# 4. Probability Of Recurrence:. In The Present Study, Three

1613 WordsMar 26, 20177 Pages
4. Probability of recurrence: In the present study, three stochastic models (Weibull, Gamma and Lognormal) have been used for the estimation of probability of earthquake recurrence in Gujarat region of India which was rocked by the great earthquake in 2001. The earthquake data of the region has only five recurrence intervals of earthquakes magnitude ≥ 6 for the period of study, from 1819 to 2001, and is listed in Table 1. The estimated mean, standard deviation and aperiodicity (equivalent to the coefficient of variation) is 36.32, 12.49 years and 0.3438, respectively. The estimated model parameters of different distributions using method of moments (MOM) are listed in Table 2. The cumulative distribution of the time intervals is shown in…show more content…
60) from the last great earthquake of 2001 in Figure 3(a,b,c) for Weibull, Gamma and Lognormal models, respectively. These are the cumulative conditional probabilities that an earthquake will have occurred at a time = t +  after the last earthquake if it has not occurred at a time t. It is seen from these curves that the time difference between curves for different values of t at a particular probability is smallest for the Wiebull, largest for the Lognormal and intermediate for the Gamma model. From the analysis we can also determine the waiting times, , to the next great earthquake corresponding to a specified probability of occurrence as a function of the time since the last great earthquake occurred, t. This dependence is given in Fig. 4 for all the models. The median waiting times , p(/t)=0.5, to the next great earthquake as a function of the time t since the last great earthquake is shown in this figure for all the models. It is clear from the figure that all the models have median waiting time closely, though, the Weibull model estimates little more median waiting time as compared to rest of the Gamma and Lognormal models. The maximum difference in the median waiting times are 1.77, 2.67 and 0.90 years between the Wibull and Gamma, Wibull and Lognormal, and Gamma and Lognormal models, respectively. All the three models have almost same median waiting times of