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In earthquake occurrence studies, the so-called q value can be considered both as one of the parameters describing the distribution of interevent times and as an index of
non-extensivity. Using simulated datasets, we compare four kinds of estimators, based on principle of maximum entropy (POME),
method of moments (MOM), maximum likelihood (MLE), and probability weighted moments (PWM) of the parameters (q and τ
0) of the distribution of inter-events times, assumed to be a generalized Pareto distribution (GPD), as defined by Tsallis
(1988) in the frame of non-extensive statistical physics. We then propose to use the unbiased version of PWM estimators to
compute the q value for the distribution of inter-event times in a realistic earthquake catalogue simulated according to the epidemic type
aftershock sequence (ETAS) model. Finally, we use these findings to build a statistical emulator of the q values of ETAS model. We employ treed Gaussian processes to obtain partitions of the parameter space so that the resulting
model respects sharp changes in physical behaviour. The emulator is used to understand the joint effects of input parameters
on the q value, exploring the relationship between ETAS model formulation and distribution of inter-event times. 相似文献
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