Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California

Abstract

We have initially developed a time-independent forecast for southern California by smoothing the locations of magnitude 2 and larger earthquakes. We show that using small m Ն2 earthquakes gives a reasonably good prediction of m Ն5 earthquakes. Our forecast outperforms other time-independent models (Kagan and Jackson, 1994;Frankel et al., 1997), mostly because it has higher spatial resolution. We have then developed a method to estimate daily earthquake probabilities in southern California by using the Epidemic Type Earthquake Sequence model (Kagan and Knopoff, 1987;Ogata, 1988;Kagan and Jackson, 2000). The forecasted seismicity rate is the sum of a constant background seismicity, proportional to our timeindependent model, and of the aftershocks of all past earthquakes. Each earthquake triggers aftershocks with a rate that increases exponentially with its magnitude and decreases with time following Omori's law. We use an isotropic kernel to model the spatial distribution of aftershocks for small (m Յ5.5) mainshocks. For larger events, we smooth the density of early aftershocks to model the density of future aftershocks. The model also assumes that all earthquake magnitudes follow the Gutenberg-Richter law with a uniform b-value. We use a maximum likelihood method to estimate the model parameters and test the short-term and time-independent forecasts. A retrospective test using a daily update of the forecasts between 1 January 1985 and 10 March 2004 shows that the short-term model increases the average probability of an earthquake occurrence by a factor 11.5 compared with the time-independent forecast.

Adaptive Smoothing of Seismicity in Time, Space, and Magnitude for Time-Dependent Earthquake Forecasts for California

“…We use the spatial completeness magnitude map estimated by from the local magnitude distribution using adaptive kernels. In addition, M 0 increases following large M ≥ 5 earthquakes, and we follow the method proposed by Helmstetter et al (2006) to model changes in the detection threshold after mainshocks with M ≥ 5 such that In contrast to model K 2 , we do not impose a magnitude distribution in model K 3 . Instead, we use a magnitude kernel K M to nonparametrically estimate the magnitude distribution, as in the time and space domains.…”

“…These models usually assume that the seismicity rate is the sum of a background rate (usually heterogeneous in space and stationary in time) and of triggered earthquakes. This class of models includes, among others, the point-process model of Kagan and Knopoff (1987), the epidemic-type aftershock sequence (ETAS) model (Ogata, 1988;Helmstetter et al 2006), the STEP model (Gerstenberger et al, 2005), and the model of Marsan and Lengliné (2008).…”

Comment on ‘Testing earthquake prediction methods: “The West Pacific short-term forecast of earthquakes with magnitude MwHRV ≥5.8”’ by V.G. Kossobokov

“…This rapid change necessitates frequent updating of forecasts. Ideally, a new forecast should be calculated after each event as discussed by Helmstetter et al (2006), but practical considerations prompted us to renew the forecast only once daily. Moreover, a delay of at least a few hours occurs between an earthquake and its processing by the Harvard team.…”

“…Helmstetter et al (2006) applied a similar technique for short-and long-term forecasts of seismicity in southern California. They use a local earthquake catalog with the magnitude threshold 2.0.…”

“…The second forecast would declare 70% spacetime dangerous, with 90% of events in alert zones. One way to evaluate the effectiveness of a forecast is to calculate its 'predictive ratio' (Kagan and Knopoff, 1977, p. 101) or 'probability gain' and 'information gain' (Daley and Vere-Jones, 2004;Helmstetter et al, 2006). The predictive ratio is the ratio of short-term forecasted earthquake occurrence rate to the Poisson rate.…”