Bringing a Bayesian Perspective to Large Dimensional Problems in Geophysics

Abstract:

The last decade has seen a substantial expansion of geophysical observations. Exploiting this wealth of data involves large ill-conditioned inverse problems requiring large numbers of uncertain parameters. A common approach in geophysics is to use some form of regularization that transforms the inversion into a well-conditioned optimization problem. While this approach is convenient and computationally inexpensive, the inherent non-uniqueness of our problems suggest that we should not simply search for a single optimal model, but rather attempt to describe the ensemble of plausible models that can fit the data and are consistent with prior information. This talk will present various applications of full Bayesian analysis techniques to large ill-posed inverse problems in geophysics. Despite significant computational cost, Bayesian sampling is a powerful tool to combine prior information, theoretical knowledge and data in order to address scientific problems probabilistically. We shall illustrate this by showing recent results for two types of problems: (1) the study of earthquakes sources and (2) imaging of the Earth interior. In particular, we will present different strategies that can be employed in order to achieve realistic uncertainty estimates.