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The Problem of the Random Earthquake in Seismic Hazard Analysis: Wasatch Front Region, Utah
The State of Utah’s rules for dam safety require that an “Operating Basis Earthquake” (OBE) be determined for all dams within seismic zones 2 and 3 of the Uniform Building Code. The OBE is described as the earthquake with a return interval of at least 200 yrs that has the greatest potential to cause damage at the site, considering all active earthquake sources which could affect it. Previous studies have shown that at most sites in the Wasatch Front region, the dominant sources of seismic hazard for 200-yr return periods are moderate-sized earthquakes of ML ≤ 6.5. This result suggests that an earthquake in this size range would be an appropriate OBE for a Wasatch Front region dam. Because such earthquakes are below the usual threshold of surface faulting, their locations and magnitudes cannot easily be predicted. Hence, in seismic hazard evaluations, these moderate-sized earthquakes are usually assumed to occur randomly throughout the region. This randomness complicates the task of selecting a specific OBE for use in engineering design purposes.
We evaluate an approach to the problem of selecting an OBE which employs the concept of the “probabilistic epicentral distance” (r0) introduced in the 1980’s by C.K. Wood and D.A. Ostenaa of the U.S. Bureau of Reclamation. In the application considered here, r0 is the radius of a circle within which the annual probability of an earthquake of 5.5 ≤ ML ≤ 6.5 is equal to some specified small number. Using an average rate of occurrence of earthquakes in this size range estimated from historical and instrumental seismicity data for the Wasatch Front region, it is found that r0 = 85, 58, 38, and 17 km for annual probabilities (inverse return periods) of 1/95, 1/200, 1/475, and 1/2373, respectively. Based on these distances, the calculated median magnitude of 5.8, and (for example) the Boore and others (1993) attenuation relation for peak horizontal acceleration (PHA), we calculate that the expected PHA’s are, respectively, 0.04, 0.05, 0.07, and 0.13 g. These PHA’s are similar to those obtained for the same annual probabilities from a simple probabilistic seismic hazard analysis in which only random earthquakes of 5.5 ≤ ML ≤ 6.5 (at distances of up to 100 km) are considered and the uncertainties in the peak accelerations predicted by the attenuation relation are ignored. However, they are factors of 1.5 to 5.7 lower than values obtained from more complete probabilistic hazard analyses for the Wasatch Front region, which take into account smaller and larger potential earthquakes and also the uncertainties in the predicted PHA’s. Thus, at least in this region, the probabilistic distance method yields an OBE which significantly under-represents the ground shaking hazard. We suggest an alternative and more conservative approach to the problem of selecting an OBE which involves the direct use of results from a regional or site-specific probabilistic seismic hazard analysis.
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