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.