Velocity covariance in the presence of anisotropic time correlated noise and transient events in GPS time series

The presence of un-modeled transient events in GPS time series significantly influences the estimate of the noise characteristics. In particular, GPS time series affected by transient events with a preferential geographical orientation are affected by a regional pattern of anisotropic noise. We provide a method to derive the covariance of GPS velocities in the presence of time-correlated noise based on the Allan variance of the rate that can account for this anisotropy. The velocity variance is calculated for different directions, allowing for the detection of direction-dependent noise properties. The resulting covariance provides realistic estimates for the uncertainties of GPS derived surface velocities and is of particular interest for the analysis of time series affected by transient signals. We show that GPS sites in subduction zones experiencing slow slip events (SSEs) exhibit a significant component of time correlated “noise” in the direction of the SSE motion and that the velocity confidence ellipses are highly eccentric in this direction. The time correlation of the noise of these sites is significantly reduced after modeling and subtracting SSEs from the time series with a concomitant reduction of the anisotropy of the estimated velocity uncertainties.