Abstract
This work considers regularization of seismic full waveform inversion (FWI), where the sparsity of the underlying model is exploited together with spatial correlations using the so-called anisotropic total variation. The problem is formulated within the Bayesian framework, which provides a systematic way accounting for uncertainties in both prior (e.g., baseline) and observations (e.g., monitoring stage, in the case of time-lapse settings). To account for sparsity in the model, Laplace priors represented in a hierarchical way are considered, which allows to derive efficient inversion algorithms following Variational Bayesian approach. The quality of the regularization is examined through numerical experiments involving acoustic FWI, and compared to a Gaussian prior based method, which suggested enhanced reconstruction accuracy. The quality of the Variational Bayesian approximation was further studied by comparing with the (exact) posterior that was sampled using the Hamiltonian Monte Carlo algorithm. Our findings suggest that the proposed Variational Bayesian inversion method accounting for sparsity in the model can provide a better trade-off between estimation quality and associated computational complexity and can be more suitable for large-scale seismic problems.
