Abstract
Statistical properties of earthquake interevent times have long been the topic of interest to seismologists and earthquake professionals, mainly for hazard-related concerns. In this paper, we present a comprehensive study on the temporal statistics of earthquake interoccurrence times of the seismically active Kachchh peninsula (western India) from thirteen probability distributions. Those distributions are exponential, gamma, lognormal, Weibull, Levy, Maxwell, Pareto, Rayleigh, inverse Gaussian (Brownian passage time), inverse Weibull (Frechet), exponentiated exponential, exponentiated Rayleigh (Burr type X), and exponentiated Weibull distributions. Statistical inferences of the scale and shape parameters of these distributions are discussed from the maximum likelihood estimations and the Fisher information matrices. The latter are used as a surrogate tool to appraise the parametric uncertainty in the estimation process. The results were found on the basis of two goodness-of-fit tests: the maximum likelihood criterion with its modification to Akaike information criterion (AIC) and the Kolmogorov-Smirnov (K-S) minimum distance criterion. These results reveal that (i) the exponential model provides the best fit, (ii) the gamma, lognormal, Weibull, inverse Gaussian, exponentiated exponential, exponentiated Rayleigh, and exponentiated Weibull models provide an intermediate fit, and (iii) the rest, namely Levy, Maxwell, Pareto, Rayleigh, and inverse Weibull, fit poorly to the earthquake catalog of Kachchh and its adjacent regions. This study also analyzes the present-day seismicity in terms of the estimated recurrence interval and conditional probability curves (hazard curves). The estimated cumulative probability and the conditional probability of a magnitude 5.0 or higher event reach 0.8–0.9 by 2027–2036 and 2034–2043, respectively. These values have significant implications in a variety of practical applications including earthquake insurance, seismic zonation, location identification of lifeline structures, and revision of building codes.
Highlights
The Kachchh (Kutch) province of Gujarat, northwestern India, is a unique stable continental region (SCR) of the world that has experienced two large intraplate earthquakes within a span of 182 years (Mw 7.8 in 1819 and Mw 7.7 in 2001)
Earthquake studies based on physical and geological models are useful; the current paper focuses on empirical earthquake recurrence modeling
In order to calculate the conditional probability of an earthquake for a known elapsed time τ, we introduce a random variable V, corresponding to a waiting time v
Summary
The Kachchh (Kutch) province of Gujarat, northwestern India, is a unique stable continental region (SCR) of the world that has experienced two large intraplate earthquakes within a span of 182 years (Mw 7.8 in 1819 and Mw 7.7 in 2001). The most disastrous Mw 7.7 (intensity X+ on the modified Mercalli intensity (MMI) scale) Republic Day Bhuj earthquake along the NWF (08:46 IST, January 26, 2001; epicentral location: 23.412° N, 70.232° E; focal depth: 23 km) caused 13,819 human deaths, US $10 billion economic loss, and damaged over one million houses (Rastogi 2001) Another large event, the 1819 Rann of Kachchh earthquake (Mw 7.8), occurred along the ABF and created fault scarp approximately 4 to 6 m high in this region (Rajendran and Rajendran 2001; Morino et al 2008). The present study contributes to this body of work by estimating earthquake recurrence intervals and associated hazards in a probabilistic environment
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