Optimal symplectic scheme and generalized discrete convolutional differentiator for seismic wave modeling

In this paper, seismic wave equation is transformed into Hamiltonian system, and a new symplectic numerical scheme is developed, which is so called optimal symplectic algorithm and generalized discrete convolutional differentiator (OSGCD). For temporal discretization, OSGCD introduces Lie operators to construct second-order and two stage symplectic scheme and adopts optimal symplectic scheme based on minimum error principle. For the spatial derivative, OSGCD employs generalized discrete convolution differentiator to approximate the spatial differential operators and uses derivative approximation to obtain stable operator coefficients. We obtain the stability condition for 2D case. In numerical experiments, OSGCD is compared with different methods and it has advantages in both accuracy and efficiency. OSGCD also has the ability for modeling long-term seismic wave propagation and modeling seismic wave in heterogeneous media.