عنوان مقاله [English]
This work aims at the assessment of the occurrence probability of future earthquakes, taking into account Coulomb stress changing based on the time-dependent models. The influence of Coulomb stress changing on the occurrence probability of characteristic earthquakes is computed, taking into account both permanent (clock advance) and transient (rate-and-state) Coulomb perturbations. Calculations are based to the time elapsed since the last characteristic earthquake on a fault and to the history of the following events. For this purpose, earthquakes with magnitude Mw≥5.8 are applied. Then, by using the BPT and the Weibull models, the occurrence probability of characteristic earthquakes for the 10, 30 and 50 year periods are estimated. The Zagros region included in the rectangle of coordinates 27-31.2 N° and 49.6-53.4 E° and faults such as Kazerun, Borazjan, Sabzpushan, Qir, Karebas and parts of MFF and ZFF were selected. For calculating coulomb stress, Coulomb 3.3 software was used.
Time-dependent models called renewal models, have been applied to investigate shocks on single faults [1-2] or in seismic sources that include, in addition to the main fault where the characteristic earthquake is generated [3-4]. In the renewal processes, the conditional probability of the next large earthquake, given that it has not happened yet, varies with time and is small shortly after the last one and then increases with time. In recent years, many models for earthquake occurrence probability were proposed. This study used BPT and Weibull models. Weibull distribution is one of the most widely used lifetime distributions in a wide range of engineering applications [5-6]. The Weibull distribution has also been widely used for specifying the distribution of earthquake recurrence times  and follows from both damage mechanics and statistical physics. For computing probabilities with Weibull distribution, γ parameter is needed that is the shape parameter of the distribution, defined as the inverse of the coefficient of variation .
Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. More recently, the Brownian Passage Time (BPT) model, assumed to adequately represent the earthquake recurrence time distribution, has been proposed to describe the probability distribution of inter-event times . One of the important properties of this model is that with increasing time since the last event, the BPT hazard rate decreases toward a non-zero constant asymptote . The expected recurrence time Tr is the necessary piece of information. Besides, a parameter as the coefficient of variation (also known as aperiodicity) α , defined as the ratio between the standard deviation and the average of the recurrence times, is required. In this study, Cv values 0.5 and 0.75 were used for individual faults as Yakovlev et al. .
As we are dealing mainly with events, for which details as fault shape and slip heterogeneity are not known, rectangular faults with uniform stress shop distribution are assumed . For modeling faults and calculating stress changes due to earthquakes, fault parameters like strike, dip, rake, rupture dimensions and receiver fault mechanism are necessary for all the triggering sources. Moreover, the rupture length and rupture width are required. In most cases in this study, these two parameters are indistinctive, so Wells and Coppersmith  empirically relations were used for computing rupture length and width.
Characteristic earthquake yearly rate was computed by using the relation given by Field et al. . Then by inversing obtained amounts, the mean recurrence time of earthquakes could be computed. The effect of Coulomb stress change on the probability for the future characteristic event can be considered from two viewpoints . The first idea is that the stress change can be equivalent to a modification of the expected mean recurrence time, Tr to the T'r, the second view point works on the idea that the time elapsed since the previous earthquake is modified t to the t'r by a shift proportional to ΔCFF. According to Stein et al. , both methods yield similar results nearly. In this study, the alternative between the first and the second view has been decided in favor of the second one. By substitution of t' into the hazard function, the probability modified by the permanent effect (P-mod) of the subsequent earthquakes were calculated.
Khodaverdian et al.  calculated shear strain rate for the most of the faults in the Iranian Plateau. These values have been used for the calculation of tectonic stressing rate 𝜏̇. For computing the probability obtained from the sum of the permanent and the transient effect (P-trans), we would have aftershock duration (ta) and Aσ parameters. The obtained amount of aftershock duration by using window algorithm for aftershocks according to Gardner and Knopoff method is 1.4 year. Accordingly, by using ta and tectonic stressing rate, Aσ parameter was obtained for each fault.
Taking into account the effects of earthquakes stress change, caused changing the results of conditional probabilities that obtained from both models, so that in some of the seismogenic sources increased probability result and in others decreased. The result shows that the probabilities obtained from the sum of the permanent and transient effect are generally smaller than the conditional probabilities obtained from the permanent effect only. This is due to the assumption of constant background rate made for the application of the rate-and-state model. The maximum obtained probability is related to the Kazerun fault that shows the high seismic activity of Kazerun fault. The uncertainties are treated in the parameters of each examined fault source, such as focal mechanism, mean recurrence time, magnitudes of earthquakes, epicenter coordinates and coefficient of variation in the statistical model. Taking into account these uncertainties by Monte Carlo technique will lead to more accurate results.