model hasn't been recovered. Since RWI (Reflection Waveform Inversion) can estimate low wavenumber component,the combination of RWI and FWI can invert the density model more accurately. A velocity-density RWI model based on crosscorrelation-based misfit function is proposed. This paper first reviews the two-parameter inversion based on the conventional acoustic wave equation,and analyze the migration characteristics of density inversion using a radiation mode;then synchronously updates velocity and density by the Gardner formula based on the high trade-off between velocity density model when running RWI,and input the RWI results as the initial model for traditional velocity-density FWI;and finally builds a velocity-density RWI+FWI inversion workflow. Application on a simple two-layer model and a resampled Sigsbee 2A model has proved that RWI could avoid inversion to be trapped in local minima and suppress density migration;and in the process of RWI,low wavenumber information of velocity and density could be accurately recovered by using the Gardner formula to update velocity and density at the same time.
杨积忠,刘玉柱,董良国.变密度声波方程多参数全波形反演策略[J].地球物理学报,2014,57(2):628-643.YANG Jizhong,LIU Yuzhu,DONG Liangguo.A multi-parameter full waveform inversion strategy for acoustic media with variable density[J].Chinese Journal of Geophysics,2014,57(2):628-643.
[2]
石玉梅,张研,姚逢昌,等.基于声学全波形反演的油气藏地震成像方法[J].地球物理学报,2014,57(2):607-617.SHI Yumei,ZHANG Yan,Yao Fengchang,et al.Methodology of seismic imaging for hydrocarbon re-servoirs based on acoustic full waveform inversion[J].Chinese Journal of Geophysics,2014,57(2):607-617.
[3]
何兵红,方伍宝,胡光辉,等.声波方程参数化模式及多参数全波形反演去耦合化策略[J].石油物探,2018,57(5):73-84.HE Binghong,FANG Wubao,HU Guanghui,et al.Parameterization of acoustic wave equation and strategy for multi-parameter full waveform inversion[J].Geophysical Prospecting for Petroleum,2018,57(5):73-84.
[4]
Köhn D,De Nil D,Kurzmann A,et al.On the influ-ence of model parametrization in elastic full waveform tomography[J].Geophysical Journal International,2012,191(1):325-345.
[5]
Jeong W,Lee H Y,Min D J.Full waveform inversion strategy for density in the frequency domain[J].Geophysical Journal International,2012,188(3):1221-1242.
[6]
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.
[7]
张广智,孙昌路,潘新朋,等.变密度声波全波形反演中密度影响因素及反演策略[J].吉林大学学报(地球科学版),2016,46(5):1500-1560.ZHANG Guangzhi,SUN Changlu,PAN Xinpeng,et al.Influence factors and strategy of inversion for density of acoustic full waveform inversion with variable density[J].Journal of Jilin University(Earth Science Edition),2016,46(5):1500-1560.
[8]
Luo J R,Wu R S.Velocity and density reconstruction based on scattering angle separation[J].Pure and Applied Geophysics,2018,175(12):4371-4387.
[9]
郭振波.弹性介质波形反演方法研究[D].山东青岛:中国石油大学(华东),2014.GUO Zhenbo.Research on Waveform Inversion in Elastic Medium[D].China University of Petroleum(East China),Qingdao,Shandong,2014.
[10]
Chi B X,Dong L Q,Liu Y Z.Correlation-based reflection full-waveform inversion[J].Geophysics,2015,80(4):R189-R202.
[11]
Pratt R G,Goulty N R.Combining wave-equation i-maging with traveltime tomography to form high-resolution images from crosshole data[J].Geophysics,1991,56(2):208-224.
[12]
Shipp R M,Singh S C.Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data[J].Geophysical Journal International,2002,151(2):325-344.
[13]
姚刚,吴迪.反射波全波形反演[J].中国科学:地球科学,2017,47(10):1220-1232.YAO Gang,WU Di.Reflection full waveform inversion[J].Science China:Earth Sciences,2017,47(10):1220-1232.
[14]
Xu S,Wang S,Chen F,et al.Full waveform inversion for reflected seismic data[C].Extended Abstracts of 74th EAGE Conference & Exhibition,2012,W024.
[15]
Zhang Y,Xu S,Bleistein N,et al.True-amplitude,angle-domain,common-image gathers from one-way wave-equation migrations[J].Geophysics,2007,72(1):S49-S58.
[16]
Wang S,Chen F,Zhang H,et al.Reflection-based full waveform inversion (RFWI) in the frequency domain[C].SEG Technical Program Expanded Abstracts,2013,32:877-881.
[17]
Mora P.Inversion=migration+tomography[J].Geophysics,1989,54(12):1575-1586.
[18]
Alkhalifah T,Wu Z.The natural combination of full and image-based waveform inversion[J].Geophysical Prospecting,2016,64(1):19-30.
[19]
Luo Y,Ma Y,Wu Y,et al.Full-traveltime inversion[J].Geophysics,2016,81(5):R261-R274.
[20]
Wang G C,Wang S X,Du Q Z,et al.Traveltime-based reflection full-waveform inversion for elastic medium[J].Journal of Applied Geophysics,2017,141(1):68-76.
[21]
Wang G C,Wang S X,Song J,et al.Elastic reflection traveltime inversion with decoupled wave equation[J].Geophysics,2018,83(5):R463-R474.
[22]
Wang T,Cheng J,Guo Q,et al.Elastic wave-equation-based reflection kernel analysis and traveltime inversion using wave mode decomposition[J].Geophysical Journal International,2018,215(1):450-470.
[23]
Ren Z,Li Z,Gu B.Elastic reflection waveform inversion based on the decomposition of sensitivity kernels[J].Geophysics,2019,84(2):R235-R250.
李青阳,吴国忱,吴建鲁.非均匀流-固边界耦合介质多参数全波形反演方法[J].地球物理学报,2019,62(9):3557-3570.LI Qingyang,WU Guochen,WU Jianlu.A multi-parameter full waveform inversion method for a heterogeneous medium with a fluid-solid coupled boundary[J].Chinese Journal of Geophysics,2019,62(9):3557-3570.
[27]
Plessix R E.A review of the adjoint-state method for computing the gradient of a functional with geophysical applications[J].Geophysical Journal Internatio-nal,2006,167(2):495-503.
[28]
Di B L,Dors C,Mansur W J.A new family of finite-difference schemes to solve the heterogeneous acoustic wave equation[J].Geophysics,2012,77(5):T187-T199.
[29]
段沛然,李青阳,赵志强,等.等效交错网格高阶有限差分法标量波波场模拟[J].地球物理学进展,2019,34(3):1032-1040.DUAN Peiran,LI Qingyang,ZHAO Zhiqiang,et al.High-order finite-difference method based on equivalent staggered grid scheme for scalar wavefield simulation[J].Progress in Geophysics,2019,34(3):1032-1040.
[30]
李青阳,吴国忱,段沛然.准规则网格高阶有限差分法非均质弹性波波场模拟[J].石油地球物理勘探,2019,54(3):539-550.LI Qingyang,WU Guochen,DUAN Peiran.Elastic wavefield formodeling in heterogeneous media based on the quasi-regular grid high-order finite difference[J].Oil Geophysical Prospecting,2019,54(3):539-550.
[31]
吴建鲁,吴国忱,王伟,等.基于等效交错网格的流固耦合介质地震波模拟[J].石油地球物理勘探,2018,53(2):272-279.WU Jianlu,WU Guochen,WANG Wei,et al.Seismic forward modeling in fluid-solid media based on equi-valent staggered grid scheme[J].Oil Geophysical Prospecting,2018,53(2):272-279.
[32]
Forgues E,Lambar G.Parameterization study for acoustic and elastic ray+Born inversion[J].Journal of Seismic Exploration,1997,6(3):253-277.
[33]
Virieux J,Operto S.An overview of full-waveform inversion in exploration geophysics[J].Geophysics,2009,74(6):WCC1-WCC26.
[34]
Sirgue L,Pratt R G.Efficient waveform inversion and imaging:A strategy for selecting temporal frequencies[J].Geophysics,2014,79(1):231-248.
[35]
Liang Z,Wu G,Zhang X.Time domain full waveform inversion with low frequency wavefield decompression[J].Journal of Geophysics and Engineering,2018,15(6):2330-2338.
[36]
Gardner G,Gardner L,Gregory A.Formation velocity and density-the diagnostics basics for stratigraphic traps[J].Geophysics,1974,39(6):770-780.
[37]
Van L T,Mulder W A.A correlation-based misfit criterion for wave-equation traveltime tomography[J].Geophysical Journal International,2010,182(3):1383-1394.
