Change Point Analysis in Earthquake Data

Abstract

Earthquake forecasts are very important in human life in terms of estimating hazard and managing emergency systems. Defining of earthquake characteristics plays an important role in these forecasts. Of these characteristics, one is the frequency distribution of earthquakes and and the other is the magnitude distribution of the earthquakes. Each statistical distribution has many parameters describing the actual distribution. There are various statistical distributions used to model the earthquake numbers. As is well known, these are binomial, Poisson, geometric and negative binomial distributions. It is generally assumed that earthquake occurrences are well described by the Poisson distribution because of its certain characteristics (for some details, see Kagan, 2010; Leonard & Papasouliotis, 2001). In their study, Rydelek & Sacks (1989) used the Poisson distribution of earthquakes at any magnitude level. The Poisson distribution is generally used for earthquakes of a large magnitude, and the earthquake occurrences with time/space can be modeled with the Poisson process in which, as is known, the Poisson distribution is one that counts the events that have occurred over a certain period of time. There is a significant amount of research on the change point as applied to earthquake data. Amorese (2007) used a nonparametric method for the detection of change points in frequency magnitude distributions. Yigiter & Inal (2010) used earthquake data for their method developed for the estimator of the change point in Poisson process. Aktas et al. (2009) investigated a change point in Turkish earthquake data. Rotondi & Garavaglia (2002) applied the hierarchical Bayesian method for the change point in data, taken from the Italian NT4.1.1 catalogue. Recently, much research in the literature has focused on whether there is an increase in the frequency of earthquake occurrences. It is further suggested that any increase in the frequency of earthquakes, in some aspects, is due to climate change in the world. There is considerable debate on whether climate change really does increase the frequency of natural disasters such as earthquakes and volcano eruptions. In many studies, it is emphasized that there is serious concern about impact of climate change on the frequencies of hazardous events (Peduzzi, 2005; Lindsey, 2007; Mandewille, 2007 etc.). In Peduzzi’s study (2005), there are some indicators about increasing number of the earthquakes especially affecting human settlements, and it is also reported that there is an increase in the percentage of earthquakes affecting human settlements from 1980 onwards. The change point analysis can be used to study the increase or decrease in the frequency of the earthquake occurrences.