The exploitation of ever increasing Interferometric Synthetic Aperture Radar (InSAR) data sets to monitor the Earth's surface deformation is an important goal of today's geodesy. In this study our observations consist of deformations along the Line-Of-Sight direction of the satellite. Our observations are the result of the combination of a multitude of sources (either volcano-tectonic or nontectonic deformation). In most cases, we are facing a Blind source separation (BSS) problem. Natural approaches to tackle BSS problems are multivariate statistical techniques that attempt to decompose the data set into a limited number of statistically independent sources, under the assumption that the different physical mechanisms contributing to the observations have independent footprints in space and/or time. We show the capabilities of a variational Bayesian independent component analysis (vbICA) algorithm in dealing with synthetic InSAR time series and compare it to the commonly used FastICA algorithm. We explore the effectiveness of the spatial and temporal mode decompositions. We apply vbICA on data relative to the San Joaquin Valley and the Central San Andreas fault (CSAF), California, spanning the time range 2015/03/01–2019/07/14. The proposed approach likely isolates the contribution of shallow and deep aquifers to the surface deformation as well as the elastic and inelastic deformation. We present a 1-dimensional compaction estimation of the elastic and inelastic storage coefficients adopting a formalism that takes into account the last century water level history. Concerning the CSAF, the algorithm helps separating tectonic loading from seasonal behavior concentrated in the Quaternary sediments of the Salinas Valley.