Professor LI Xiaofan and his team present an alternative method for accurately and efficiently modeling seismic wave fields, which 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.

Their 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.

Figure 1. Snapshots of seismic wave fields (a) in a two-layered medium model at time 500 ms, generated by MDSCD, (b) using the Fourier pseudospectral method, and (c) the conventional high-order FD method.(Image by LI)

Figure 2. Snapshots of seismic wave fields in a 2D homogeneous medium model generated by MDSCD after (a) 400 time steps, (b) 2000 time steps, and (c) 5000 time steps. Snapshots of seismic wave fields in the same medium model generated by the Fourier pseudospectral method after (d) 400 time steps, (e) 2000 time steps, and (f) 5000 time steps.(Image by LI)

Li et al. Scalar Seismic-Wave Equation Modeling by a Multisymplectic Discrete Singular Convolution Differentiator Method. Bulletin of the Seismological Society of America. 2011, 101(4), 1710–1718.（Download Here）