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.
BleiDM and JordanMI (2004) Variational methods for the Dirichlet process. In Proceedings of the 21st International Conference on Machine Learning, Banff, Canada, page 12. New York,NY: ACM.
2.
BrayA and SchoenbergFP (2013) Assessment of point process models for earthquake forecasting. Statistical Science, 28, 510–20.
3.
BrehmDJ and BraileLW (1998). Intermediate-term earthquake prediction using precursory events in the New Madrid seismic zone. Bulletin of the Seismological Society of America, 88, 564–80.
4.
CalaisE, FreedA, Van ArsdaleR and SteinS (2010) Triggering of New Madrid seismicity by late-pleistocene erosion. Nature, 466, 608.
5.
CongdonP (2007) Bayesian Statistical Modelling. Vol. 704. West Sussex: John Wiley & Sons.
6.
CramerCH (2001) A seismic hazard uncertainty analysis for the New Madrid seismic zone. Engineering Geology, 62, 251–66.
7.
CramerCH and BoydOS (2014) Why the New Madrid earthquakes are m 7–8 and the Charleston earthquake is m 7. Bulletin of the Seismological Society of America, 104, 2884–2903.
8.
CsontosR and VanArsdale R (2008). New Madrid seismic zone fault geometry. Geosphere, 4, 802–13.
9.
CsontosR, Van ArsdaleR, CoxR and WaldronB (2008) Reelfoot rift and its impact on quaternary deformation in the central Mississippi river valley. Geosphere, 4, 145–58.
10.
DahlD (2006) Model-based clustering for expression data via a Dirichlet process mixture model.In Bayesian Inference for Gene Expression and Proteomics, edited by DoKim-Anh, M¨llerPeter and VannucciMarina, pages 201–18. Cambridge:Cambridge University Press.
11.
ErisogluM, CalisN, ServiT, ErisogluU and TopaksuM (2011) The mixture distribution models for interoccurence times of earthquakes. Russian Geology and Geophysics, 52, 737–44.
12.
FanW and BouguilaN (2013). Variational learning of a Dirichlet process of generalized Dirichlet distributions for simultaneous clustering and feature selection. Pattern Recognition, 46, 2754–69.
13.
FergusonTS (1973) A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1, 209–30.
14.
GrillenzoniC (2019) Local curve and surface detection in spatial data using Gaussian mixtures. GEM-International Journal on Geomathematics, 10, 19.
15.
GutenbergB and RichterCF (1956) Earthquake magnitude, intensity, energy, and accelera- tion: (Second paper). Bulletin of the Seismo- logical Society of America, 46, 105–45.
16.
HebdenJS and SteinS (2009) Time-dependent seismic hazard maps for the New Madrid seismic zone and Charleston, South Carolina, areas. Seismological Research Letters, 80, 12–20.
17.
HuG, HufferF and ChenM-H (2019) New development of Bayesian variable selection criteria for spatial point process with applications. arXiv preprint arXiv:1910.06870.
18.
HuangR, YuG, WangZ, ZhangJ and ShiL (2013) Dirichlet process mixture model for document clustering with feature partition. IEEE Transactions on Knowledge and Data Engineering, 25, 1748–59.
19.
JuliaJ, HerrmannRB, AmmonCJ and AkinciA (2004) Evaluation of deep sediment velocity structure in the New Madrid seismic zone. Bulletin of the Seismological Society of America, 94, 334–40.
20.
KamatR and KamathR (2017) Earthquake cluster analysis: K-means approach. Journal of Chemical and Pharmaceutical Sciences, 10, 250–53.
21.
KennerSJ and SegallP (2000) A mechanical model for intraplate earthquakes: Application to the New Madrid seismic zone. Science, 289, 2329–32.
22.
KuyukH, YildirimE, DoganE and HorasanG (2012) Application of k-means and Gaussian mixture model for classification of seismic activities in Istanbul. Nonlinear Processes in Geophysics, 19, 411–19.
23.
MalyshevA (2016) Estimating the predictability of the seismicity rate: The 1964 eruption of Shiveluch volcano. Journal of Volcanology and Seismology, 10, 347–59.
24.
McKennaJ, SteinS and SteinCA (2007) Is the New Madrid seismic zone hotter and weaker than its surroundings?Special Papers: Geological Society of America, 425, 167.
25.
NealRM (2000) Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9, 249–65.
26.
NewmanA, SteinS, WeberJ, EngelnJ, MaoA and DixonT (1999) Slow deformation and lower seismic hazard at the New Madrid seismic zone. Science, 284, 619–21.
27.
NoviantiP, SetyoriniD and RaesiaU (2017) K-means cluster analysis in earthquake epicenter clustering. International Journal of Advances in Intelligent Informatics, 3, 81–9.
28.
OgataY (1998) Space-time point-process models for earthquake occurrences. Annals of the Institute of Statistical Mathematics, 50, 379–402.
29.
OmoriF (1894) On the after-shocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo, 7, 111–20.
30.
OtariG and KulkarniR (2012) A review of application of data mining in earthquake prediction. International Journal of Computer Science and Information Technologies, 3, 3570–74.
31.
RamdaniF, KettaniO and TadiliB (2015) Evidence for subduction beneath Gibraltar Arc and Andean regions from k-means earthquake centroids. Journal of Seismology, 19, 41–53.
32.
RhoadesDA (2013) Mixture models for improved earthquake forecasting with short-to-medium time horizons. Bulletin of the Seismological Society of America, 103, 2203–15.
33.
RhoadesDA and GerstenbergerMC (2009) Mixture models for improved short-term earthquake forecasting. Bulletin of the Seismological Society of America, 99, 636–46.
34.
SchoenbergFP (2003) Multidimensional residual analysis of point process models for earthquake occurrences. Journal of the American Statistical Association, 98, 789–95.
35.
SpiegelhalterDJ, BestNG, CarlinBP and Van Der LindeA (2002) Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64, 583–639.
36.
UtsuT, OgataY, RitsukoS and Matsu'ura (1995) The centenary of the Omori formula for a decay law of aftershock activity. Journal of Physics of the Earth, 43, 1–33.
37.
VeenA and SchoenbergFP (2006) Assessing spatial point process models using weighted K-functions: Analysis of California earthquakes. In Case Studies in Spatial Point Process Modeling, edited by BaddeleyA, GregoriP, MateuJ, StoicaR and StoyanD, pages 293–306. New York, NY: Springer.
38.
ZhangZ, DaiG and JordanM (2010) Matrix-variate Dirichlet process mixture models. Journal of Machine Learning Research ’ Proceedings Track, 9, 980–87.
39.
ZobackMD and ZobackML (1991) Tectonic stress field of North America and relative plate motions. Neotectonics of North America, 1, 339–66.
40.
ZobackML (1992) Stress field constraints on intraplate seismicity in eastern North America. Journal of Geophysical Research: Solid Earth, 97, 11761–782.
41.
ZobackML and ZobackMD (1989). Tectonic stress field of the continental United States. Geophysical Framework of the Continental United States: Geological Society of America Memoir, 172, 523–39.
