Detection and Characterization of Ground Displacement Sources from Variational Bayesian Independent Component Analysis of GPS Time Series

A critical point in the analysis of ground displacements time series is the development of data driven methods that allow to discern and characterize the different sources that generate the observed displacements. A widely used multivariate statistical technique is the Principal Component Analysis (PCA), which allows to reduce the dimensionality of the data space maintaining most of the variance of the dataset explained. It reproduces the original data using a limited number of Principal Components, but it also shows some deficiencies. Indeed, PCA does not perform well in finding the solution to the so-called Blind Source Separation (BSS) problem, i.e. in recovering and separating the original sources that generated the observed data. This is mainly due to the assumptions on which PCA relies: it looks for a new Euclidean space where the projected data are uncorrelated. Usually, the uncorrelation condition is not strong enough and it has been proven that the BSS problem can be tackled imposing on the components to be independent. The Independent Component Analysis (ICA) is, in fact, another popular technique adopted to approach this problem, and it can be used in all those fields where PCA is also applied. An ICA approach enables us to explain the time series imposing a fewer number of constraints on the model, and to reveal anomalies in the data such as transient signals. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, we use a variational bayesian ICA (vbICA) method, which models the probability density function (pdf) of each source signal using a mix of Gaussian distributions. This technique allows for more flexibility in the description of the pdf of the sources, giving a more reliable estimate of them. Here we present the application of the vbICA technique to GPS position time series. First, we use vbICA on synthetic data that simulate a seismic cycle (interseismic + coseismic + postseismic + seasonal + noise), and study the ability of the algorithm to recover the original (known) sources of deformation. Secondly, we apply vbICA to different tectonically active scenarios, such as earthquakes in central and northern Italy, as well as the study of slow slip events in Cascadia.