Bayesian modeling for uncertainty quantification in seismic compressive sensing

Abstract

Compressive sensing is used to improve the efficiency of seismic data acquisition and survey design. Nevertheless, most methods are ad hoc, and their only aim is to fill in the gaps in the data. Algorithms might be able to predict missing receivers’ values, however, it is also desirable to be able to associate each prediction with a degree of uncertainty. We used beta process factor analysis (BPFA) and its variance. With this, we achieved high correlation between uncertainty and respective reconstruction error. Comparisons with other algorithms in the literature and results on synthetic and field data illustrate the advantages of using BPFA for uncertainty quantification. This could be useful when modeling the degree of uncertainty for different source/receiver configurations to guide future seismic survey design.