How AVO information can be practically incorporated in full waveform inversion

Kristopher A. H. Innanen

The claim made in a companion paper, namely that certain formulas for multiparameter reflection full waveform inversion are easy to analyze as well as implement, is robustly challenged in this paper. We ask a question we think is, in fact, a central matter in the future of FWI as applied to pre-critical reflection seismic data (which is the most common and cost-effective kind of seismic data we collect). If FWI automatically converges to the right answer for a particular parameter, through operations on data which are mixtures of the effects of several parameters, it must do some kind of "unmixing" akin to that in AVO inversion. If it cannot, there is no solution to what FWI practitioners refer to as parameter cross-talk. How does this happen? Is it automatic to any FWI procedure-gradient based, quasi-Newton, and Newton alike? Or do we need to properly pose the problem to manage multiple parameters? In this paper we parse our quasi-Newton update formulas, seeking (1) the internal ability to diagnose illposedness, (2) the ability to produce balanced updates using different subsets of data, and (3) the ability to suppress parameter cross-talk within them. We ultimately conclude that the quasi-Newton update formula we refer to as the parameter-type approximation is properly equipped to incorporate our basic ideas of AVO inversion into FWI.