A Bayesian Approach to Elastic Full-Waveform Inversion: Application to a Semi-Real Near Surface Model.

Established methods for the inversion of surface waves, such as the inversion of dispersion curves, are limited to 1D subsurface structures. In contrast, full-waveform inversion has the potential to reconstruct high-resolution subsurface models even for 2D subsurface models. However, full-waveform inversion in near-surface seismic applications is very challenging due to the high nonlinearity of the optimization problem and the very high computational cost. Traditional methods solve the full-waveform inversion making use of gradient-based algorithms that minimize an error function, which commonly measures the distance between observed and predicted waveforms. This deterministic approach only provides a “best-fitting” model and cannot account for the uncertainties affecting the predicted solution. On the other hand, casting this inverse problem into a probabilistic framework must deal with the formidable computational effort of the Bayesian approach. We present a gradient-based Markov Chain Monte Carlo full-waveform inversion in which the posterior sampling is accelerated by compressing the data and model spaces through the discrete cosine transform, and by also defining a proposal that is a local, Gaussian approximation of the target posterior probability density. We demonstrate the applicability of this approach by performing a multiparameter inversion test on a near surface semi-real velocity model.