Bulletin of the Seismological Society of America, Vol. 74, No. 6, pp. 2593-2611, December 1984 STOCHASTIC TIME-PREDICTABLE MODEL FOR EARTHQUAKE OCCURRENCES BY T . ANAGNOS AND A. S. KIREMIDJIAN ABSTRACT Recent geophysical studies have indicated that an earthquake recurrence interval and the size of the preceding event are positively correlated. This observation is the basis for the deterministic time-predictable recurrence model of Shimazaki and Nakata. Using the basic assumptions of the time-predictable recurrence model, we develop a stochastic model of earthquake occurrence that incorporates temporal dependence. This paper discusses the formulation of the model and the effect of including temporal dependence. Hazard estimates for a section of the San Andreas fault near Parkfield, where data has suggested time- predictable behavior, are obtained for illustrative purposes. Comparisons are made with the Poisson model. Results indicate that currently used Poisson models may give lower estimates of the seismic hazard when there has been a seismic gap. Of the various sensitivity analyses performed, it is observed that slip rate has the largest effect on exceedence probabilites computed from the stochastic time-predictable model. Therefore, accurate determinations of slip rates (both seismic and aseismic) can substantially reduce the uncertainty in seismic hazard estimates. INTRODUCTION Consideration of the temporal and spatial patterns of earthquake occurrence is an important aspect of seismic hazard analysis and has drawn much attention. Many of the techniques currently used for hazard evaluation rest on the Poisson assumptions for earthquake occurrences (Cornell, 1968). Although a Poisson model isan adequate description for some available occurrence data (Gardner and Knopoff, 1974), the independence assumptions are not consistent with any geophysical description of the earthquake generating process. A model which isbased on physical concepts and which leads to more accurate estimates of earthquake occurrence probabilities is desirable in seismic hazard analysis. Recent developments in seismology and geophysics have lead to two alternative representations for earthquake recurrence patterns. These include the "time-pre- dictable" and "slip-predictable" models (Bufe et al., 1977; Shimazaki and Nakata, 1980; Sykes and Quittmeyer, 1981). In this paper, the time-predictable assumptions are used to develop a stochastic model for earthquake occurrence. The main characteristic of this model is that the time of occurrence of a future earthquake event depends on the size and the time of occurrence of the last event. Thus, the larger the last earthquake, the longer the time to the next earthquake. In contrast, the slip-predictable hypothesis is based on the assumption that the size of the last event has no effect on subsequent occurrences, and the time to the next occurrence is random. The size of the next event, however, is positively correlated with the elapsed time since the last earthquake occurrence. A stochastic formulation for the slip-predictable model was presented by the authors in an earlierpaper (Kiremidjian and Anagnos, 1984). The hazard along a section of the San Andreas fault at Parkfield is computed for purposes of illustratingthe time-predictable stochastic model. The results from the proposed model are compared to those from the Poisson model. The comparison 2593