The relationship between ray tracing、symplectic algorithm and wave field simulation is presented. The long time conservation property of symplectic algorithm and the necessity of ray tracing using symplectic algorithm are demonstrated. In addition, wave field simulation using Maslov asymptotic theory and symplectic algorithm for linear layer model is performed. The comparison of the numerical solution with the analytic solution is carried out.

In this paper We Consider three way which change transient quadrate conservation sche-meinto exact quadrate conservation scbeme.