Combining Genetic Algorithms, Gibbs Sampler, and Gradient-based Inversion to Estimate Uncertainty in 2D FWI

Generally, the local full-waveform inversion (LFWI) is solved in a deterministic framework, in which a single solution is produced, without quantifying its uncertainties. We propose a multi-step strategy for uncertainty estimation in FWI and we demonstrate its applicability to the acoustic 2D Marmousi model. To cast the LFWI in a probabilistic framework, we use a genetic algorithm driven optimization, combined with a Markov chain Monte Carlo method (Gibbs sampler). The so derived posterior probability distribution (PPD) defines a possible set of starting models for subsequent LFWI which, in turn, transforms the initial set of starting models in a new set of final models exhibiting narrower PPDs and containing the true model.