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Risk Engineering, Inc., 4155 Darley Ave., Suite A, Boulder, Colorado 80303
Abstract
Probabilistic seismic hazard analysis (PSHA) is conducted because there is a perceived earthquake threat: active seismic sources in the region may produce a moderate-to-large earthquake. The analysis considers a multitude of earthquake occurrences and ground motions, and produces an integrated description of seismic hazard representing all events. For design, analysis, retrofit, or other seismic risk decisions a single "design earthquake" is often desired wherein the earthquake threat is characterized by a single magnitude, distance, and perhaps other parameters. This allows additional characteristics of the ground shaking to be modeled, such as duration, nonstationarity of motion, and critical pulses. This study describes a method wherein a design earthquake can be obtained that accurately represents the uniform hazard spectrum from a PSHA. There are two key steps in the derivation. First, the contribution to hazard by magnitude M, distance R, and 
must be maintained separately for each attenuation equation used in the analysis. Here, is the number of standard deviations that the target ground motion is above or below the median predicted motion for that equation. Second, the hazard for two natural frequencies (herein taken to be 10 and 1 Hz) must be examined by seismic source to see if one source dominates the hazard at both frequencies. This allows us to determine whether it is reasonable to represent the hazard with a single design earthquake, and if so to select the most-likely combination of M, R, and (herein called the "beta earthquake") to accurately replicate the uniform hazard spectrum. This closes the loop between the original perception of the earthquake threat, the consideration of all possible seismic events that might contribute to that threat, and the representation of the threat with a single (or few) set of parameters for design or analysis.
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