Civil Engineering Association

Probabilistic Seismic Hazard Analysis and Design Earthquakes: Closing the Loop

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 oc-
currences 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 du-
ration, 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 e must be maintained sep-
arately for each attenuation equation used in the analysis. Here, e 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 e (herein called the "beta earth-
quake") 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.