Abstract
A family of finite difference schemes for the acoustic wave equation in heterogeneous media is introduced. The precision and computational cost are analyzed in two cases. First, a two-layered medium is considered. The order of convergence at the interface is derived for each scheme. Given an a priori accuracy on the solution, the computational cost is studied as a function of the order of accuracy of the finite difference scheme. It is demonstrated that this function has a minimum. The previous results are extended to the case of random media by a numerical study. Similar conclusions about precision and cost are found.
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