Statistical Modelling 22 (4) (2022), 245–272

A matrix-variate dirichlet process to model earthquake hypocentre temporal patterns

Meredith A Ray,
Division of Epidemiology,
Biostatistics and Environmental Health,
University of Memphis School of Public Health,
Memphis, Tennessee,
USA.
e-mail: maray@memphis.edu

Dale Bowman,
Department of Mathematical Sciences,
University of Memphis,
Memphis, Tennessee,
USA.

Ryan Csontos,
Department of Earth Sciences,
University of Memphis,
Memphis, Tennessee,
USA.

Roy B. Van Arsdale,
Department of Earth Sciences,
University of Memphis,
Memphis, Tennessee,
USA.

Hongmei Zhang,
Division of Epidemiology,
Biostatistics and Environmental Health,
University of Memphis School of Public Health,
Memphis, Tennessee,
USA.

Abstract:

Earthquakes are one of the deadliest natural disasters. Our study focuses on detecting temporal patterns of earthquakes occurring along intraplate faults in the New Madrid seismic zone (NMSZ) within the middle of the United States from 1996–2016. Based on the magnitude and location of each earthquake, we developed a Bayesian clustering method to group hypocentres such that each group shared the same temporal pattern of occurrence. We constructed a matrix-variate Dirichlet process prior to describe temporal trends in the space and to detect regions showing similar temporal patterns. Simulations were conducted to assess accuracy and performance of the proposed method and to compare to other commonly used clustering methods such as Kmean, Kmedian and partition-around-medoids. We applied the method to NMSZ data to identify clusters of temporal patterns, which represent areas of stress that are potentially migrating over time. This information can then be used to assist in the prediction of future earthquakes.

Keywords:

Bayesian, Dirichlet process, Earthquake, hypocentres, spatial clustering

Downloads:

Example code and a movie in zipped archive.

Movie caption: The New Madrid seismic zone hypocenter locations color-coded by cluster assignment. Clusters were identified using the linear Dirichlet Process methodology. Blue dots denote the center of each cluster and were calculated using the average time within each cluster. Purple dots are city locations labeled in Figures 2 and 3. Note: Adobe Flash Player is needed to play the video.

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