Analysing the Interevent Time Distribution to Identify Seismicity Phases: A Bayesian Nonparametric Approach to the Multiple-Changepoint Problem

Abstract

In the study of earthquakes, several aspects of the underlying physical process, such as the time non-stationarity of the process, are not yet well understood, because we lack clear indications about its evolution in time. Taking as our point of departure the theory that the seismic process evolves in phases with different activity patterns, we have attempted to identify these phases through the variations in the interevent time probability distribution within the framework of the multiple-changepoint problem. In a nonparametric Bayesian setting, the distribution under examination has been considered a random realization from a mixture of Dirichlet processes, the parameter of which is proportional to a generalized gamma distribution. In this way we could avoid making precise assumptions about the functional form of the distribution. The number and location in time of the phases are unknown and are estimated at the same time as the interevent time distributions. We have analysed the sequence of main shocks that occurred in Irpinia, a particularly active area in southern Italy: the method consistently identi®es changepoints at times when strong stress releases were recorded. The estimation problem can be solved by stochastic simulation methods based on Markov chains, the implementation of which is improved, in this case, by the good analytical properties of the Dirichlet process.

Statistical identification of seismicity phases

“…In this study, we have assigned to the parameters of the prior distributions the following values: a 0 = 3, b 0 = 1, c 0 = 18, d 0 = 11, g 0 = 1.25, h 0 = 11, f 0 = 8 and M = 260; for the criterion of choice, we refer to Pievatolo & Rotondi (2000).…”

“…We note that less than 4 hr separate the shock of M S = 7.1 at t 17 from that at t 32 , and the quakes in 1931 March were little over a day apart. In this study, we have assigned to the parameters of the prior distributions the following values: a 0 = 3, b 0 = 1, c 0 = 18, d 0 = 11, g 0 = 1.25, h 0 = 11, f 0 = 8 and M = 260; for the criterion of choice, we refer to Pievatolo & Rotondi (2000).…”

“…Considering the parameters θ , ω as random variables, each distribution F is distributed as a mixture of Dirichlet processes. The model is described in greater detail in Pievatolo & Rotondi (2000), where a method is proposed to assign the hyperparameters of the priors on the parameters of the generalized gamma distribution.…”

Sequential Kernel Estimation of the Conditional Intensity of Nonstationary Point Processes

“…From a statistical viewpoint, however, dropping data is a complex and controversial issue, at least as the design of window size. For example, Pievatolo and Rotondi (2000) claim that for events of magnitude Z = 5 the radius should be 30 km only. Figure 1 provides descriptive plots.…”

Comparative seismic hazard analysis of two Spanish regions

“…It is important to highlight that nonparametric methods can be valuable supplements to several conventional parametric approaches, and they can also be a good first step in an exploratory data analysis. Nowadays, there exist a lot of references related to nonparametric estimation applied to earthquake data [18][19][20][21][22][23][24].…”