Viscoelastic full-waveform inversion: treating attenuation uncertainty, characterizing cross-talk, and quantifying confidence in inversion results

Scott Keating

Full waveform inversion (FWI) is a powerful technique for estimating the subsurface properties which affect seismic wave propagation but it is often limited by simplistic treatment of wave propagation physics. In particular, attenuation and dispersion, which play major roles in most seismic experiments, are commonly neglected. This omission often occurs because of the many complicating factors a treatment of attenuation introduces. Particularly notable challenges include a strong degree of cross-talk, in which attenuation and elastic property estimates are incorrectly influenced by one another, and the need to decide which of several plausible models of seismic attenuation to include in the inversion. In this thesis, I propose approaches to mitigate these challenges and make the inclusion of attenuation in FWI more practical.

While it is necessary to assume a specific relation between attenuation, dispersion, and frequency in FWI, many such relations exist, and these can differ significantly in some of their specific predictions. In general, subsurface attenuation can differ substantially from the attenuationfrequency relation assumed. In this thesis, I propose a flexible inversion approach which mitigates the errors caused by this type of discrepancy by relaxing the assumption that the assumed relation holds over all frequencies, and instead requiring consistency only over smaller bands of frequencies. This approach can be effective in mitigating the impact of errors in the assumed attenuation physics.

Understanding the behaviour of cross-talk as a function of acquisition geometry is often considered essential when using FWI to estimate more than one physical property. Cross-talk with attenuation variables has not previously been deeply investigated in this way, because the conventional approaches used for assessing cross-talk are poorly suited for the modes of cross-talk that are important when considering attenuation. I propose an alternative approach for assessing cross-talk in this thesis. This approach is better able to treat attenuation and also allows for consideration of both the optimization strategy used and cross-talk between spatially separated variables, important features of cross-talk not treated in conventional approaches. I use this approach to identify important cross-talk behaviours in viscoelastic FWI.

Finally, I propose an approach for targeted uncertainty quantification in FWI. This approach does not account for all potential uncertainties in the FWI problem, but does quantify a major part of the uncertainty associated with cross-talk. I present numerical examples to illustrate how this approach can be used to assess confidence in viscoelastic FWI results.