11:00 AM - 1:00 PM
[STT40-P03] Clustering of Earthquake Event Data Based on Space-Time Point Process Model Using Nonparametric Bayesian Method
Epidemic-Type Aftershock-Sequences (ETAS) model (Ogata 1988) is a point process model that is known as a major statistical method to analyze seismic activity from earthquake event data. The point process is a stochastic process that deals with a set of occurrence times of randomly occurring events, characterized by an intensity function that expresses the likelihood of an event occurring at each time. Later, the ETAS model was extended to include the location of the epicenter in addition to the time of occurrence (e.g., Kagan 1991, Musmeci & Vere-Jones 1992), and integrated into a space-time ETAS model (Ogata, 1998). Let the time of the earthquake be t1, t2, …, then the intensity function λ in the space-time ETAS model is expressed in the form λ(t,x,y)=μ(x,y)+Σi; tiγi (t,x,y), which is the sum of the time-independent term and the time-dependent term, where γi is a decreasing function of t, and the sum is taken for all earthquakes that occurred before time t. Thus, in the space-time ETAS model, seismic activity is divided into stationary seismic activity, in which the spatial distribution of intensity does not change over time, and non-stationary seismic activity, whose intensity decays with time. In this presentation, we refer to the former seismic activity as background seismic activity, and to the latter one as aftershock activity. To predict the location of future earthquakes from earthquake event data, it is important to analyze the background seismic activity by removing the influence of non-stationary aftershock activity. Zhuang et al. (2002) proposed a method using kernel estimation of the intensity function of background seismic activity μ(x,y).
In this presentation, we propose a method using the nonparametric Bayesian inference for estimating the background intensity function in the space-time ETAS model and evaluate the performance of the proposed method by using artificial data. In addition, we apply the proposed method to real data in the central and western Honshu area of Japan using the epicenter catalog compiled by the Japan Meteorological Agency, and we discuss the results. In the proposed method, we employ an infinite mixture Gaussian model to estimate the background intensity function. The infinite mixture Gaussian model is based on the assumptions that the function to be estimated is a weighted sum of an infinite number of Gaussian distributions, and each data is generated from one of an infinite number of them, thus the data set as a whole is generated from the mixture of a finite number of them. In contrast to the usual finite mixture Gaussian model, where the number of mixtures is fixed as a hyperparameter, the infinite mixture model estimates the number of mixtures itself, which allows for greater flexibility in modeling phenomena. This has a wide range of applications such as clustering of acoustic signals and topic analysis of text data. We estimate the intensity by a Bayesian method using an approximation algorithm called blocked Gibbs sampling (e.g., Ishwaran & James 2004, Shibue & Komaki 2017).
To verify the performance of the proposed method, we simulate seismic activities and generate earthquake events according to the model. We analyze the data by the conventional method of Zhuang et al. (2002) and our proposed method and compare the performance of the two methods by calculating the error between the estimated background intensity function and the true intensity function. The results show that the proposed method gives better estimates. In the conventional method, the estimated results of the background intensity are distributed in such a way that the values become sharply larger in certain areas due to the effect of aftershocks clustered in a small area near the occurrence of a big earthquake. In contrast, the proposed method estimates an intensity function that reflects the relatively sparse distribution of background seismic activity.
In this presentation, we propose a method using the nonparametric Bayesian inference for estimating the background intensity function in the space-time ETAS model and evaluate the performance of the proposed method by using artificial data. In addition, we apply the proposed method to real data in the central and western Honshu area of Japan using the epicenter catalog compiled by the Japan Meteorological Agency, and we discuss the results. In the proposed method, we employ an infinite mixture Gaussian model to estimate the background intensity function. The infinite mixture Gaussian model is based on the assumptions that the function to be estimated is a weighted sum of an infinite number of Gaussian distributions, and each data is generated from one of an infinite number of them, thus the data set as a whole is generated from the mixture of a finite number of them. In contrast to the usual finite mixture Gaussian model, where the number of mixtures is fixed as a hyperparameter, the infinite mixture model estimates the number of mixtures itself, which allows for greater flexibility in modeling phenomena. This has a wide range of applications such as clustering of acoustic signals and topic analysis of text data. We estimate the intensity by a Bayesian method using an approximation algorithm called blocked Gibbs sampling (e.g., Ishwaran & James 2004, Shibue & Komaki 2017).
To verify the performance of the proposed method, we simulate seismic activities and generate earthquake events according to the model. We analyze the data by the conventional method of Zhuang et al. (2002) and our proposed method and compare the performance of the two methods by calculating the error between the estimated background intensity function and the true intensity function. The results show that the proposed method gives better estimates. In the conventional method, the estimated results of the background intensity are distributed in such a way that the values become sharply larger in certain areas due to the effect of aftershocks clustered in a small area near the occurrence of a big earthquake. In contrast, the proposed method estimates an intensity function that reflects the relatively sparse distribution of background seismic activity.