Viscoacoustic FWI with a stable Q-compensated gradient
JIANG Shuqi1,2,3, ZHOU Hui1,2,3, CHEN Hanming1,2,3, ZHANG Mingkun1,2,3, FU Yuxin1,2,3, LI Honghui4
1. National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing), Beijing 102249, China; 2. CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum (Beijing), Beijing 102249, China; 3. College of Geophysics, China University of Petroleum (Beijing), Beijing 102249, China; 4. Geophysical Exploration Technology Research Center, BGP Inc., CNPC, Zhuozhou, Hebei 072751, China
Abstract:The full-waveform inversion (FWI) based on attenuation medium usually adopts the viscoacoustic wave equation,and calculates the gradient of an objective function with respect to the velocity of the media by the adjoint state method. Since both the source wavefield and adjoint wavefield are attenuated,the gradient weakens with depth resulting in reducing the modification of subsurface parameters,which slows down the convergence of the inversion. To speed up the inversion efficiency,this paper develops a viscoacoustic FWI based on the decoupled fractional Laplacian (DFL) wave equation,and provides a new gradient compensation strategy based on a stabilization factor. The new compensation strategy achieves stable compensation by setting one stabilized factor in compensation,balances the amplitudes in the recovered gradient,meanwhile maintains correct kinematics. Compared with the conventional viscoacoustic FWI,the viscoacoustic FWI with this gradient compensation strategy has faster convergence speed and higher inversion accuracy.
TARANTOLA A. Inversion of seismic reflection data in the acoustic approximation[J]. Geophysics,1984,49(8):1259-1266.
[2]
TARANTOLA A. A strategy for nonlinear elastic inversion of seismic reflection data[J]. Geophysics,1986,51(10):1893-1903.
[3]
MA Y,HALE D. Quasi-Newton full-waveform inversion with a projected Hessian matrix[J]. Geophysics,2012,77(5):R207-R216.
[4]
MÉTIVIER L,BRETAUDEAU F,BROSSIER R,et al. Full waveform inversion and the truncated Newton method:quantitative imaging of complex subsurface structures[J]. Geophysical Prospecting,2014,62(6):1353-1375.
[5]
苗永康. 基于L-BFGS算法的时间域全波形反演[J]. 石油地球物理勘探,2015,50(3):469-474.MIAO Yongkang. Full waveform inversion in time domain based on limited-memory BFGS algorithm[J]. Oil Geophysical Prospecting,2015,50(3):469-474.
[6]
MÉTIVIER L,BROSSIER R. The SEISCOPE optimization toolbox:A large-scale nonlinear optimization library based on reverse communication[J]. Geophysics,2016,81(2):F1-F15.
[7]
刘宇航,黄建平,杨继东,等. 弹性波全波形反演中的四种优化方法对比[J].石油地球物理勘探,2022,57(1):118-128.LIU Yuhang,HUANG Jianping,YANG Jidong,et al. Comparison of four optimization methods in elastic full-waveform inversion[J]. Oil Geophysical Prospecting,2022,57(1):118-128.
[8]
CASTELLANOS C,MÉTIVIER L,OPERTO S,et al. Fast full waveform inversion with source encoding and second-order optimization methods[J]. Geophysical Journal International,2015,200(2):720-744.
[9]
LAZARATOS S,CHIKICHEV I,WANG K. Improving the convergence rate of full wavefield inversion using spectral shaping[C]. SEG Technical Program Expanded Abstracts,2011,30:2428-2432.
GUITTON A,AYENI G, DÍAZ E. Constrained full-waveform inversion by model reparameterization[J]. Geophysics, 2012,77(2):R117-R127
[12]
KJARTANSSON E. Constant Q-wave propagation and attenuation[J]. Journal of Geophysical Research:Solid Earth,1979,84(B9):4737-4748.
[13]
WANG Y,ZHOU H,CHEN H,et al. Adaptive stabilization for Q-compensated reverse time migration[J]. Geophysics,2018,83(1):S15-S32.
[14]
ZHAO X,ZHOU H,WANG Y,et al. A stable approach for Q-compensated viscoelastic reverse time migration using excitation amplitude imaging condition[J]. Geophysics,2018,83(5):S459-S476.
[15]
SUN J,ZHU T. Stable attenuation compensation in reverse-time migration[C]. SEG Technical Program Expanded Abstracts,2015,34:3942-3947.
[16]
SUN J,ZHU T. Strategies for stable attenuation compensation in reverse-time migration[J]. Geophysical Prospecting,2018,66(3):498-511.
[17]
CHEN H,ZHOU H,RAO Y. Source wavefield reconstruction in fractional Laplacian viscoacoustic wave equation-based full waveform inversion[J]. IEEE Transactions on Geoscience and Remote Sensing,2021,59(8):6496-6509.
[18]
LIU H P,ANDERSON D L,KANAMORI H. Velocity dispersion due to inelasticity:implications for seismology and mantle composition[J]. Geophysical Journal International,1976,47(1):41-58.
[19]
WANG Y. Generalized viscoelastic wave equation[J]. Geophysical Journal International,2016,204(2):1216-1221.
[20]
GUO P,MCMECHAN G A. Evaluation of three first-order isotropic viscoelastic formulations based on the generalized standard linear solid[J]. Journal of Seismic Exploration,2017,26(3):199-226.
[21]
刘志强,黄磊,李钢柱,等. 基于正交贴体网格的黏弹介质地震波模拟[J]. 石油地球物理勘探,2023,58(4):839-846.LIU Zhiqiang,HUANG Lei,LI Gangzhu,et al. Numerical simulation of seismic waves in viscoelastic media based on orthogonal body-fitted grid[J]. Oil Geophysical Prospecting,2023,58(4):839-846.
[22]
吴玉,符力耘,陈高祥. 基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移[J]. 地球物理学报,2017,60(4):1527-1537.WU Yu,FU Liyun,CHEN Gaoxiang. Forward modeoling and reverse time migration of viscoacoustic media using decoupled fractional Laplacians[J]. Chinese Journal of Geophysics,2017,60(4):1527-1537.
[23]
WANG N,ZHU T,ZHOU H,et al. Fractional Laplacians viscoacoustic wavefield modeling with k-space-based time-stepping error compensating scheme[J]. Geophysics,2020,85(1):T1-T13.
[24]
陈汉明,汪燚林,周辉. 一阶速度—压力常分数阶黏滞声波方程及其数值模拟[J]. 石油地球物理勘探,2020,55(2):302-310.CHEN Hanming,WANG Yilin,ZHOU Hui. A novel constant fractional-order Laplacians viscoacoustic wave equation and its numerical simulation method[J]. Oil Geophysical Prospecting,2020,55(2):302-310.
[25]
赵强,朱成宏,姜大建,等. 变分数阶粘弹波动方程最小二乘快速解法[J]. 石油物探,2023,62(2):258-270.ZHAO Qiang,ZHU Chenghong,JIANG Dajian,et al. Fast algorithm of variable fractional-order viscoelastic wave equation by least square approximation[J]. Geophysical Prospecting for Petroleum,2023,62(2):258-270.
[26]
ZHU T,HARRIS J M. Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians[J]. Geophysics,2014,79(3):T105-T116.
[27]
CHEN H,ZHOU H, LI Q, et al. Two efficient modeling schemes for fractional Laplacian viscoacoustic wave equation[J]. Geophysics,2016,81(5):T233-T249.
[28]
陈汉明,周辉,田玉昆. 分数阶拉普拉斯算子黏滞声波方程的最小二乘逆时偏移[J]. 石油地球物理勘探,2020,55(3):616-626.CHEN Hanming,ZHOU Hui,TIAN Yukun. Least-squares reverse-time migration based on a fractional Laplacian viscoacoustic wave equation[J]. Oil Geophysical Prospecting,2020,55(3):616-626.
[29]
PLESSIX R E. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications[J]. Geophysical Journal International,2006,167(2):495-503.