Symplectic partitioned Runge-Kutta method for solving the acoustic wave equation

In this paper, we develop a new symplectic numerical scheme based on Hamiltonian system of the acoustic wave equation, which is called the NSPRK method in brief. The NSPRK method uses the nearly-analytic discrete operators to approximate the high-order differential operators, and employs the second-order symplectic partitioned Runge-Kutta method to numerically solve the Hamiltonian system. For the proposed NSPRK method in this paper, we obtain the stability conditions for 1D and 2D cases, the numerical dispersion relation for the 1D case and 2D numerical errors. Meanwhile, we compare the NSPRK against the conventional syrnplectic method and the fourth-order LWC method in computational efficiency. Finally, we apply the NSPRK method to model acoustic wave propagating in a three-layer isotropic medium and an abnormal body model. The promising numerical results illustrate that the NSPRK method can effectively suppress the numerical dispersion caused by discretizing the acoustic-wave equation when coarse grids are used or models have large velocity contrasts between adjacent layers. Therefore, the NSPRK method can greatly increase the computational efficiency and save computer memory.