A Family of Numerical Schemes for the Computation of Elastic Waves

A family of numerical schemes, based on finite difference operators is introduced for the computation of elastic waves. We use a displacement-stress formulation of the model. After deriving some stability results, we give an analysis of the computational cost. Imposing an accuracy criterion on the phase velocity, we derive the numerical parameters. We also show that an optimum order of approximation exists for a given precision. Key Words. Elastic Wave Equation, Numerical Schemes, Stability, Computational Cost AMS(MOS) subject classifications. 65M06, 65M12, 73D25 1 Introduction High order finite-difference schemes for the acoustic wave equation, and the elastic wave equation have gained interest for some time, because of the computational cost of the simulation of such phenomena. Problems such as the inverse problem of seismology require also many of these simulations. General discussions on the application of finite-differences in seismology can be found in Alford et al [1], Kelly ..