TTI介质伪解析解耦波动方程

Pseudo-analytical decoupled wave equation for TTI media

地球介质中最常见的一种各向异性介质就是倾斜横向各向同性(tilted transversely isotropic,简称TTI)介质,目前TTI介质的正演和逆时偏移是地震勘探工业界研究的前沿热点,TTI介质中的高精度地震波正演和逆时偏移必须要考虑TTI各向异性的影响,否则会使得模拟和成像结果不够准确.本文基于Tsvankin提出的TI介质相速度精确频散方程,针对常规TTI介质解耦波动方程时间精度的不足引入伪解析法(pseudoanalytical method,简称PAM)提出一种新的基于伪解析法的TTI介质解耦波动方程,能在时间方向和空间方向都达到高精度纯P波模拟.数值模拟结果显示,本文构造的基于伪解析法的TTI介质解耦波动方程具有高精度且没有任何伪横波误差.

The tilted transversely isotropic（ simplified by TTI）media is the most common media on the earth. Currently the TTI anisotropic forward modeling and reverse time migration（ simplified by RTM） are the research hotspots of seismic exploration industry.The TTI anisotropic effects must be considered for high-precision seismic wave forward modeling and RTM in TTI media,otherwise the modeling and imaging results will inaccurate. Starting with the exact phase velocity dispersion equation for TI media,this paper proposed a new TTI decoupled wave equation based on the pseudoanalytical method（ simplified by PAM）. This new anisotropic wave equation can overcome the accuracy deficiency of conventional decoupled anisotropic wave equation in the time direction and can reach high precision simulation of pure P-wave both in the time direction and spatial orientation. The simulation results show that the constructed TTI decoupled wave equation based on the PAM possesses high precision and free of any pseudo-SV wave.