Bayesian Estimation of Fault Slip Distribution for Slow Slip Events Based on an Efficient Hybrid Optimal Directional Gibbs Sampler and Its Application to the Guerrero 2006 Event

An efficient Bayesian approach is proposed to infer fault slip from geodetic data in a Slow Slip Event (SSE). The physical model of the slip process reduces to a multiple linear regression with constraints. Assuming a Gaussian model for the geodetic data and considering a multivariate truncated normal prior distribution for the unknown fault slip, the resulting posterior distribution is also a multivariate truncated normal. A prior slip distribution having a detailed correlation structure to impose natural coherence in the fault slip is proposed. Regarding the posterior, an ad hoc algorithm based on a Hybrid Optimal Directional Gibbs sampler is proposed that allows to sample efficiently from the resulting high-dimensional posterior slip distribution without supercomputing resources. A synthetic fault slip example illustrates the flexibility and accuracy of the proposed approach. This methodology is also applied to a real data set for the 2006 Guerrero, Mexico, SSE, where the objective is to recover the fault slip on a known interface that produces displacements observed at ground geodetic stations. As a by-product, our approach further allows us to estimate the Moment Magnitude for the 2006 Guerrero SSE with uncertainty quantification.