In a companion paper (Ma et al., 2014), we proposed a series of nearly analytic symplectic Runge–Kutta (NSPRK) methods with fourth‐order spatial accuracy and with second‐, third‐, and fourth‐order temporal accuracy. In this article, the NSPRK(2,4) scheme, which is temporally second order and the most efficient of the NSPRK schemes, is applied to 3D seismic modeling. We apply the NSPRK(2,4) scheme to simulate acoustic or elastic wave propagation in common 3D medium models, including a three‐layer acoustic model and a vertical transversely isotropic model. A model with a fluid‐filled fracture is used to study elastic wave propagation. When it was necessary to truncate the computational domain, we used the classical split‐field perfectly matched layer (PML) approach to eliminate reflected waves. Compared with conventional methods, the NSPRK method requires only a little additional computation and memory storage on PML domains to obtain a large absorption effect. Numerical results show no visible numerical dispersion, although all simulations were done on relatively coarse grids. These promising numerical results support the use of NSPRK‐type schemes on large‐scale practical models. The NSPRK method with symplecticity‐preserving properties can provide more accurate wave amplitudes than other methods.

Online Material: MATLAB code.

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