  We propose an efficient Bayesian approach to infer a fault displacement from
geodetic data in a slow slip event. Our physical model of the slip process
reduces to a multiple linear regression subject to 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 multivariate truncated normal. Regarding the posterior, we
propose an algorithm based on Optimal Directional Gibbs that allows us to
efficiently sample from the resulting high-dimensional posterior distribution
of along dip and along strike movements of our fault grid division. A synthetic
fault slip example illustrates the flexibility and accuracy of the proposed
approach. The methodology is also applied to a real data set, for the 2006
Guerrero, Mexico, Slow Slip Event, 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 of our approach, we are able to estimate
moment magnitude for the 2006 Guerrero Event with uncertainty quantification.
