We analyzed the historical seismicity in southern California to develop a rational approach for calculating the seismic hazard from background seismicity of magnitude 6.5 or smaller. The basic assumption for the approach is that future earthquakes will be clustered spatially near locations of historical mainshocks of magnitudes equal to or greater than 4. We analyzed the declustered California seismicity catalog to compute the rate of earthquakes on a grid and then smoothed these rates to account for the spatial distribution of future earthquakes. To find a suitable spatial smoothing function, we studied the distance (r) correlation for southern California earthquakes and found that they follow a 1/rµ power-law relation, where µ increases with magnitude. This result suggests that larger events are more clustered in space than smaller earthquakes. Assuming the seismicity follows the Gutenberg-Richter distribution, we calculated peak ground accelerations (PGA) for 10% probability of exceedance in 50 yr. PGA estimates range between 0.25 and 0.35 g across much of southern California. These ground-motion levels are generally less than half the levels of hazard that are obtained using the entire seismic source model that also includes geologic and geodetic data. We also calculated the overall uncertainty for the hazard map using a Monte Carlo method and found that the coefficient of variation is about 0.24 ± 0.01 for much of the region.

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