“Real-time” Transient Detection Algorithms Dr. Kang Hyeun Ji, Thomas Herring MIT

Algorithms The transient detection methods developed at MIT are a combination of state estimation and principal component analysis (PCA). The process noise states from a smoothing Kalman filter are used in PCA to compute eigenvalues that tell us the amount of power in a component and eigenvectors that tell us the spatial pattern of the component. Two approaches are possible for near real-time implementation of this type of algorithm: – A moving window approach where new data are added and old data removed and PCA recomputed. – Using the eigenvalue patterns from previously seen events to see if these events are re-occurring. We will examine this approach in this presentation.

Eigenvector Method Basic approach is to simply multiply the eigenvector of a selected candidate transient event by the daily updated time series residuals of the sites in the eigenvector. Site residuals are computed by detrending based on earlier data. Since most transients involve less than 50 sites, this calculation can be done very fast (basically dot- product of two component vectors (NE or NEU). Standard deviation of the result can be computed using conventional propagation of errors methods. Since “real-time” data will be missing sites at times, the eigenvector needs to be normalized to account for missing data. If all sites have equal weight, this normalization is by the amplitude squared of the eigenvector elements of the sites being used (when all sites present amplitude is 1). Simple product can be appended to on-going results each day. Estimate of standard deviation allow measure of significance of changes.

Examples We show three examples of applying this method: – Akutan volcano inflation event seen in Are there other events of this type in the PBO analyses of these data? – Cascadia slow slip events: Are the small event detectable with this method? – San Gabriel Valley 2005 water event. Can we detect more of these events and can this be used as a monitoring method for fluid injection and removal?

Akutan Volcano Inflation events Inflation event seen on Akutan Volcano in early (Black vectors PCA, Red Mogi model) Using the black vector spatial pattern, we compute the product with the time series of the sites as we would in a “real- time” approach. As a function of time we determine the amplitude of the spatial pattern

“Real-time application to Akutan (PBO time series) Blue is original smoothed state vector solution. Red dots are eigenvector product when all data are available. Black are times when some sites are missing and eigenvector is normalized. There is an indication of a weak inflation event starting in 2011 that had not been seen before.

Cascadia slow slip events Here we look for the pattern of the Jan 2007 event which is one of the largest ones since PBO GPS data analysis used for these tests. May 2008, 2009 and August 2010 have similar spatial pattern.

“Real-time” time series Blue is the full PCA analysis. Red are when all sites are available. Black values have some sites missing. NOTE: There is a small event associated with low levels of tremor in late 2007 which can be seen here (and is clearly seen with the full PCA analysis). Small ETS event

San Gabriel Valley 2005 rain event Heavy rains in 2005 caused a clear anomalous transient signal in the GPS sites around the San Gabriel Valley. Red Vectors here are the horizontal pattern and time series. Blue vectors are the height component. Apply red-eigenvectors to complete NE time series of the sites from the SCEC transient real data set.

Detrended time series of San Gabriel sites 2005 event 2005 event clearly seen, but are there other signals presents? Apply 2005 horizontal eigenvectors to SCEC time- series.

Blue is water level change at well in the center of the basin (arbitrary scale) event is not the only one that can now be seen in the horizontal motions of the GPS sites.

Same results with red 30-day averages of GPS results and water level “scaled” to GPS amplitude (0.4 mm/foot of water) with rate 1.4 mm/yr - Leakage of tectonic signal?). Correlation coefficient 0.92; 0.94 when water leads GPS by 2 months).

Summary The algorithm using eigenvectors from previous events works well and has shown some unexpected results already. Eigenvectors can be obtained from sources other than principal component analysis of transient events. Fast events and models are other possible sources. Algorithm is fast and simple. It could be implemented in csh/awk script or in a scripting language such as Python. We are working on eigenvector normalization when there are missing data and data with large uncertainties. For implementation, SCEC will probably need to handle update of new time series values (e.g. PBO generates rapids every day but sometime several days will be posted at nearly the same time. Similarly final (IGS final orbit) solutions are released in weekly batches so these releases need to be monitored to see which new data are available for inclusion in the algorithm.