Efficient Explicit Finite Difference Method for Acoustic Wave Using Locally Adjustable Time-Steps

In this paper we propose a new algorithm for the local temporal discretization for explicit finite difference method applied to acoustic wave equation, named Region Triangular Transition (RTT). In heterogeneous media with strong discontinuities in physical properties, as it happens in seismic modeling, conventional finite-difference modelling is based on a time-stepping scheme with a constant (global) time step, determined by the medium with higher wave velocity propagation. This causes oversampling in time for some regions of the model. Therefore, the use of different temporal discretization can greatly reduce the computational cost involved when solving this kind of problem. In the proposed algorithm, the local time discretization can be related by any integer value and it is robust allowing us to employ time-stepping up to the stability limit of the finite difference approximations used. It is shown how dispersion error varies with the medium wave velocity propagation and numerical results validate the proposed algorithm showing how time adaptivity can contribute to the minimization of the error due to time discretization in heterogeneous media.