Abstract
AbstractIn this paper, seismic wave equation is transformed into the Hamiltonian system, and a new symplectic numerical scheme is developed, which is called the optimal symplectic algorithm and generalized discrete convolutional differentiator (OSGCD). For temporal discretization, OSGCD introduces Lie operators to construct two‐stage and second‐order symplectic scheme and adopts the optimal symplectic scheme based on the minimum error principle. For the spatial discretization, OSGCD employs the 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 a 2D case. In numerical experiments, OSGCD is compared with different methods, showing advantages in both accuracy and efficiency. The OSGCD also has the ability for modeling long‐term seismic wave propagation and modeling seismic waves in heterogeneous media.
Published Version
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