Visco-acoustic Full Waveform Inversion

Acoustic full waveform inversion is nowadays an established technology to determine velocity background images from low-frequency and long-offset data sets with a focus on the diving waves. The depth of investigation can vary from a few hundred meters to a few kilometres. While anisotropy is often accounted for, dispersion and absorption effects are more often ignored. We propose a visco-acoustic time-domain full waveform inversion formulated. To reduce the numerical cost, we employ only one memory variable per stress field but distribute the different relaxation mechanisms over adjacent cells in the finite difference scheme. Through an effective medium approach, we here take advantage of the diffusive nature of the absorption and dispersion phenomena which can be discretised over a coarser grid than the propagation phenomenon, although this introduces some scattering effects as shown with a small numerical example. The visco-acoustic inversion is parameterized with the NMO velocity, eta-parameter, one inverse quality factor and density. We illustrate the trade-off between velocity and quality factor through sequential and simultaneous inversions of a synthetic example. We then apply the visco-acoustic full waveform inversion on a narrow azimuth data set to show the potential benefit of accounting for dispersion and absorption effects.