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S. Wiemer

Publications and source records attributed to S. Wiemer.

4 recordsLinked to original sources
USGS2007

Earthquake likelihood model testing

INTRODUCTION 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 task and a wide range of possible testing procedures exist. Jolliffe and Stephenson ( 2003 ) present different forecast verifications from atmospheric science, among them likelihood testing of probability forecasts and testing the occurrence of binary events. Testing binary events requires that for each forecasted event, the spatial, temporal and magnitude limits be given. Although major earthquakes can be considered binary events, the models within the RELM project express their forecasts on a spatial grid and in 0.1 magnitude units; thus the results are a distribution of rates over space and magnitude. These forecasts can be tested with likelihood tests. In general, likelihood tests assume a valid null hypothesis against which a given hypothesis is tested. The outcome is either a rejection of the null hypothesis in favor of the test hypothesis or a nonrejection, meaning the test hypothesis cannot outperform the null hypothesis at a given significance level. Within RELM, there is no accepted null hypothesis and thus the likelihood test needs to be expanded to allow comparable testing of equipollent hypotheses. To test models against one another, we require that forecasts are expressed in a standard format: the average rate of earthquake occurrence within pre-specified limits of hypocentral latitude, longitude, depth, magnitude, time period, and focal mechanisms. Focal mechanisms should either be described as the inclination of P -axis, declination of P -axis, and inclination of the T -axis, or as strike, dip, and rake angles. Schorlemmer and Gerstenberger ( 2007 , this issue) designed classes of these parameters such that similar models will be tested against each other. These classes make the forecasts comparable between models. Additionally, we are limited to testing only what is precisely defined and consistently reported in earthquake catalogs. Therefore it is currently not possible to test such information as fault rupture length or area, asperity location, etc. Also, to account for data quality issues, we allow for location and magnitude uncertainties as well as the probability that an event is dependent on another event. As we mentioned above, only models with comparable forecasts can be tested against each other. Our current tests are designed to examine grid-based models. This requires that any fault-based model be adapted to a grid before testing is possible. While this is a limitation of the testing, it is an inherent difficulty in any such comparative testing. Please refer to appendix B for a statistical evaluation of the application of the Poisson hypothesis to fault-based models. The testing suite we present consists of three different tests: L-Test, N-Test, and R-Test. These tests are defined similarily to Kagan and Jackson ( 1995 ). The first two tests examine the consistency of the hypotheses with the observations while the last test compares the spatial performances of the models.

Seismological Research Letters↗
USGS2001

Anomalously high b-values in the South Flank of Kilauea volcano, Hawaii: Evidence for the distribution of magma below Kilauea's East rift zone

The pattern of b-value of the frequency-magnitude relation, or mean magnitude, varies little in the Kaoiki-Hilea area of Hawaii, and the b-values are normal, with b = 0.8 in the top 10 km and somewhat lower values below that depth. We interpret the Kaoiki-Hilea area as relatively stable, normal Hawaiian crust. In contrast, the b-values beneath Kilauea's South Flank are anomalously high (b = 1.3-1.7) at depths between 4 and 8 km, with the highest values near the East Rift zone, but extending 5-8 km away from the rift. Also, the anomalously high b-values vary along strike, parallel to the rift zone. The highest b-values are observed near Hiiaka and Pauahi craters at the bend in the rift, the next highest are near Makaopuhi and also near Puu Kaliu. The mildest anomalies occur adjacent to the central section of the rift. The locations of the three major and two minor b-value anomalies correspond to places where shallow magma reservoirs have been proposed based on analyses of seismicity, geodetic data and differentiated lava chemistry. The existence of the magma reservoirs is also supported by magnetic anomalies, which may be areas of dike concentration, and self-potential anomalies, which are areas of thermal upwelling above a hot source. The simplest explanation of these anomalously high b-values is that they are due to the presence of active magma bodies beneath the East Rift zone at depths down to 8 km. In other volcanoes, anomalously high b-values correlate with volumes adjacent to active magma chambers. This supports a model of a magma body beneath the East Rift zone, which may widen and thin along strike, and which may reach 8 km depth and extend from Kilauea's summit to a distance of at least 40 km down rift. The anomalously high b-values at the center of the South Flank, several kilometers away from the rift, may be explained by unusually high pore pressure throughout the South Flank, or by anomalously strong heterogeneity due to extensive cracking, or by both phenomena. The major b-value anomalies are located SSE of their parent reservoirs, in the direction of motion of the flank, suggesting that magma reservoirs leave an imprint in the mobile flank. We hypothesize that the extensive cracking may have been acquired when the anomalous parts of the South Flank, now several kilometers distant from the rift zone, were generated at the rift zone near persistent reservoirs. Since their generation, these volumes may have moved seaward, away from the rift, but earthquakes occurring in them still use the preexisting complex crack distribution. Along the decollement plane at 10 km depth, the b-values are exceptionally low (b = 0.5), suggesting faulting in a more homogeneous medium. ?? 2001 Elsevier Science B.V. All rights reserved.

Journal of Volcanology and Geothermal Research↗