Estimation of earthquake hazard parameters from incomplete data files. Part III. Incorporation of uncertainty of earthquake-occurrence model

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.