Time Adaptivity Stable Finite Difference for Acoustic Wave Equation

Acoustic wave modeling is widely used to synthesize seismograms theoretically, being the basis of the reverse time migration strategy. Explicit Finite Difference Method (FDM) is often employed to find numerical solution of this problem and in this case, spatial discretization is related to the shortest wavelength to be captured and temporal discretization is determined by stability condition. In this case small grid size has to be used to assure a stable and accurate solution and algorithms with locally adjustable time steps can be of advantageous use when treating heterogeneous domains. In this paper, we are concerned with a temporal adaptivity algorithm: Region Triangular Transition algorithm (RTT), discussing its accuracy and its computational efficiency when applied to complex heterogeneous domains. To evaluate computational efficiency of this algorithm we present, in this work, how computational cost varies with the subregions sizes ratio of the heterogeneous medium when compared with computational cost of the conventional algorithm using only one time step, showing how this adaptivity algorithm can be used in complex domains to reduce the amount of values to be calculated. Some discussion are made concerning how dispersion error can be reduced when adaptive schemes are used.