Abstract:As earth media are generally characterized by inelasticity and anisotropy, both anisotropy and viscosity should be considered in research on seismic wave propagation in underground spaces. At present, pseudo-acoustic wave equations are the ones mainly applied in wavefield simulation, migration imaging, and waveform inversion regarding anisotropic media. As these equations are deve-loped on the basis of a shear-wave (S-wave) velocity directly set to zero, numerical pseudo-S wave artifacts and simulation instability are prone to occur when medium parameters do not satisfy the assumed conditions. Given the problem faced with pseudo-acoustic wave equations, this paper solves the high-precision pure acoustic wave equation for 3D tilted transversely isotropic (TTI) media by combining the Poisson operator with finite diffe-rence. Moreover, considering the influence of attenuating media on the amplitude and phase of seismic waves, this paper derives a simplified pure visco-acoustic wave equation for 3D TTI media on the basis of the isotropic visco-acoustic wave equation. This equation can be used to simulate the phase distortion and amplitude attenuation of pure acoustic waves. The effectiveness and applicability of the proposed method are verified with a 3D la-yered model, a TTI wedge model, and a modified Marmousi model.
徐世刚, 包乾宗, 任志明. 简化的三维TTI介质黏滞纯声波方程及其数值模拟[J]. 石油地球物理勘探, 2022, 57(2): 331-341.
XU Shigang, BAO Qianzong, REN Zhiming. A simplified pure visco-acoustic wave equation for 3D TTI media and its numerical simulation. Oil Geophysical Prospecting, 2022, 57(2): 331-341.
ALKHALIFAH T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250.
[2]
ZHOU H B,BLOOR R,ZHANG G Q.An anisotropic acoustic wave equation for modeling and migration in 2D TTI media[C].SEG Technical Program Expanded Abstracts,2006,25:194-198.
[3]
DU X,BANCROFT J C,LINES L R.Anisotropic reverse-time migration for tilted TI media[J].Geophy-sical Prospecting,2007,55(6):853-869.
[4]
FLETCHER R P,DU X,FOWLER P J.Reverse time migration in tilted transversely isotropic (TTI) media[J].Geophysics,2009,74(6):WCA179-WCA187.
[5]
李博,李敏,刘红伟,等.TTI介质有限差分逆时偏移的稳定性探讨[J].地球物理学报,2012,55(4):1366-1375.LI Bo,LI Min,LIU Hongwei,et al.Stability of reverse time migration in TTI media[J].Chinese Journal of Geophysics,2012,55(4):1366-1375.
[6]
杨富森,李振春,王小丹.稳定的TTI介质拟声波逆时偏移及伪横波的联合压制策略[J].地球物理学进展,2016,31(1):396-402.YANG Fusen,LI Zhenchun,WANG Xiaodan.Stable TTI pseudo-acoustic wave reverse time migration and joint suppression strategy of pseudo-qSV wave[J].Progress in Geophysics,2016,31(1):396-402.
[7]
LIU F Q,MORTON S A,JIANG S S,et al.Decoupled wave equations for P and SV waves in an acoustic VTI media[C].SEG Technical Program Expanded Abstracts,2009,28:2844-2848.
[8]
CHU C L,MACY B K,ANNO P D.Approximation of pure acoustic seismic wave propagation in TTI media[J].Geophysics,2011,76(5):WB97-WB107.
[9]
杜启振,郭成锋,公绪飞.VTI介质纯P波混合法正演模拟及稳定性分析[J].地球物理学报,2015,58(4):1290-1304.DU Qizhen,GUO Chengfeng,GONG Xufei.Hybrid PS/FD numerical simulation and stability analysis of pure P-wave propagation in VTI media[J].Chinese Journal of Geophysics,2015,58(4):1290-1304.
[10]
LI X Y,ZHU H J.A finite-difference approach for solving pure quasi-P-wave equations in transversely isotropic and orthorhombic media[J].Geophysics,2018,83(4):C161-C172.
[11]
黄金强,李振春.基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移[J].地球物理学报,2017,60(2):704-721.HUANG Jinqiang,LI Zhenchun.Modeling and reverse time migration of pure quasi-P-waves in complex TI media with a low-rank decomposition[J].Chinese Journal of Geophysics,2017,60(2):704-721.
慕鑫茹,黄建平,李振春,等.基于最佳平方逼近的TTI介质解耦qP波与qSV波逆时偏移[J].石油地球物理勘探,2019,54(6):1280-1292.MU Xinru,HUANG Jianping,LI Zhenchun,et al.Reverse time migration of decoupled qP-and qSV-waves in TTI media with the optimal quadratic approximation[J].Oil Geophysical Prospecting,2019,54(6):1280-1292.
[14]
顾汉明,张奎涛,刘春成,等.基于Low-rank一步法波场延拓的黏声各向异性介质纯qP波正演模拟[J].石油地球物理勘探,2020,55(4):733-746.GU Hanming,ZHANG Kuitao,LIU Chuncheng,et al. Low-rank one-step wave extrapolation for pure qP-wave forward modeling in viscoacoustic anisotropic media[J].Oil Geophysical Prospecting,2020,55(4):733-746.
[15]
何兵寿,武雪峤,高琨鹏.TI介质中qP波方程逆时偏移技术的研究现状与展望[J].石油物探,2021,60(1):34-45,69.HE Bingshou,WU Xueqiao,GAO Kunpeng.Research status and prospect of qP wave reverse time migration in TI media[J].Geophysical Prospecting for Petro-leum,2021,60(1):34-45,69.
[16]
CARCIONE J M,KOSLOFF D,Kosloff R.Wave propagation simulation in a linear viscoacoustic medium[J].Geophysical Journal International,1988,93(2):393-401.
[17]
吾拉力·胡尔买提,曲英铭,李振春,等.双相黏弹VTI介质一阶速度-应力方程正演模拟及双程波照明研究[J].石油地球物理勘探,2021,56(3):505-518.WORRAL Qurmet,QU Yingming,LI Zhenchun,et al.First-order velocity-stress equation forward mode-ling and two-way wave illumination in two-phase viscoelastic VTI media[J].Oil Geophysical Prospecting,2021,56(3):505-518.
[18]
BAI J Y,YINGST D,BLOOR R,et al.Viscoacoustic waveform inversion of velocity structures in the time domain[J].Geophysics,2014,79(3):R103-R119.
[19]
LI G F,ZHENG H,ZHU W L,et al.Tomographic inversion of near-surface Q factor by combining surface and cross-hole seismic surveys[J].Applied Geophy-sics,2016,13(1):93-102.
[20]
WANG E J,LIU Y,JI Y X,et al.Q full-waveform inversion based on the viscoacoustic equation[J].Applied Geophysics,2019,16(1):77-91.
[21]
蔡瑞乾,孙成禹,伍敦仕,等.黏声波动方程变机制数有限差分正演[J].石油地球物理勘探,2019,54(3):529-538.CAI Ruiqian,SUN Chengyu,WU Dunshi,et al.Finite-difference numerical modeling with variable mechanisms for viscoacoustic wave equation[J].Oil Geophysical Prospecting,2019,54(3):529-538.
[22]
汪勇,徐佑德,高刚,等.二维黏滞声波方程的优化组合型紧致有限差分数值模拟[J].石油地球物理勘探,2018,53(6):1152-1164.WANG Yong,XU Youde,GAO Gang,et al.Numerical simulation of 2D visco-acoustic wave equation with an optimized combined compact difference scheme[J].Oil Geophysical Prospecting,2018,53(6):1152-1164.
[23]
XU W C,YANG G Q,LI H Z,et al.Pure viscoacoustic equation of TTI media and applied it in anisotropic RTM[C].SEG Technical Program Expanded Abstracts,2015,34:525-529.
[24]
杜启振,杨慧珠.方位各向异性黏弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2014.DU Qizhen,YANG Huizhu.Finite-element methods for viscoelastic and azimuthally anisotropic media[J].Acta Physica Sinica,2003,52(8):2010-2014.
[25]
ZHU T Y,CARCIONE J M,HARRIS J M.Approximating constant-Q seismic propagation in the time domain[J].Geophysical Prospecting,2013,61(5):931-940.
[26]
CARCIONE J M.A generalization of the Fourier pseu-dospectral method[J].Geophysics,2010,75(6):A53-A56.
[27]
ZHU T Y,HARRIS J M.Modeling acoustic wave pro-pagation in heterogeneous attenuating media using decoupled fractional Laplacians[J].Geophysics,2014,79(3):T105-T116.
[28]
SUN J Z,ZHU T Y,FOMEL S.Viscoacoustic mode-ling and imaging using low-rank approximation[J].Geophysics,2015,80(5):A103-A108.
[29]
CHEN H M,ZHOU H,LI Q Q,et al.Two efficient modeling schemes for fractional Laplacian viscoacoustic wave equation[J].Geophysics,2016,81(5):T233-T249.