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

摘要

Most probabilistic seismic-hazard analysis procedures require that at leastthree seismic source parameters be known, namely the mean seismic activity rate λ, theGutenberg–Richter b-value, and the area-characteristic (seismogenic source) maximumpossible earthquake magnitudemmax. In almost all currently used seismic-hazard assessmentprocedures that utilize these three parameters, it is explicitly assumed that all threeremain constant over time and space. However, closer examination of most earthquakecatalogs has indicated that significant spatial and temporal variations existed in theseismic activity rate λ, as well as in the Gutenberg–Richter b-value. In this study, themaximum likelihood estimation of these earthquake hazard parameters considersthe incompleteness of the catalogs, the uncertainty in the earthquake magnitude determination,as well as the uncertainty associated with the applied earthquake-occurrencemodels. The uncertainty in the earthquake-occurrence models is introduced by assumingthat both the mean seismic activity rate λ and the Gutenberg–Richter b-value arerandom variables, each described by the gamma distribution. This approach results inthe extension of the classic frequency–magnitude Gutenberg–Richter relation and thePoisson distribution of the number of earthquakes with their compounded counterparts(Benjamin, 1968; Campbell, 1982, 1983). The proposed procedure was applied in theestimation of the seismicity parameters in an area that had experienced the strongest andmost devastating earthquake in contemporary South African history, namely the 29September 1969 Mw 6.3 Ceres–Tulbagh event. In this example, it was shown that theintroduction of uncertainty in the earthquake-occurrence model reduced the mean returnperiods, leading to an increase of the estimated seismic hazard. Additionally, this studyconfirmed 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 estimatedseismic hazard.