High-precision modeling of seismic-wave propagation in heterogeneous media is very important to seismological investigation. However, such modeling is one of the difficult problems in the seismological research fields. For developing methods of seismic inversion and high-resolution seismic-wave imaging, the modeling problem must be solved as perfectly as possible. Moreover, for long-term computations of seismic waves (e.g., Earth’s free-oscillations modeling and seismic noise-propagation modeling), the capability of seismic modeling methods for long-time simulations is in great demand. In this paper, an alternative method for accurately and efficiently modeling seismic wave fields is presented; it is based on a multisymplectic discrete singular convolution differentiator scheme (MDSCD). This approach uses optimization and truncation to form a localized operator, which preserves the fine structure of the wave field in complex media and avoids noncausal interaction when parameter discontinuities are present in the medium. The approach presented has a structure-preserving property, which is suitable for treating questions of high-precision or long-time numerical simulations. Our numerical results indicate that this method can suppress numerical dispersion and allow for research into long-time numerical simulations of wave fields. These numerical results also show that the MDSCD method can effectively capture the inner interface without any special treatment at the discontinuity.

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