1. Hector Mine & Landers Earthquakes
Case Study in Detection of Transient Crustal Deformation
Brendan Crowell1, Dafna Avraham1, Yehuda Bock1, Danan Dong2, Peng Fang1, Paul Jamason1, Susan Owen2, Melinda Squibb1, Frank Webb2
1Scripps Institution of Oceanography, University of California-San Diego, La Jolla, CA
2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA
Introduction
Modeling Problems
Outlier Detection Algorithm
Trend Detection Algorithm
Geophysical Anomalies
The algorithms we developed successfully detect many GPS time series that exhibit geophysical anomalies, which often occur in the form of anthropogenic effects (such a groundwater removal and oil extraction), volcanic signals, or postseismic deformation.
The Scripps Orbit and Permanent Array Center and the Jet Propulsion Laboratory currently, with funding from a NASA MEaSUREs project, generate time series for over 1800 global and regional GPS stations, with the majority of stations in Western North America
The time series are analyzed with the now standard fitting of:
slopes (velocities)
offsets (coseismic, equipment change, etc.)
periodic (annual and semiannual terms) terms
postseismic (exponential or logarithmic) parameters
While the parameters that make the time series model are excellent for most stations, some are poorly modeled, have bad data or contain nonlinear effects not taken into account. For the purposes of quality control and detection of interesting signals in the time series, we have developed a few simple algorithms to scan the time series every week to detect instances when the model does not represent the data well.
Our algorithms look for the following:
outliers
“signals”
residual linear trends
The flagged stations are posted on the GPS Explorer data portal where we look for spatial clustering to gain insight into any un-modeled geophysical or other physical effects.
We also investigate a strain transient centered on the Obsidian Buttes fault just south of the Salton Sea detected from analysis of a long-history of survey-mode GPS measurements taken over the last 25+ years. We identify an event in 2005 by looking at strain rates and find that nearby CGPS stations had anomalous motion, but were not picked out by the detection criteria. Offsets were added to our GPS time series and the modeled fits at the stations were much improved.
San Gabriel basin
Los Angeles basin
Problem: A model that does not consistently fit the data constitutes a modeling problem. Similarly, data that deviates away from the model in a particular pattern represents a signal.
Problem: Outliers are problematic because they skew the data, and in turn, they can bias the model. Extreme outliers must be removed.
Problem: A detrended series that still exhibits significant trend indicates that the data contains unaccounted for information and/or modeling.
Santa Ana basin
Method: Using the correlation coefficient, r, we can measure the strength of the linear association between time (X) and distance (Y) in GPS data. Since -1<r <1, with a value of 0 representing no linear association, and a value close to 1 or -1 representing a strong linear association, we determined that a value greater than .7 or less than -.7 signifies trend.
Anthropogenic effects: The algorithms detect anomalous sites (in orange) in the Los Angeles basin, Santa Ana basin, and San Gabriel basin, which are regions where anthropogenic effects occur.
Method: Create a threshold for each residual series that is equal to 5 times the interquartile range (IQR). The IQR is a very robust estimator of the spread of the series since it is more resistant to outliers than the standard deviation. Thus, residuals that cross this threshold correspond to outliers.
Method: Search each GPS site for existence of eight-month windows during which the residual series does not change sign, and therefore does not resemble white noise. This signifies a lack of important, but unaccounted for, model terms.
Yellowstone
Mount St. Helens
Long Valley Caldera
Volcanic Signals: Volcanoes affect ground motion in patterns that the anomaly detection algorithms consistently recognize, which is seen above as concentrations of detected sites in volcanic regions (Mt. St. Helens, Long Valley Caldera, and Yellowstone).
Anomalies in GPS Time Series
Modeling Problems: These are seen when the model does not represent the data well. This happens either because the model is lacking an important model term(s), or because the data has gaps and jumps that mislead the model.
Signals: Many signals such as postseismic decays, anthropogenic effects, and volcanic signals are recognized as data that deviate away from the model in particular patterns.
Outliers: Outliers are caused by many different sources. If the outliers are extreme, they can distort the model, and it is therefore very important to detect and remove them from the data.
Trend: Due to geophysical forces, GPS time series inherently contain a linear velocity (trend). Thus, the series are detrended before further analysis is performed. Nevertheless, some series still contain a significant trend, especially when two or more trends are estimated. The existence of trend in a detrended series signifies the need for further modeling of the data, and so trend detection is critical.
Alternative Approaches
Parkfield Earthquake
Hector Mine & Landers Earthquakes
When anomalies are too small to be picked up by the above methodologies, it may be imperative to combine campaign GPS measurements and look at spatiotemporal changes in strain rate.
San Simeon Earthquake
Postseismic Deformation: The algorithms effectively detect post-seismic deformation, which is the anomalous trademark of medium to large earthquakes (1992 Mw=7.3 Landers, 1999 Mw= 7.1 Hector Mine, 2003 Mw=6.5 San Simeon, and 2004 Mw= 6.0 Parkfield). The epicenter for each earthquake is circled in red on the map above.