Hidden Markov Models for Low-Frequency Earthquake Recurrence

Abstract

Low-frequency earthquakes (LFEs) are small magnitude earthquakes with frequencies of 1–10 Hertz which often occur in overlapping sequence forming persistent seismic tremors. They provide insights into large earthquake processes along plate boundaries. LFEs occur stochastically in time, often forming temporally recurring clusters. The occurrence times are typically modeled using point processes and their intensity functions. We demonstrate how to use hidden Markov models coupled with visualization techniques to model inter-arrival times directly, classify LFE occurrence patterns along the San Andreas Fault, and perform model selection. We highlight two subsystems of LFE activity corresponding to periods of alternating episodic and quiescent behavior.

Keywords:

• Classification
• Model selection
• San Andreas fault
• Visualization
• Viterbi path

Supplementary Materials

The supplementary material contains (i) R code used for the analysis, (ii) tables of results for gamma, Weibull, log-normal and normal hidden Markov models in Section 4.1, (iii) additional pseudo-residual plots and sojourn checks for Section 4.1, (iv) additional probability density plots and plot of state splitting sequence for Section 4.3, (v) Viterbi path visualizations for the entire observation period and years 2005, 2006, and 2007 for Section 4.4, (vi) sojourn checks for subsystems in Section 4.5.

Acknowledgments

The authors wish to thank Jodie Buckby for sharing code to fit and optimize hidden Markov models, and providing general assistance. We are grateful to Marco Brenna for advice regarding geological interpretations, visualization, and additional edits. The authors also wish to acknowledge the use of New Zealand eScience Infrastructure (NeSI) high performance computing facilities and consulting support as part of this research. New Zealand’s national facilities are provided by NeSI and funded jointly by NeSI’s collaborator institutions and through the Ministry of Business, Innovation & Employment’s Research Infrastructure program. URL https://www.nesi.org.nz. The authors acknowledge the suggestions of two anonymous reviewers in enhancing this article.

Disclosure Statement

The authors report that there are no competing interests to declare.