Well-log parameterized full waveform inversion 2: formulation of the two parameter case
Ninoska Amundaray, Scott Keating, Matthew Eaid, Kristopher A. Innanen
Addition of prior information in elastic full waveform inversion (EFWI) tends to aid faster and better model convergence by prioritizing relevant features of the medium where the simulated waveform is propagating. When this is employed as a parameterization, FWI formulations can be slightly simplified by reducing the number of terms used during the inversion. This idea was previously applied to an isotropic-elastic medium, which utilized the correlation between well-log data to aid the construction of a single parameter by fitting a trendline. While, models obtained using a version of the single log-guided parameterization have demonstrated encouraging results when little data variation exists. In this study, we advocate the inclusion of another parameter to this type of formulation, as way to (1) capture larger data variation and (2) expand the applicability of the formulation. To accomplish this, we propose a method that captures information from a direction omitted by the first parameter (or trendline), by combining spatial geometry with principal component analysis (PCA). Current results obtained using the updated log-guided parameterization demonstrate some positive remarks in terms of model convergence and measured parameter variation. But, to further exploit the addition of the second term in FWI applications, more understanding about parameter tuning must be carry out.