The recent development of dense and continuously operating Global Navigation Satellite System (GNSS) networks worldwide has led to a significant increase in geodetic data sets that sometimes capture transient-deformation signals. It is challenging, however, to extract such transients of geophysical origin from the background noise inherent to GNSS time series and, even more so, to separate them from other signals, such as seasonal redistributions of geophysical fluid mass loads. In addition, because of the very large number of continuously recording GNSS stations now available, it has become impossible to systematically inspect each time series and visually compare them at all neighboring sites. Here we show that Multichannel Singular Spectrum Analysis (M-SSA), a method derived from the analysis of dynamical systems, can be used to extract transient deformations, seasonal oscillations, and background noise present in GNSS time series. M-SSA is a multivariate, nonparametric, statistical method that simultaneously exploits the spatial and temporal correlations of geophysical fields. The method allows for the extraction of common modes of variability, such as trends with nonconstant slopes and oscillations shared across time series, without a priori hypotheses about their spatiotemporal structure or their noise characteristics. We illustrate this method using synthetic examples and show applications to actual GPS data from Alaska to detect seasonal signals and microdeformation at the Akutan active volcano. The geophysically coherent spatiotemporal patterns of uplift and subsidence thus detected are compared to the results of an idealized model of such processes in the presence of a magma chamber source.
Statistical methods
Data-Adaptive Detection of Transient Deformation in Geodetic Networks. Journal of Geophysical Research: Solid Earth. 2016;121 (3) :2129-2152 .Abstract
.
The Role of Oscillatory Modes in U.S. Business Cycles. Fondazione Eni Enrico Mattei (FEEM) [Internet]. 2012;26 :1. Publisher's VersionAbstract
.
Gap Filling of Solar Wind Data by Singular Spectrum Analysis. Geophysical Research Letters. 2010;37 :L15101.Abstract
.
Predicting weather regime transitions in Northern Hemisphere datasets. Climate Dynamics. 2007;29 (5) :535–551.
.
Oscillatory Climate Modes in the Eastern Mediterranean and Their Synchronization with the North Atlantic Oscillation. Journal of Climate. 2010;23 (15) :4060–4079.Abstract
.
Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific. Climate Dynamics. 1995;12 :101–112.Abstract
.
Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance. Physica D: Nonlinear Phenomena. 2010;239 (3) :145–166.Abstract
.
Cluster analysis of typhoon tracks. Part II: Large-scale circulation and ENSO. Journal of Climate. 2007;20 (14) :3654–3676.
.
Interdecadal oscillations and the warming trend in global temperature time series. Nature. 1991;350 (6316) :324–327.Abstract
.
Oscillatory modes of extended Nile River records (A.D. 622–1922). Geophysical Research Letters. 2005;32 (10) :L10702.Abstract
.
Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D. 1989;35 (3) :395–424.Abstract
.
Low-order stochastic model and ``past-noise forecasting" of the Madden-Julian oscillation. Geophysical Research Letters. 2013;40 :5305–5310.
.
Trends, interdecadal and interannual oscillations in global sea-surface temperatures. Climate Dynamics. 1998;14 (7) :545–569.Abstract
.
Probabilistic clustering of extratropical cyclones using regression mixture models. Climate Dynamics. 2007;29 (4) :423–440.
.
Impacts of natural disasters on a dynamic economy. In: Extreme Events : Observations, Modeling, and Economics. American Geophysical Union and Wiley-Blackwell ; 2015. pp. 343–360.Abstract
.