High-Resolution Long-Term and Short-Term Earthquake Forecasts for California

We present two models for estimating the probabilities of future earthquakes in California, to be tested in the Collaboratory for the Study of Earthquake Predictability (CSEP). The first is a time-independent model of adaptively smoothed seismicity that we modified from Helmstetter et al. (2007). The model provides five-year forecasts for earthquakes with magnitudes M >= 4.95. We show that large earthquakes tend to occur near the locations of small M >= 2 events, so that a high-resolution estimate of the spatial distribution of future large quakes is obtained from the locations of the numerous small events. We further assume a universal Gutenberg-Richter magnitude distribution. In retrospective tests, we show that a Poisson distribution does not fit the observed rate variability, in contrast to assumptions in current earthquake predictability experiments. We therefore issued forecasts using a better-fitting negative binomial distribution for the number of events. The second model is a time-dependent epidemic-type aftershock sequence (ETAS) model that we modified from Helmstetter et al. (2006) and that provides next-day forecasts for M >= 3.95. In this model, the forecasted rate is the sum of a background rate (proportional to the time-independent model rate) and of the expected rate of triggered events due to all prior earthquakes. Each earthquake triggers events with a rate that increases exponentially with its magnitude and decays in time according to the Omori-Utsu law. An isotropic kernel models the spatial density of aftershocks for small (M <= 5.5) events, while for larger quakes, we smooth early aftershocks to forecast later events. We estimate parameter values by optimizing retrospective forecasts and find that the short-term model realizes a probability gain of about 6.0 per earthquake over the time-independent model.