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.

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