Greedy Automatic Signal Decomposition and Its Application to Daily GPS Time Series

Abstract

The recognition of transient motion in terrestrial continuous Global Positioning System (GPS) time series implies the knowledge of certain time functions that we assume to be ever present in the time series. By assuming that the permanent time functions are the long‐term secular velocity of the Earth and the seasonal oscillations, we define the total remaining signal as transient motion. Here we adopt the multitransient as a versatile function for modeling transient motion over a range of time scales. We define the multitransient as the sum of two or more transient decaying functions with different characteristic time scales and identical onset times. We then demonstrate the greedy approach to fitting the time series by using a minimum number of multitransients (sparse functions) in addition to the permanent time functions in a linear regression. The Greedy Automatic Signal Decomposition algorithm decomposes the signal into three parts: (1) background seasonal motion, (2) secular and transient motion, and (3) a residual (noise). We describe the greedy algorithm with synthetic examples before demonstrating its application to time series of daily GPS solutions. The implementation of the multitransient allows for a more realistic plate‐trajectory model, whereby a full range of transient signal time scales, from short‐duration slow slip to longer‐duration processes such as postseismic slab accelerations or postseismic decay, can all be estimated with the same function. Since Greedy Automatic Signal Decomposition algorithm automatically estimates trend, its application to a GPS network allows for the common mode filter to be applied seamlessly.

Earthquake Swarms, Slow Slip and Fault Interactions at the Western‐End of the Hellenic Subduction System Precede the Mw 6.9 Zakynthos Earthquake, Greece

“…As a first step in our analysis, we removed outliers from the GPS signal by applying the Hampel filter, a common approach for reducing noise (Pearson, 2005) (Figures S9 and S10). Subsequently, we applied the Greedy Automatic Signal Decomposition algorithm (GrAtSiD; Bedford & Bevis, 2018) to decompose the GPS signal into (i) the seasonal oscillation signal, (ii) secular and transient motions, and (iii) the residual signal. The secular motion corresponds to the long-term velocity of the station, which is in principle stable, while the transient signal is estimated by fitting a minimum number of multitransient signals that are defined as the sum of two or more exponentially decaying time functions.…”

First Field Evidence of Coseismic Land‐Level Change Associated with the 25 December 2016 Mw 7.6 Chiloé, Chile, Earthquake

“…1b for location). We apply a common mode filter and model the time series with the GrAtSiD algorithm (Bedford and Bevis, 2018). The vertical bar indicates the timing of our VEM measurements at Isla Quilán in October 2017 Figure 2b for site locations.…”

Slow Slip Triggers the 2018 Mw 6.9 Zakynthos Earthquake Within the Weakly Locked Hellenic Subduction System, Greece

“…Given the assumption that the non‐tectonic, non‐seasonal noise has a Gaussian (white) distribution, the recovery of Gaussian residuals by the GrAtSiD trajectory model in this case indicates an appropriate fitting of the time series (Bedford & Bevis, 2018) for the frequencies of interest (2–3 months long). Accordingly, under‐ or over‐fitting of the time series would be indicated by a residual with flicker (pink) noise spectral characteristics (Bedford & Bevis, 2018). While a flicker noise spectrum is commonly assumed to be the dominant noise signature in GNSS displacement time series (Dmitrieva et al., 2015; Langbein, 2008), it was demonstrated in Bedford and Bevis (2018) that this assumption could be an artifact of signal decomposition in which tectonic and seasonal signals leak into the assumed noise portion of the signal, and that an assumption of Gaussian noise is just as valid as an assumption of flicker noise for the non‐seasonal, non‐tectonic portion of the signal.…”

“…The transient signals, reported by Mouslopoulou et al. (2020), were recovered from the median of a total of 250 trajectory models, using the Greedy Automatic Signal Decomposition algorithm (GrAtSiD) (Bedford & Bevis, 2018). This algorithm decomposes, using a linear regression, the GPS signal into (a) the seasonal oscillation signal; (b) the secular and transient motions, and (c) the residual (noise) signal.…”