We consider here a method for numerical propagation of elastic waves in heterogeneous media based on the weak formulation of the elastodynamic equilibrium equations. The method provides high accuracy in the spatial domain and converges exponentially. It is appropriate for any formulation of the elastic wave equation in any number of spatial dimensions, but for simplicity is only presented here for isotropic media. Absorbing boundary conditions are incorporated into the method naturally and various time-stepping algorithms are investigated. In the conclusion we compare various implementations of the method to second and fourth order finite differences.
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