基于波动方程转换的时间域多尺度全波形反演速度建模
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摘要
为了避免全波形反演的周波跳跃现象,提出了基于波动方程转换的时间域多尺度全波形反演速度建模策略,在时间域实现了从低波数到高波数的多尺度全波形反演。首先从声波方程参数化模式出发,研究了阻抗-速度和速度-密度两种参数化模式下速度的辐射模式:在阻抗-速度参数化模式下,速度扰动主要引起大角度波场扰动;在速度-密度参数化模式下,速度扰动对各个角度的波场扰动贡献量完全相同。基于此,提出了先利用阻抗-速度方程构建低波数全波形反演速度模型,再以此作为初始模型,利用速度-密度方程构建高波数全波形反演速度模型的方法。该方法有效避免了混合域全波形反演中的数据转换问题以及频率域反演中的吉普斯现象,同时充分发挥了时间域全波形反演在波动方程数值模拟计算效率方面的优势,保留了时间域数据匹配易控制的特点。通过MarmousiⅡ模型数据测试,对比分析了两种参数化模式下的速度梯度特征,实现了从阻抗-速度方程的低波数全波形反演速度建模到速度-密度方程的高波数全波形反演速度建模,说明该方法能够在初始速度缺失低波数的条件下充分刻画出断层的形态和位置,使断面清晰,地层起伏与真实模型吻合。
To reduce cycle skipping of full-waveform inversion,a time-domain multi-scale full waveform inversion for velocity modeling based on wave equation transform is proposed.Velocity radiation patterns in different parameterized modes are studied,such as impedance-velocity and velocity-density.In the impedance-velocity parameterization mode,the velocity disturbance causes large-angle wave field disturbance; in the velocity-density parameterization mode,the velocity disturbance contributes equally for the wavefield disturbance at each angle.The impedance-velocity equation is used for low-wavenumber full-waveform inversion,to obtain a low-wavenumber velocity as the initial model to perform high-wavenumber full-waveform inversion.This method effectively avoids data transform in mixed-domain full waveform inversion and the Gibbs phenomenon in frequency-domain full waveform inversion.Meanwhile,the method fully exploits the advantages of time-domain full waveform inversion in calculation efficiency of numerical simulation and retains the characteristics of easy control of data matching in time-domain.A synthetic model was designed to compare and analyze the velocity gradient characteristics of the two kinds of parameterized models.The velocity building was realized by multi-scale full waveform inversion,from low-wavenumber velocity inversion using impedance-velocity equation to high-wavenumber velocity inversion using density-velocity equation.Tests on the Marmousi II model data showed that the proposed method could fully depict the fault shape and position,even if the initial velocity lacked low wavenumber components.
To reduce cycle skipping of full-waveform inversion,a time-domain multi-scale full waveform inversion for velocity modeling based on wave equation transform is proposed.Velocity radiation patterns in different parameterized modes are studied,such as impedance-velocity and velocity-density.In the impedance-velocity parameterization mode,the velocity disturbance causes large-angle wave field disturbance; in the velocity-density parameterization mode,the velocity disturbance contributes equally for the wavefield disturbance at each angle.The impedance-velocity equation is used for low-wavenumber full-waveform inversion,to obtain a low-wavenumber velocity as the initial model to perform high-wavenumber full-waveform inversion.This method effectively avoids data transform in mixed-domain full waveform inversion and the Gibbs phenomenon in frequency-domain full waveform inversion.Meanwhile,the method fully exploits the advantages of time-domain full waveform inversion in calculation efficiency of numerical simulation and retains the characteristics of easy control of data matching in time-domain.A synthetic model was designed to compare and analyze the velocity gradient characteristics of the two kinds of parameterized models.The velocity building was realized by multi-scale full waveform inversion,from low-wavenumber velocity inversion using impedance-velocity equation to high-wavenumber velocity inversion using density-velocity equation.Tests on the Marmousi II model data showed that the proposed method could fully depict the fault shape and position,even if the initial velocity lacked low wavenumber components.
引文
[1] 胡光辉,王立歆,王杰,等.基于早至波的特征波波形反演建模方法[J].石油物探,2015,54(1):71-76HU G H,WANG L X,WANG J,et al.Characteristics waveform inversion based on early arrival waves[J].Geophysical Prospecting for Petroleum,2015,54(1):71-76
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[9] CHEN G X,WU R S,CHEN S.Reflection multi-scale envelope inversion[J].Geophysical Prospecting,2018,66(7):1258-1271
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[11] LUO J R,WU R S.Seismic envelope inversion:reduction of local minima and noise resistance[J].Geophysical Prospecting,2015,63(3):597-614
[12] WU R S,CHEN G X.Multi-scale seismic envelope inversion using a direct envelope Frechet derivative for strong-nonlinear full waveform inversion[R].California:Modeling and Imaging Laboratory,Earth & Planetary Sciences,University of California,2018
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[15] 包乾宗,陈俊霓,吴浩.基于地震数据包络的多尺度全波形反演方法[J].石油物探,2018,57(4):584-591BAO Q Z,CHEN J N,WU H.Multi-scale full waveform inversion based on logarithmic envelope of seismic data[J].Geophysical Prospecting for Petroleum,2018,57(4):584-591
[16] GHOLAMI Y,BROSSIER R,OPERTO S,et al.Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1:Sensitivity and trade-off analysis[J].Geophysics,2013,78(2):R81-R105
[17] PRIEUX V,BROSSIER R,OPERTO S,et al.Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field.Part 2:imaging compressive-wave and shear-wave velocities[J].Geophysical Journal International,2013,194(3):1665-1681
[18] OPERTO S,CHOLAMI Y,PRIEUX V,et al.A guided tour of multiparameter full waveform inversion for multicomponent data:from theory to practice[J].The Leading Edge,2013,32(9):1040-1054
[19] 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):705-716HE B H,FANG W B,HU G H,et al.Parameterization of acoustic wave equation and strategy for multi-parameter full waveform inversion[J].Geophysical Prospecting for Petroleum,2018,57(5):705-716
[20] FORGUES E,LAMBARE G.Parameterization study for acoustic and elastic ray plus Born inversion[J].Journal of Seismic Exploration,1997,6(4):253-278
[21] 张鲁新,符力耘,裴正林.不分裂卷积完全匹配层与旋转交错网格有限差分在孔隙弹性介质模拟中的应用[J].地球物理学报,2010,53(10):2470-2483ZHANG L X,FU L Y,PEI Z L.Finite difference modeling of Biot's poroelastic equations with unsplit convolutional PML and rotated staggered grid[J].Chinese Journal of Geophysics,2010,53(10):2470-2483
[22] 胡光辉,王立歆,方伍宝.全波形反演方法及应用[M].北京:石油工业出版社,2014:12-15HU G H,WANG L X,FANG W B.Full waveform inversion method and application[M].Beijing:Petroleum Industry Press,2014:12-15
[23] 李海山,杨午阳,雍学善.三维一阶速度-应力声波方程全波形反演[J].石油地球物理勘探,2018,53(4):730-736LI H S,YANG W Y,YONG X S.Three-dimensional full waveform inversion based on the first-order velocity-stress acoustic wave equation[J].Oil Geophysical Prospecting,2018,53(4):730-736
[24] 杨积忠,刘玉柱,董良国.基于Born敏感核函数的速度、密度双参数全波形反演[J].地球物理学报,2016,59(3):1082-1094YANG J Z,LIU Y Z,DONG L G.Multi-parameter full waveform inversion for velocity and density based on Born sensitivity kernels[J].Chinese Journal of Geophysics,2016,59(3):1082-1094
[2] 胡光辉,李熙盛,郭丽,等.构造约束全波形反演及其海上资料应用[J].石油物探,2018,57(4):592-596HU G H,LI X S,GUO L,et al.Structure-constrained full waveform inversion and its application in marine seismic data[J].Geophysical Prospecting for Petroleum,2018,57(4):592-596
[3] HU G.Three-dimensional acoustic full waveform inversion:method,algorithm and application to Valhall petroleum field[D].Grenoble:Universite de Josph Fourier,2012
[4] PRATT R G,SHIN C,HICKS G T.Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion[J].Geophysical Journal International,1998,133(2):341-362
[5] SIRGUE L,PRATT R G.Efficient waveform inversion and imaging:A strategy for selecting temporal frequencies[J].Geophysics,2004,69(1):231-248
[6] CHI B X,DONG L G,LIU Y Z.Full waveform inversion method using envelope objective function without low frequency data[J].Journal of Applied Geophysics,2014,109(10):36-46
[7] BOZDA E,TRAMPERT J,TROMP J.Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements[J].Geophysical Journal International,2011,185(2):845-870
[8] CHI B X,DONG L G,LIU Y Z.Full waveform inversion method based on envelope objective function[J].Extended Abstracts of 75th EAGE Conference & Technical Exhibition,2013:1-5
[9] CHEN G X,WU R S,CHEN S.Reflection multi-scale envelope inversion[J].Geophysical Prospecting,2018,66(7):1258-1271
[10] 罗静蕊,吴如山,高静怀.地震包络反演对局部极小值的抑制特性[J].地球物理学报,2016,59(7):2510-2518LUO J R,WU R S,GAO J H.Local minima reduction of seismic envelope inversion[J].Chinese Journal of Geophysics,2016,59(7):2510-2518
[11] LUO J R,WU R S.Seismic envelope inversion:reduction of local minima and noise resistance[J].Geophysical Prospecting,2015,63(3):597-614
[12] WU R S,CHEN G X.Multi-scale seismic envelope inversion using a direct envelope Frechet derivative for strong-nonlinear full waveform inversion[R].California:Modeling and Imaging Laboratory,Earth & Planetary Sciences,University of California,2018
[13] WU R S,LUO J R,WU B Y.Ultra-low-frequency information in seismic data and envelope inversion[J].Expanded Abstracts of 83rd Annual Internat SEG Mtg,2013:3078-3082
[14] FICHTNER A,KENNETT B,IGEL H,et al.Theoretical background for continental and global-scale full-waveform inversion in the time-frequency domain[J].Geophysical Journal of the Royal Astronomical Society,2008,175(2):665-685
[15] 包乾宗,陈俊霓,吴浩.基于地震数据包络的多尺度全波形反演方法[J].石油物探,2018,57(4):584-591BAO Q Z,CHEN J N,WU H.Multi-scale full waveform inversion based on logarithmic envelope of seismic data[J].Geophysical Prospecting for Petroleum,2018,57(4):584-591
[16] GHOLAMI Y,BROSSIER R,OPERTO S,et al.Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1:Sensitivity and trade-off analysis[J].Geophysics,2013,78(2):R81-R105
[17] PRIEUX V,BROSSIER R,OPERTO S,et al.Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field.Part 2:imaging compressive-wave and shear-wave velocities[J].Geophysical Journal International,2013,194(3):1665-1681
[18] OPERTO S,CHOLAMI Y,PRIEUX V,et al.A guided tour of multiparameter full waveform inversion for multicomponent data:from theory to practice[J].The Leading Edge,2013,32(9):1040-1054
[19] 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):705-716HE B H,FANG W B,HU G H,et al.Parameterization of acoustic wave equation and strategy for multi-parameter full waveform inversion[J].Geophysical Prospecting for Petroleum,2018,57(5):705-716
[20] FORGUES E,LAMBARE G.Parameterization study for acoustic and elastic ray plus Born inversion[J].Journal of Seismic Exploration,1997,6(4):253-278
[21] 张鲁新,符力耘,裴正林.不分裂卷积完全匹配层与旋转交错网格有限差分在孔隙弹性介质模拟中的应用[J].地球物理学报,2010,53(10):2470-2483ZHANG L X,FU L Y,PEI Z L.Finite difference modeling of Biot's poroelastic equations with unsplit convolutional PML and rotated staggered grid[J].Chinese Journal of Geophysics,2010,53(10):2470-2483
[22] 胡光辉,王立歆,方伍宝.全波形反演方法及应用[M].北京:石油工业出版社,2014:12-15HU G H,WANG L X,FANG W B.Full waveform inversion method and application[M].Beijing:Petroleum Industry Press,2014:12-15
[23] 李海山,杨午阳,雍学善.三维一阶速度-应力声波方程全波形反演[J].石油地球物理勘探,2018,53(4):730-736LI H S,YANG W Y,YONG X S.Three-dimensional full waveform inversion based on the first-order velocity-stress acoustic wave equation[J].Oil Geophysical Prospecting,2018,53(4):730-736
[24] 杨积忠,刘玉柱,董良国.基于Born敏感核函数的速度、密度双参数全波形反演[J].地球物理学报,2016,59(3):1082-1094YANG J Z,LIU Y Z,DONG L G.Multi-parameter full waveform inversion for velocity and density based on Born sensitivity kernels[J].Chinese Journal of Geophysics,2016,59(3):1082-1094