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A compact three‐dimensional fourth‐order scheme for elasticity using the first‐order formulation

We develop a compact fourth‐order scheme for the three‐dimensional elastic wave equation in frequency space, using the first‐order velocity‐stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one‐directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second‐order scheme.