An iterative finite-difference solution for quasi-P and quasi-SV wave equations in TTI media
Huang Yijian1, Liu Yongdong2, Zhang Wenbo3
1. State Key Laboratory of Continental Dynamics/Institute of Oil and Gas,Northwest University,Xi'an,Shaanxi 710069,China;
2. Guangdong Institute of Engineering Survey,Guangzhou,Guangdong 510510,China;
3. BGP Inc.,CNPC,Zhuozhou,Hebei 072751,China
Abstract：In this work,we transform the available temporal and spatial derivatives coupled quasi-P and quasi-SV wave equations for transversely isotropic media with a tilted symmetric axis(TTI) media from time-space domain to time-frequency domain.We present two approaches to calculate their solutions by finite-difference(FD) approximation and provide the stability conditions.While one approach computes the wave fields of each time step by solving a large sparse linear system based on FD approximation of the wave equations,the other approach computes the wave fields through an iterative algorithm built by FD approximation after assigning initial zero wavefield values,on the basis of the former approach,and thus no need to solve the large linear system.The iterative computation for each grid node uses only a small number of node values.Comparisons with the model test results of pseudo-spectral approach demonstrate the presented iterative FD approach is correct and is more efficient but less accurate.Analysis to the variation curves between updating value and iteration times shows the convergence of the iterative algorithm.
