In order to simulate the interaction of seismic waves with cavernous/fractured reservoirs, a finite-difference technique based on locally refined time-and-space grids is used. The need to use these grids is due primarily to the differing scale of heterogeneities in the reference medium and the reservoir. Domain Decomposition methods allow for the separation of the target area into subdomains containing the reference medium (coarse grid) and reservoir (fine grid). Computations for each subdomain can be carried out in parallel. The data exchange between each subdomain within a group is done using MPI through nonblocking iSend/iReceive commands. The data exchange between the two groups is done simultaneously by coupling the coarse and fine grids. The results of a numerical simulation of a carbonate reservoir are presented and discussed.