Parameter cross-talk and leakage between spatially-separated unknowns in viscoelastic full waveform inversion

Scott Keating, Kristopher A. Innanen

Elastic and attenuative effects play a major role in the determination of wave amplitudes and phases observed at seismic sensors. Viscoelastic full waveform inversion (FWI) has the potential to recover much of the information content of measured seismic data by simultaneously accounting for these effects. However, viscoelastic FWI introduces a set of new challenges and open research questions, related to its use of frequency-variations and phase information. These impact our understanding of anelastic parameter resolution, especially the phenomenon of cross-talk. Cross-talk is typically characterized through analysis of the radiation patterns of point scatterers; however, the point scatterer model is not well suited to viscoelastic FWI, because: (1) attenuation introduces a significant potential for cross-talk between variables distant from one another in space, and (2) interpreting the effect of frequency and phase dependence on the radiation patterns of point scatterers is not straightforward. We present and examine a numerical approach to assessing viscoelastic cross-talk based on differences between various model residual quantities. With it, we ob-serve strong cross-talk both between velocity and Q variables, and into density for a variety of acquisition geometries. Of particular note is our characterization of the tendency for Q variables to leak into elastic variables from which they are spatially separated. This type of cross-talk is not easily characterized through the use of radiation patterns.