A hybrid method to estimate uncertainty in 2D FWI: application to an inclusion model

Full-waveform inversion (FWI) is a valuable tool to derive high-resolution models of the subsurface having available a reliable macro-models containing the correct large-wavelengths of the model. FWI is generally cast in the framework of deterministic approaches, and hence it returns a single best-fitting model in which no information is given regarding the associated uncertainties of the model parameters. However, in practice, many inverse problems are ill-posed meaning that many solutions explain observations and theory equally well. Hence, estimating the uncertainties that affects the final result of an inverse problem provides valuable insights on the equivalence region of the solutions (Fernández et al., 2012). Sajeva et al. (2016) proposed a workflow to determine uncertainties in two-dimensional FWI. This workflow can be divided in two parts. In the first part, a genetic algorithm combined with a Gibbs Sampler (GS) (Sambridge, 1999; Aleardi, 2014) derives a low-resolution P-wave velocity (Vp) model and its uncertainties. In the second part, the PPD derived by the GS is used to perform a set of full-waveform inversions using iterative descent-based techniques, which in turn are used to perform a statistical analysis of the final high-resolution solution. In this work, we apply this method to a simple example model modified from Mora (1989), that consists in a background gradient model with a reflection and a spherical inclusion.