Given the location and magnitude of an earthquake, the spatial distribution of peak ground shaking can be estimated using attenuation relations (e.g. Campbell, 1981; Joyner and Boore, 1981; Fukushima and Irikura, 1982; Abrahamson and Silva, 1997; Boore, et al., 1997; Campbell, 1997; Sadigh, et al., 1997; Field, 2000). Attenuation relations for small and large magnitude events have already been developed for southern California (Allen, 2004), and are under development for northern California.
ElarmS uses the attenuation relations in a two-stage process. One second after the first P-wave trigger the first estimate of magnitude is available and the attenuation relations provide PGA as a function of distance from the epicenter. The error in the PGA estimates as a function of time for the 32 earthquakes in the test dataset from southern California is shown in Figure 13.20b. As time progresses, the stations closest to the epicenter experience their PGA and this information is used to adjust the initial attenuation relation. The improvement in the PGA estimate is only marginal as shown in Figure 13.20c, but inclusion of PGA observations once available does remove outliers i.e. cases when the magnitude based estimate is very high or low.
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