Testing alarmbased earthquake predictions
Abstract
Motivated by a recent resurgence in earthquake predictability research, we present a method for testing alarmbased earthquake predictions. The testing method is based on the Molchan diagrama plot of miss rate and fraction of spacetime occupied by alarmand is applicable to a wide class of predictions, including probabilistic earthquake forecasts varying in space, time, and magnitude. A single alarm can be simply tested using the cumulative binomial distribution. Here we consider the more interesting case of a function from which a continuum of wellordered alarms can be derived. For such an `alarm function' we construct a cumulative performance measure, the area skill score, based on the normalized area above a trajectory on the Molchan diagram. A score of unity indicates perfect skill, a score of zero indicates perfect nonskill, and the expected score for a random alarm function is ^{1}/_{2}. The area skill score quantifies the performance of an arbitrary alarm function relative to a reference model. To illustrate the testing method, we consider the 10yr experiment by J. Rundle and others to predict M >= 5 earthquakes in California. We test forecasts from three models: relative intensity (RI), a simple spatial clustering model constructed using only smoothed historical seismicity; pattern informatics (PI), a model that aims to capture seismicity dynamics by pattern recognition; and the U. S. Geological Survey National Seismic Hazard Map (NSHM), a model that comprises smoothed historical seismicity, zones of `background' seismicity, and explicit fault information. Results show that neither PI nor NSHM provide significant performance gain relative to the RI reference model. We suggest that our testing method can be used to evaluate future experiments in the Collaboratory for the Study of Earthquake Predictability and to iteratively improve reference models for earthquake prediction hypothesis testing.
 Publication:

Geophysical Journal International
 Pub Date:
 February 2008
 DOI:
 10.1111/j.1365246X.2007.03676.x
 Bibcode:
 2008GeoJI.172..715Z
 Keywords:

 Probabilistic forecasting; Probability distributions; Earthquake dynamics; Earthquake interaction;
 forecasting;
 and prediction; Seismicity and tectonics; Statistical seismology