Some Computational Aspects of the Time and Frequency Domain Formulations of Seismic Waveform Inversion

Seismic waveform inversion relies on efficient solutions of the elasto-dynamic wave equations. The associated inverse problem can be formulated either in the time domain or in the frequency domain. The choice between these two approaches mainly depends on their numerical efficiency. Here, I discuss some of the computational aspects of the frequency-domain solution of the visco-acoustic vertical transverse isotropic wave equations based on a Krylov subspace iterative solver and a complex shifted Laplace preconditioner. In the context of least-square migration or non-linear impedance inversion, the frequency domain approaches are currently not attractive because a complete frequency band response is required. However, in the context of waveform tomography when a small number of frequency responses are inverted, the frequency-domain approaches become relevant, especially when viscous effects are modeled, depending on the geological context.

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