辛几何算法在射线追踪中的应用  

RAY TRACING BY SYMPLECTIC ALGORITHM

作　　者：陈景波[1] 秦孟兆[1] 

机构地区：[1]中国科学院数学与系统科学研究院计算数学与科学工程计算研究所

出　　处：《数值计算与计算机应用》2000年第4期255-265,共11页Journal on Numerical Methods and Computer Applications

基　　金：国家重点基础研究项目! G1999;032800;国家九五自然科学基金! 49894190.

摘　　要：Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tracing must rely on the ray equations in Hamiltonian form. In this paper, fourth order symplectic scheme and nonsymplectic Runge-Kutta scheme are compared in ray tracing for sinusoidal velocity model. The result indicates that ray paths obtained by two schemes are almost the same. But on keeping Hamilton quantities, the symplectic scheme is far better than the Runge-Kutta scheme. On computing travel time for Htamiltonian system with T parameter, we use trapezoid formula for numerical integration. The result coincides with that obtained using Hamiltonian system with t parameter.Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tracing must rely on the ray equations in Hamiltonian form. In this paper, fourth order symplectic scheme and nonsymplectic Runge-Kutta scheme are compared in ray tracing for sinusoidal velocity model. The result indicates that ray paths obtained by two schemes are almost the same. But on keeping Hamilton quantities, the symplectic scheme is far better than the Runge-Kutta scheme. On computing travel time for Htamiltonian system with T parameter, we use trapezoid formula for numerical integration. The result coincides with that obtained using Hamiltonian system with t parameter.

关 键 词：辛几何算法 射线跟踪 射线方程 数值解 地震波 

分 类 号：O186[理学—数学]