Some effects of the memory kernel singularity on wave propagation and inversion in viscoelastic media - II. Inversion

Viscoelastic inversion is developed for a realistic, simple, causal hereditary model with a power-law attenuation. In this class of models the energy travels with a delay behind the wave front because the effective speed of the seismic signal is lower than the infinite-frequency limit of the propagation speed which determines the wave front propagation. In inversion this discrepancy affects the correct positioning of scatterers and interfaces. Our inversion method is an extension of Ribodetti's imaging method. Using a power-law model, propagation- and attenuation-related parameters are uncoupled for the acquisition geometries used in laboratory and in field seismic experiments. The method is applied to ultrasonic laboratory data where we have complete control of the acquisition parameters and the physical properties of the medium to be recovered are well known. An application to ultrasonic data for a wavefield scattered from a hollow PVC sample and a lava sample immersed in a water tank demonstrates that the proposed inversion method allows reliable parameter estimation in the power-law class of viscoacoustic models.