Blind source separation problem in GPS time series

Abstract

A critical point in the analysis of ground displacement time series, as those recorded by space geodetic techniques, is the development of data-driven methods that allow the different sources of deformation to be discerned and characterized in the space and time domains. Multivariate statistic includes several approaches that can be considered as a part of data-driven methods. A widely used technique is the principal component analysis (PCA), which allows us to reduce the dimensionality of the data space while maintaining most of the variance of the dataset explained. However, 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 generate the observed data. This is mainly due to the fact that PCA minimizes the misfit calculated using an L 2 norm (χ 2 ), looking for a new Euclidean space where the projected data are uncorrelated. The independent component analysis (ICA) is a popular technique adopted to approach the BSS problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, we test the use of a modified variational Bayesian ICA (vbICA) method to recover the multiple sources of ground deformation even in the presence Electronic supplementary material The online version of this article

Pre- and post-seismic deformation related to the 2015, Mw7.8 Gorkha earthquake, Nepal

“…In our case we tested the PCA approach and observed that most components were a mix of seasonal and postseismic signals. By contrast, different sources of deformation, which tend to be statistically independent from one another, tend to be represented by different components in an ICA (Gualandi et al, 2015). This approach is thus particularly well suited to separate the contributions due to tectonics and surface hydrology.…”

“…The vbICA technique then allows us to determine the best reference frame onto which project the data in order to optimally separate the contribution of each singular source. We refer the interested reader to the Supplementary Material (Section S1) as well as to Choudrey (2002), Choudrey and Roberts (2003), and Gualandi et al (2015) for more details. We preferred an ICA over a more standard PCA as a PCA does not do well at separating different sources of deformation (e.g.…”

“…Using a linear decomposition approach, like vbICA, we can thus perform just one spatial interpolation per component instead of one for every single epoch. The vbICA analysis applied to the pre-seismic (detrended) time series yields that three ICs are optimal to reconstruct the time series, based on the Automatic Relevance Determination (ARD) criterion described in Gualandi et al (2015) (point 1). The three ICs are shown in Fig.…”

Poroelasticity and Fluid Flow Modeling for the 2012 Emilia-Romagna Earthquakes: Hints from GPS and InSAR Data

“…Figure 1 shows the location of the 14 stations considered in this study with respect to the fault position, while Figure s1 (Supplementary Materials) shows the GPS position time series. The detrended, filtered displacement time series are the input of an independent component analysis (ICA) performed adopting a variational Bayesian approach (vbICA, [23]) and modified in order to take into account missing data [24,25]. This method, applied to geodetic time series, performs a spatiotemporal separation of the geodetic data into a limited number of signals, subsequently interpreted as the actual physical sources that generated the observed displacements.…”

Developing a Complex Independent Component Analysis (CICA) Technique to Extract Non-stationary Patterns from Geophysical Time Series

“…Forootan andKusche (2012, 2013) argue that different physical processes generate statistically independent source signals that are superimposed in geophysical time series; thus, application of ICA likely helps separating (extracting) their contribution from the total signal. Therefore, in the recent studies (e.g., Awange et al 2014;Boergens et al 2014;Gualandi et al 2016;Ming et al 2016), ICA has been preferred over the ordinary extensions of the PCA/EOF approach, such as the rotated EOF (REOF) technique applied in, e.g., Richman (1986) and Lian and Chen (2012).…”