The problem with existing finite-difference formulations of the elastic wave equation is that they have a limited stability range, and the necessity of taking small time steps can result in excessively high computation costs. It is possible to formulate a finite-difference scheme which is stable for arbitrarily large time steps. However, the solutions obtained by the unconditionally stable scheme are unacceptably inaccurate for time steps outside the stability range of finite-difference schemes currently in use.

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