Compressive-wavefield simulations

Felix J. Herrmann, (1) , Yogi Erlangga (1) , Tim. T. Y. Lin (1)

1 EOS - Department of Earth and Ocean Sciences [Vancouver]

Full-waveform inversion's high demand on computational resources forms, along with the non-uniqueness problem, the major impediment withstanding its widespread use on industrial-size datasets. Turning modeling and inversion into a compressive sensing problem—where simulated data are recovered from a relatively small number of independent simultaneous sources—can effectively mitigate this high-cost impediment. The key is in showing that we can design a sub-sampling operator that commutes with the time-harmonic Helmholtz system. As in compressive sensing, this leads to a reduction in simulation cost. Moreover, this reduction is commensurate with the transform-domain sparsity of the solution, implying that computational costs are no longer determined by the size of the discretization but by transform-domain sparsity of the solution of the CS problem which forms our data. The combination of this sub-sampling strategy with our recent work on implicit solvers for the Helmholtz equation provides a viable alternative to full-waveform inversion schemes based on explicit finite-difference methods.

Domaines: Traitement du signal et de l'image [eess.SP]; Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]

Felix J. Herrmann,, Yogi Erlangga, Tim. T. Y. Lin. Compressive-wavefield simulations. SAMPTA'09, May 2009, Marseille, France. Special session on geometric multiscale analysis. ⟨hal-00451799⟩