Fast Iterative Solution of the Time-Harmonic Elastic Wave Equation at Multiple Frequencies

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Seismic Full-Waveform Inversion is an imaging technique to better understand the earth's subsurface. Therefore, the reflection intensity of sound waves is measured in a field experiment and is matched with the results from a computer simulation in a least-squares sense. From a computational point-of-view, but also from an economic view point, the efficient numerical solution of the elastic wave equation on current hardware is the main bottleneck of the computations, especially when a large three-dimensional computational domain is considered. In our research, we focused on an alternative problem formulation in frequency-domain. The mathematical challenge then becomes to efficiently solve the time-harmonic elastic wave equation at multiple frequencies. The resulting sequence of shifted linear systems is solved with a new framework of Krylov subspace methods derived for this specific problem formulation. Our numerical analysis gives insight in the theoretical convergence behavior of the new algorithm.