High-resolution Time-independent Grid-based Forecast for M ≥ 5 Earthquakes in California

Agnes Helmstetter, Yan Y. Kagan, & David D. Jackson

Published 2007, SCEC Contribution #983

We have developed time-independent forecasts for California assuming that small earthquakes can be used to map the distribution of large damaging earthquakes, as suggested by Kafka and Levin (2000). Indeed, large earthquakes often nucleate in areas that have a large density of small events.

We have first declustered the catalog to remove large fluctuations of seismic activity that do not represent the long-term average. We have then estimated the spatial density of seismicity using a kernel method to smooth the location of magnitude M ≥ 2 earthquakes. Note that our model only predicts hypo-centers, not rupture areas. Clearly, large earthquakes some-times propagate in areas with little seismicity, as observed for the 1857 earthquake that ruptured the southern section of the San Andreas fault, which is now mostly devoid of small earthquakes. Our model should thus be coupled with a fault model to forecast rupture areas for large earthquakes.

Our model is very similar to the time-independent forecasts of Helmstetter et al. (2006), which is in its turn an adaptation to local modern catalogs of the program by Kagan and Jackson (1994). Compared with Helmstetter et al. (2006), we have extended our forecasts to all of California and made small changes in the process. We have slightly modified the declustering method. We have modified the estimation of the smoothing distance di used to estimate the spatial density of seismicity. Our new method is simpler and computationally more efficient, but gives very similar results. We have also estimated the completeness magnitude M0 in each cell and corrected our model to account for spatial variations of M0.

We have developed two time-independent models for the Regional Earthquake Likelihood Models (RELM) earthquake forecast testing (Kagan et al. 2003, Schorlemmer et al. 2005). The first one evaluates the expected rate of all M ≥ 5 earthquakes, while the other one estimates the probability of independent events only. The two models have the same spatial distribution, but different total numbers of predicted events and slightly different magnitude distributions.

Instead of the Gutenberg-Richter law (Gutenberg and Richter 1944) with a uniform b-value of 1 used by Helmstetter et al. (2006), we use a tapered Gutenberg-Richter law with a corner magnitude Mc = 8, with b = 0.95 for the first model (all events) and b = 0.89 for the second model (estimated from independent events). We modify the magnitude distribution in the Geysers geothermal area, which has a much larger value b {approx} 2 for M ≥ 3.3.

Helmstetter, A., Kagan, Y. Y., & Jackson, D. D. (2007). High-resolution Time-independent Grid-based Forecast for M ≥ 5 Earthquakes in California. Seismological Research Letters, 78(1), 78-86. doi: 10.1785/gssrl.78.1.78.