Robust, automatic GPS station velocities and velocity time series

Abstract:

Automation in GPS coordinate time series analysis makes results more objective and reproducible, but not necessarily as robust as the human eye to detect problems. Moreover, it is not a realistic option to manually scan our current load of >20,000 time series per day. This motivates us to find an automatic way to estimate station velocities that is robust to outliers, discontinuities, seasonality, and noise characteristics (e.g., heteroscedasticity). Here we present a non-parametric method based on the Theil-Sen estimator, defined as the median of velocities v_ij=(x_j–x_i)/(t_j–t_i) computed between all pairs (i, j). Theil-Sen estimators produce statistically identical solutions to ordinary least squares for normally distributed data, but they can tolerate up to 29% of data being problematic. To mitigate seasonality, our proposed estimator only uses pairs approximately separated by an integer number of years (N–δt)<(t_j–t_i )<(N+δt), where δt is chosen to be small enough to capture seasonality, yet large enough to reduce random error. We fix N=1 to maximally protect against discontinuities. In addition to estimating an overall velocity, we also use these pairs to estimate velocity time series. To test our methods, we process real data sets that have already been used with velocities published in the NA12 reference frame. Accuracy can be tested by the scatter of horizontal velocities in the North American plate interior, which is known to be stable to ~0.3 mm/yr. This presents new opportunities for time series interpretation. For example, the pattern of velocity variations at the interannual scale can help separate tectonic from hydrological processes. Without any step detection, velocity estimates prove to be robust for stations affected by the M_w7.2 2010 El Mayor-Cucapah earthquake, and velocity time series show a clear change after the earthquake, without any of the usual parametric constraints, such as relaxation of postseismic velocities to their preseismic values.