Abstract

This article applies the Bernoulli process (the binomial distribution) to probabilistic seismic‐hazard analysis (PSHA), and the results are identical with the Poisson process. To determine the parameter p required of the binomial distribution, the probabilities associated with the seismic hazard are divided into two categories. The first consists of spatial probabilities that represent the likelihood that the target value of site ground motion is exceeded, given that an event of exceedance of m0 occurs somewhere within a seismic source or a specific region. The spatial probabilities are not within any period but dependent on the chosen spatial range and lower limit of magnitude m0. The second is referred to as temporal probability, because this type of probability is always within a period, for example, 0.2g peak ground acceleration (PGA) with a probability of 0.1 in 50 yrs. From the point of view of the binomial distribution, a temporal probability or a seismic‐hazard curve is conditional on given spatial range and m0, and is calculated on the basis of the number rather than the physical temporal process of earthquakes. Applying binomial distribution to PSHA does not require the independence of earthquakes but of ground motions at the site. Therefore, the aftershocks may not be removed from the catalog. In addition, the return period can be directly defined by the spatial probability and the average annual rate of exceedance of m0.

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