David D. Jackson

The Regional Earthquake Likelihood Models (RELM) project aims to produce and evaluate alternate models of earthquake potential (probability per unit volume, magnitude, and time) for California. Based on differing assumptions, these models are produced to test the validity of their assumptions and to explore which models should be incorporated in seismic hazard and risk evaluation. Tests based on physical and geological criteria are useful but we focus on statistical methods using future earthquake catalog data only. We envision two evaluations: a test of consistency with observed data and a comparison of all pairs of models for relative consistency. Both tests are based on the likelihood method, and both are fully prospective ( i.e. , the models are not adjusted to fit the test data). To be tested, each model must assign a probability to any possible event within a specified region of space, time, and magnitude. For our tests the models must use a common format: earthquake rates in specified “bins” with location, magnitude, time, and focal mechanism limits. Seismology cannot yet deterministically predict individual earthquakes; however, it should seek the best possible models for forecasting earthquake occurrence. This paper describes the statistical rules of an experiment to examine and test earthquake forecasts. The primary purposes of the tests described below are to evaluate physical models for earthquakes, assure that source models used in seismic hazard and risk studies are consistent with earthquake data, and provide quantitative measures by which models can be assigned weights in a consensus model or be judged as suitable for particular regions. In this paper we develop a statistical method for testing earthquake likelihood models. A companion paper (Schorlemmer and Gerstenberger 2007, this issue) discusses the actual implementation of these tests in the framework of the RELM initiative. Statistical testing of hypotheses is a common …

International audienceWe 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 compute the stress tensor in the upper crust of southern California as a function of time and compare observed seismicity with the estimated stress at the time of each earthquake. Several recent developments make it possible to do this much more realistically than before: (1) a wealth of new geodetic and geologic data for southern California and (2) a catalog of moment tensors for all earthquakes with magnitudes larger than 6 since 1850 and larger than 5 since 1910. We model crustal deformation using both updated geodetic data and geologically determined fault slip rates. We subdivide the crust into elastic blocks, delineated by faults which move freely at a constant rate below a locking depth with a rate determined by the relative block motion. We compute normal and shear stresses on nodal planes for each earthquake in the catalog. We consider stress increments from previous earthquakes (“seismic stress”) and aseismic tectonic stress, both separately and in combination. The locations and mechanisms of earthquakes are best correlated with the aseismic shear stress. Including the cumulative coseismic effects from past earthquakes does not significantly improve the correlation. Correlations between normal stress and earthquakes are always very sensitive to the start date of the catalog, whether we exclude earthquakes very close to others and whether we evaluate stress at the hypocenter or throughout the rupture surface of an earthquake. Although the correlation of tectonic stress with earthquake triggering is robust, other results are unstable apparently because the catalog has so few earthquakes.