Time‐Dependent Probabilistic Seismic Hazard Analysis for Seismic Sequences Based on Hybrid Renewal Process Models

Probabilistic seismic hazard analysis (PSHA) is a methodology with a long history and has been widely implemented. However, in the conventional PSHA and sequence‐based probabilistic seismic hazard analysis (SPSHA) approaches, the occurrence of mainshocks is modeled as the homogeneous Poisson process, which is unsuitable for large earthquakes. To account for the stationary occurrence of small‐to‐moderate (STM) mainshocks and the nonstationary behavior of large mainshocks, we propose a time‐dependent sequence‐based probabilistic seismic hazard analysis (TD‐SPSHA) approach by combining the time‐dependent mainshock probabilistic seismic hazard analysis (TD‐PSHA) and aftershock probabilistic seismic hazard analysis, consisting of four components: (1) STM mainshocks, (2) aftershocks associated with STM mainshocks, (3) large mainshocks, and (4) aftershocks associated with large mainshocks. The approach incorporates an exponential‐magnitude, exponential‐time model for STM mainshocks, and a renewal‐time, characteristic‐magnitude model for large mainshocks to assess the time‐dependent hazard for mainshocks. Then nonhomogeneous Poisson process is used to model the occurrence of associated aftershocks, in which the aftershock sequences can be modeled using the Reasenberg and Jones (RJ) model or the epidemic‐type aftershock sequence (ETAS) model. To demonstrate the proposed TD‐SPSHA approach, a representative site of the San Andreas fault is selected as a benchmark case, for which five time‐dependent recurrence models, including normal, lognormal, gamma, Weibull, and Brownian passage time (BPT) distributions, are chosen to determine the occurrence of large mainshocks. Then sensitivity tests are presented to show the effects on TD‐SPSHA, including (1) time‐dependent recurrence models, (2) mainshock magnitude, (3) rupture distance, (4) aftershock duration, (5) escaped time since the last event, and (6) future time interval. Furthermore, the bimodal hybrid renewal model is utilized by TD‐SPSHA for another case site. The comparison results illustrate that the sequence hazard analysis approach ignoring time‐varying properties of large earthquakes for long periods and the effects of associated aftershocks will result in a significantly underestimated hazard. The TD‐SPSHA‐based hazard curves using the ETAS model are larger than those of the RJ model. The proposed TD‐SPSHA approach may be of significant interest to the field of earthquake engineering, particularly in the context of structural design or seismic risk analysis for the long term.