Analysis of the covariance matrix in FWI through density of covariance maps
Abstract
Full waveform inversion (FWI) is a tool for the inversion of seismic data. There are several sources of uncertainty in the results provided by FWI. The quantification of such uncertainties has been studied through the resolution matrix (Res), which rests on a quadratic approximation that interprets the Hessian matrix as the posterior covariance matrix. Despite efforts in the use of Res, there is no published analysis of the uncertainties contained in the full correlation matrix, (R). Our approach leads to build the full R matrix, which, at the end of the day, is the final quantity that includes all the information associated with uncertainties.
We focused on uncertainties related to variation in the starting models of the FWI, and thus propose a method to study the full R matrix, which is-called the Density of Correlation Map, D. By using the D map, we found that the highest uncertainty zones in the FWI inverted model are near the sources, the model boundaries, and the interfaces. We argue that D can be a complement for the study and estimation of uncertainties in FWI.
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