地球物理学报  2016, Vol. 59 Issue (6): 2232-2244 PDF

Pseudo acoustic equation for TI medium attenuation based on the GSLS model
XU Wen-Cai, YANG Guo-Quan, LI Zhen-Chun, SUN Xiao-Dong, WANG Jiao
School of Geosciences, China University of Petroleum (East China), Shandong Qingdao, 266580, China
Abstract: It is well known that the underground medium is far from being an acoustic material. Neglecting anisotropy and attenuation in seismic wave propagation can result in inaccuracy imagery, such as problems of diffracted wave convergence and seismic wave attenuation. So it is urgent to take anisotropy and viscosity into account, and necessary to consider both of the characteristics in practical production. In this paper, starting from the basic theory of elastic waves in TI media, and introducing the GSLS theory of isotropic medium into anisotropic material, we derive a pseudo acoustic equation for anisotropic attenuation based on the GSLS model by the acoustic approximation method. The numerical results show that the VTI viscoacoustic wave equation can not only describe the propagation of wave in anisotropic media accurately, but also reflect the effects of absorption and attenuation. Reverse time migration of the HESS model on the VTI medium shows that the attenuation pseudo acoustic equations can image more clearly, such as the complex structure with high steep dip angles, make deep amplitude distribution more balanced, and obtain more accurate and reliable amplitude imaging profiles..
Key words: Anisotropic medium      Acoustics approximation      Velocity stress equation      Quasi acoustic wave equation
1 引言

2 基于GSLS模型各向异性衰减拟声波方程 2.1 各向异性介质标准线性固体模型基本理论

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2.2 基于GSLS模型TI介质衰减拟声波方程推导

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2.3 从VTI到TTI

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3 模型试算

3.1 二维均匀各向异性介质模型正演模拟

 图 1 Q为10(a)、20(b)、无穷大(c)，t=4.8 s时的VTI介质波场快照 Fig. 1 Snapshots at 4.8 s of three different Q values ((a) 10, (b) 20, (c) infinity) of VTI media
 图 2 (1 km, 1 km)点处的波形图(a)、振幅谱(b) Fig. 2 Waveform (a) and amplitude spectrum (b) at point (1 km, 1 km)
 图 3 θ为45°,Q为10(a)、20(b)、无穷大(c)，t=4.8 s时的VTI介质波场快照 Fig. 3 Snapshots at 4.8 s of three different Q values ((a) 10, (b) 20, (c) infinity) of TTI media，θ=45°

3.2 低速体模型正演模拟

 图 4 P波速度场(a)、Q模型(b)、ε模型(c)以及δ模型(d) Fig. 4 P wave velocity (a), Q model (b), ε model (c) and δ model (d)

 图 5 炮记录 (a) 完全弹性模型; (b) Q衰减模型. Fig. 5 Shot records (a) Elastic model； (b) Q attenuation model.
 图 6 炮集第340道的波形图 Fig. 6 Waveforms of 340th channel of shot records
 图 7 炮集第340道S谱 (a) 完全弹性介质； (b) Q衰减模型. Fig. 7 S wave spectrum of 340th channel in shot records (a) Completely elastic medium； (b) Q attenuation model.

4 逆时偏移中的运用 4.1 VTI_HESS模型逆时偏移

 图 8 HESS_VTI模型：P波速度模型(a)、Q模型(b)、ε模型(c)以及δ模型(d) Fig. 8 P wave velocity (a), Q model (b), ε model (c) and δ model (d) of HESS_VTI model

 图 9 HESS_VTI模型逆时偏移结果：常规声波方程(a)，各向同性黏声波方程(b)，各向异性拟声波方程(c)以及各向异性衰减拟声波方程(d) Fig. 9 Reverse time migration results of HESS_VTI model： (a) Conventional acoustic wave equation, (b) Isotropic viscoacoustic wave equation, (c) Anisotropic pseudo-acoustic wave equation, (d) Anisotropic viscoacoustic wave equation
4.2 逆冲模型逆时偏移

 图 10 逆冲模型：P波速度模型(a)、Q模型(b)、ε模型(c)、δ模型(d)θ模型(e) Fig. 10 P wave velocity (a), Q model (b), ε model (c), δ model (d) and θ model (e) of thrust model

 图 11 逆冲模型逆时偏移结果：各向同性黏声波方程(a)，各向异性拟声波方程(b)以及各向异性衰减拟声波方程(c) Fig. 11 Reverse time migration results of thrust model：(a) Isotropic viscoacoustic wave equation， (b) Anisotropic pseudo-acoustic wave equation，(c) Anisotropic viscoacoustic wave equation
5 结论与认识

TTI介质一阶方程可以由VTI介质一阶方程变换得到.设TI介质的对称轴和XOZ平面内的观测系统Z轴的夹角为θ，相应的旋转矩阵在三维体(x，y，z)内是：

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