Error Analysis of Numerical Schemes for the Wave Equation in Heterogeneous Media

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. Key Words. Wave Equation, Heterogeneous Media, Numerical Schemes, Computational Cost AMS(MOS) subject classifications. 65M06, 65M12, 65M15 1 Introduction Finite difference schemes for the wave equation have been extensively studied in homogeneous media (cf [1]). The error introduced by the numerical procedure is called dispersion (cf [2]). This phenomenon causes differ..