Inversion of Surface Deformation Data for Rapid Estimates of Source Parameters and Uncertainties: A Bayesian Approach

New satellite missions (e.g., the European Space Agency's Sentinel-1 constellation), advances in data downlinking, and rapid product generation now provide us with the ability to access space-geodetic data within hours of their acquisition. To truly take advantage of this opportunity, we need to be able to interpret geodetic data in a prompt and robust manner. Here we present a Bayesian approach for the inversion of multiple geodetic data sets that allows a rapid characterization of posterior probability density functions (PDFs) of source model parameters. The inversion algorithm efficiently samples posterior PDFs through a Markov chain Monte Carlo method, incorporating the Metropolis-Hastings algorithm, with automatic step size selection. We apply our approach to synthetic geodetic data simulating deformation of magmatic origin and demonstrate its ability to retrieve known source parameters. We also apply the inversion algorithm to interferometric synthetic aperture radar data measuring co-seismic displacements for a thrust-faulting earthquake (2015 M-w 6.4 Pishan earthquake, China) and retrieve optimal source parameters and associated uncertainties. Given its robustness and rapidity in estimating deformation source parameters and uncertainties, our Bayesian framework is capable of taking advantage of real-time geodetic measurements. Thus, our approach can be applied to geodetic data to study magmatic, tectonic, and other geophysical processes, especially in rapid-response operational settings (e.g., volcano observatories). Our algorithm is fully implemented in a MATLAB (R)-based software package (Geodetic Bayesian Inversion Software) that we make freely available to the scientific community.