In seismology, variations in the subsurface of the earth are often present on many scales: from scales much larger than the typical seismic wavelength down to scales that are much smaller (Figure 1). A new variable grid-spacing and time-step finite-difference method is developed for efficient seismic modeling in multi-scale heterogeneous media. This method accommodates multi-scale features by allowing fine grid-spacing and time-steps for zones with small-scale features, and coarse grid-spacing and time-steps for zones with large-scale structures. Furthermore, a parallel version of the algorithm has been developed for efficient computation of large problems.

One application of the developed technique is to model cross-well field data with inclusion of tube waves and tube-wave-related arrivals caused by the presence of the two perforated cased boreholes. The good agreement between the synthetic (Figure 2) and the field (Figure 3) observations shows the validity of the method.