Abstract:
Most probabilistic seismic-hazard analysis procedures require that at least
three seismic source parameters be known, namely the mean seismic activity rate λ, the
Gutenberg–Richter b-value, and the area-characteristic (seismogenic source) maximum
possible earthquake magnitudemmax. In almost all currently used seismic-hazard assessment
procedures that utilize these three parameters, it is explicitly assumed that all three
remain constant over time and space. However, closer examination of most earthquake
catalogs has indicated that significant spatial and temporal variations existed in the
seismic activity rate λ, as well as in the Gutenberg–Richter b-value. In this study, the
maximum likelihood estimation of these earthquake hazard parameters considers
the incompleteness of the catalogs, the uncertainty in the earthquake magnitude determination,
as well as the uncertainty associated with the applied earthquake-occurrence
models. The uncertainty in the earthquake-occurrence models is introduced by assuming
that both the mean seismic activity rate λ and the Gutenberg–Richter b-value are
random variables, each described by the gamma distribution. This approach results in
the extension of the classic frequency–magnitude Gutenberg–Richter relation and the
Poisson distribution of the number of earthquakes with their compounded counterparts
(Benjamin, 1968; Campbell, 1982, 1983). The proposed procedure was applied in the
estimation of the seismicity parameters in an area that had experienced the strongest and
most devastating earthquake in contemporary South African history, namely the 29
September 1969 Mw 6.3 Ceres–Tulbagh event. In this example, it was shown that the
introduction of uncertainty in the earthquake-occurrence model reduced the mean return
periods, leading to an increase of the estimated seismic hazard. Additionally, this study
confirmed that accounting for magnitude uncertainties had the opposite effect, that is, it brought about increases in the return periods, or, equivalently, a reduction of the estimated
seismic hazard.
