A Network Strain Filter for Detecting Transient Deformation Signals

Data from large-scale, continuous geodetic arrays have been used to identify numerous transient signals due to, for example, aseismic fault slip and magmatic intrusion. Because of the large volumes of data these networks provide, automated methods are required to detect transient signals that may be too small to be found by visual inspection of the time series. We have developed a new method for detecting transient signals from large-scale geodetic arrays, which is referred to as a Network Strain Filter (NSF). The NSF models geodetic (principally GPS) time series as a sum of contributions from both steady and transient tectonic deformations, site-specific local benchmark motion, reference frame errors, and white noise. The underlying principle is to exploit the spatially coherent nature of tectonic signals. This is accomplished by representing the spatial variation of tectonic deformation with a wavelet basis. In the time domain the deformation is modeled as a sum of steady state and integrated random walk components. Model parameters are estimated using Extended Kalman filtering techniques. The estimated strain-rate field depends on how the solution is smoothed in both the spatial and temporal domains. The amount of temporal smoothing is determined from the data "on line" in the Extended Kalman Filter, using a logarithmic form of the hyperparameter which forces the hyperparameter to remain positive. Spatial smoothing is determined by the number of wavelet scales retained in the final estimation. Including too many small scales maps local signal into tectonic strain, over fitting the data. In contrast, not including enough small scales overly smoothes the strain field, and under fits the data. Our strategy is to choose the minimum wavelet scale such that the residual variance is in accord with a priori estimates of the data variance. Tests of the NSF with simulated data using the southern California Integrated GPS Network (SCIGN) station distribution demonstrate that the method recovers the input temporally varying strain field, even at low signal to noise ratio when the strain signal can not be visually detected in the raw position time series. Application of the method to data from Southern California and Japan will be presented.