Fitting Hidden Markov Model to Earthquake Data: A Case Study in the Aegean Sea

Year 2021, Volume: 11 Issue: 1, 44 - 53, 09.06.2021

Özgür Danışman Umay Kocer

Abstract

Studies about stochastic modeling of earthquake data have increased considerably in recent years. It is a well-known fact that earthquakes occur as a result of unobservable changes in underground stress levels. The hidden Markov model provides a suitable framework for modeling earthquake data due to its assumptions. We present a hidden Markov model to examine hidden changes in the underground stress level and to make some probabilistic earthquake forecasts in the Aegean Sea. The Aegean region is selected for the modeling because of the active nature of earthquake occurrences. A hidden Markov chain is defined in which the corresponding states are stress levels of the ground. Four models with different numbers of hidden states are constructed and compared according to the Akaike and Bayesian information criteria. The proposed model is capable of forecasting the short-term probabilities of both earthquake magnitudes and also locations. Baum-Welch algorithm, which is an iterative expectation-maximization algorithm, is used for the estimation of model parameters. The traditional Baum-Welch algorithm considers only one variable as an observation for the iterations. In this paper, a naive and quite simple approach is used for the Baum-Welch algorithm to estimate the model parameters with more than one observation. It is possible to obtain the marginal and joint probability distributions of multiple observations with this approach.

Keywords

Hidden Markov model, Baum-Welch algorithm, Multiple observations, Earthquake, Forecasting, Aegean Sea

Thanks

The authors would like to thank the anonymous referees for their invaluable and helpful comments for the improvement of the study.

Saklı Markov Modelinin Deprem Verilerine Uygulanması: Ege Denizinde Bir Örnek Olay

Abstract

Deprem verilerinin olasılıksal modellemesi ile ilgili çalışmalar son yıllarda giderek artmaktadır. Depremlerin yer altındaki gerilim düzeyindeki gözlenemeyen değişimler sonucu oluştukları bilinen bir gerçektir. Saklı Markov modelleri varsayımlarından dolayı deprem verilerini modellemek için uygun bir çerçeve sunar. Yeraltı gerilim düzeyindeki gözlenemeyen değişimleri göz önünde bulundurmak ve Ege denizinde bazı olasılıksal deprem tahmini yapmak için gizli Markov modeli sunmaktayız. Ege bölgesi, deprem oluşumu bakımından aktif bir bölge olduğu için seçilmiştir. Gizli durumları yeraltı stres düzeyi olan bir gizli Markov modeli tanımlanmıştır. Gizli durum sayıları farklı olan dört ayrı model tanımlanmış ve bu modeler Akaike ve Bayesian bilgi kriterlerine göre karşılaştırılmıştır. Önerilen model deprem büyüklükleri ve bölgelerine ilişkin kısa dönem olasılık tahminleri verebilmektedir. Model parametrelerini tahmin etmek için iteratif bir algoritma olan Baum-Welch algoritması kullanılmıştır. Geleneksel Baum-Welch algoritması iterasyonlarda yalnız bir gözlem değişkeni kullanır. Bu çalışmada, Baum-Welch algoritmasının birden fazla gözlem değişkeni bulunduğunda kullanımı için oldukça kolay ve anlaşılır bir bakış açısı önerilmiştir. Bu yaklaşımla çoklu gözlem değişkenlerinin marjinal ve ortak olasılık fonksiyonlarını elde etmek mümkün olmaktadır.

Keywords

Saklı Markov modeli, Baum-Welch algoritması, Çoklu gözlem, Deprem, Tahmin, Ege Denizi

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