Seismic activity analysis of five major earthquake source segments in the Sumatra megathrust zone
Each segment and two adjacent segments points of view
DOI:
https://doi.org/10.5459/bnzsee.1555Abstract
The Sumatra megathrust zone has five major earthquake sources, namely the Aceh-Andaman, Nias-Simeulue, Mentawai-Siberut, Mentawai-Pagai, and Enggano segments. This paper provides seismic activity analysis in these five segments via an unobserved process study of tectonic plate movements, which is conducted in two cases: each of the five segments independently (Case 1), and a pair of two adjacent segments (Case 2). To do this, two specific types of Hidden Markov Models (HMMs), i.e., Poisson-HMMs and Copula-HMMs, dealing with unobserved process issues, are applied. In practice, the data used is the annual frequency of mainshock earthquakes with a magnitude of >4.6 that occurred from 1971 to 2018. This data is obtained by working out the declustering process and estimating the magnitude of completeness from a particular earthquake catalogue. Due to the incompleteness of the data sets, the parameters of the two HMMs are estimated using the Expectation-Maximization algorithm. Results show that for Case 1, the model that fits the data for each of the five segments is the 3-state Poisson-HMM. The three states, in this instance, stand for the rates of seismic activity that correspond to the dynamic level of tectonic plate movements. Furthermore, in Case 2, the selected model for the Aceh-Andaman with Nias-Simeulue is the 2-state Gumbel Copula-HMM. Meanwhile, for the three groups remaining, namely Nias-Simeulue with Mentawai-Siberut, Mentawai-Siberut with Mentawai-Pagai, and Mentawai-Pagai with Enggano, the appropriate models are Gaussian, Gumbel, and Frank Copulas, respectively. In this case, the number of states represents the seismic activity association of two adjacent segments that corresponds to the association level of two adjacent tectonic plate dynamics.
References
Reid A (2015). “History and Seismology in the Ring of Fire: Punctuating the Indonesian Past”. E-Book ISBN: 9789004288058, In Environment, Trade and Society in Southeast Asia Brill, 16pp. https://doi.org/10.1163/9789004288058_006 DOI: https://doi.org/10.1163/9789004288058_006
Irsyam M, Cummins PR, Asrurifak M, Faizal L, Natawidjaja DH. Widiyantoro S, Meilano I, Triyoso W, Rudiyanto A, Hidayati S, Ridwan M, Hanifa NR and Syahbana AJ (2020). “Development of the 2017 national seismic hazard maps of Indonesia”. Earthquake Spectra, 36: 112-136. https://doi.org/10.1177/8755293020951206 DOI: https://doi.org/10.1177/8755293020951206
McCaffrey R (2009). “The tectonic framework of the Sumatran subduction zone”. Annual Review of Earth and Planetary Sciences, 37: 345-366. https://doi.org/10.1146/annurev.earth.031208.100212 DOI: https://doi.org/10.1146/annurev.earth.031208.100212
Haridhi HA, Huang BS, Kuo-Liang W, Denzema D, Prasetyo RA and Chao-Shing L (2018). “A study of large earthquake sequences in the Sumatra subduction zone and its possible implications”. TAO: Terrestrial, Atmospheric and Oceanic Sciences, 29(6): 635-652. https://doi.org/10.3319/tao.2018.08.22.01 DOI: https://doi.org/10.3319/TAO.2018.08.22.01
Meisl CS, Safaie S., Elwood KJ, Gupta R and Kowsari R (2006). “Housing reconstruction in northern Sumatra after the December 2004 great Sumatra earthquake and tsunami”. Earthquake Spectra, 22(S3): 777-802. https://doi.org/10.1193/1.2201668 DOI: https://doi.org/10.1193/1.2201668
Bothara J, Beetham D, Brunsdon D, Stannard M, Brown R, Hyland C, Lewis W, Miller S, Sanders R and Sulistio Y (2010). “General observations of effects of the 30th September 2009 Padang earthquake, Indonesia”. Bulletin of the New Zealand Society for Earthquake Engineering, 43(3): 143-173. https://doi.org/10.5459/bnzsee.43.3.143-173 DOI: https://doi.org/10.5459/bnzsee.43.3.143-173
Sieh K (2007). “The Sunda megathrust—past, present and future”. Journal of Earthquake and Tsunami, 1(01): 1-19. https://doi.org/10.1142/S179343110700002X DOI: https://doi.org/10.1142/S179343110700002X
McCloskey J, Antonioli A, Piatanesi A, Sieh K, Steacy S, Nalbant S, Cocco M, Giunchi C, Huang J and Dunlop P (2008). “Tsunami threat in the Indian Ocean from a future megathrust earthquake west of Sumatra”. Earth and Planetary Science Letters, 265(1-2): 61–81. https://doi.org/10.1016/j.epsl.2007.09.034 DOI: https://doi.org/10.1016/j.epsl.2007.09.034
Tabei T, Kimata F, Ito T, Gunawan E, Tsutsumi H, Ohta Y, Yamashina T, Soeda Y, Ismail N, Nurdin I, Sugiyanto D and Meilano I (2015). “Geodetic and geomorphic evaluations of earthquake generation potential of the northern Sumatran fault, Indonesia”. In International Symposium on Geodesy for Earthquake and Natural Hazards (GENAH) 145: 21-28. Springer, Cham. https://doi.org/10.1007/1345_2015_200 DOI: https://doi.org/10.1007/1345_2015_200
Natawidjaja DH (2018). “Updating active fault maps and sliprates along the Sumatran Fault Zone, Indonesia”. In IOP Conference Series: Earth and Environmental Science, 118 (1): 012001. IOP Publishing. https://doi.org/10.1088/1755-1315/118/1/012001 DOI: https://doi.org/10.1088/1755-1315/118/1/012001
Duputel Z, Kanamori H, Tsai VC, Rivera L, Meng L, Ampuero JP and Stock JM (2012). “The 2012 Sumatra great earthquake sequence”. Earth and Planetary Science Letters, 351: 247-257. https://doi.org/10.1016/j.epsl.2012.07.017 DOI: https://doi.org/10.1016/j.epsl.2012.07.017
Uphoff C, Rettenberger S, Bader M, Madden EH, Ulrich T, Wollherr S and Gabriel AA (2017). “Extreme scale multi-physics simulations of the tsunamigenic 2004 sumatra megathrust earthquake”. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, pp.1-16. https://doi.org/10.1145/3126908.3126948 DOI: https://doi.org/10.1145/3126908.3126948
Panet I, Mikhailov V, Diament M, Pollitz F, King G, De Viron O, Holschneider M, Biancale R and Lemoine JM (2007). “Coseismic and post-seismic signatures of the Sumatra 2004 December and 2005 March earthquakes in GRACE satellite gravity”. Geophysical Journal International, 171(1): 177-190. https://doi.org/10.1111/j.1365-246x.2007.03525.x DOI: https://doi.org/10.1111/j.1365-246X.2007.03525.x
Pesicek JD, Thurber CH, Zhang H, DeShon HR, Engdahl ER and Widiyantoro S (2010). “Teleseismic double‐difference relocation of earthquakes along the Sumatra‐Andaman subduction zone using a 3‐D model”. Journal of Geophysical Research: Solid Earth, 115(B10): 1-20. https://doi.org/10.1029/2010jb007443 DOI: https://doi.org/10.1029/2010JB007443
Orfanogiannaki K, Karlis D and Papadopoulos GA (2010). “Identifying seismicity levels via Poisson hidden Markov models”. Pure Applied Geophysics, 167(8–9): 919–931. https://doi.org/10.1007/s00024-010-0088-y DOI: https://doi.org/10.1007/s00024-010-0088-y
Orfanogiannaki K, Karlis D and Papadopoulos GA (2014). “Identification of temporal patterns in the seismicity of Sumatra using Poisson Hidden Markov models”. Research in Geophysics, 4(4969): 1-6. https://doi.org/10.4081/rg.2014.4969 DOI: https://doi.org/10.4081/rg.2014.4969
Yip CF, Ng WL and Yau CY (2018). “A hidden Markov model for earthquake prediction”. Stochastic Environmental Research and Risk Assessment, 32(5): 1415-1434. https://doi.org/10.1007/s00477-017-1457-1 DOI: https://doi.org/10.1007/s00477-017-1457-1
Zucchini W, MacDonald IL and Langrock R (2017). “Hidden Markov Models for Time series: An Introduction Using R”. eBook ISBN 9781315372488, Chapman and Hall/CRC. https://doi.org/10.1201/b20790-2 DOI: https://doi.org/10.1201/b20790
Joe H (1997). “Multivariate Models and Multivariate Dependence Concepts”. eBook ISBN 9780367803896, CRC Press. https://doi.org/10.1201/9780367803896 DOI: https://doi.org/10.1201/9780367803896
Nelsen RB (2006). “An Introduction to Copulas. 2nd Edition”. ISBN 978-0387-28659-4, New York: Springer. https://doi.org/10.1007/0-387-28678-0 DOI: https://doi.org/10.1007/0-387-28678-0
Ogata Y (1999). “Seismicity analysis through point-process modeling: A review” page 471-507 in Seismicity Patterns, their Statistical Significance and Physical Meaning. Pageoph Topical Volumes, Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8677-2_14 DOI: https://doi.org/10.1007/978-3-0348-8677-2_14
Can C, Ergun G and Gokceoglu C (2014). “Prediction of earthquake hazard by hidden Markov model (around Bilecik, NW Turkey)”. Open Geosciences, 6(3): 403-414. https://doi.org/10.2478/s13533-012-0180-1 DOI: https://doi.org/10.2478/s13533-012-0180-1
Schweizer B and Sklar A (1983). “Probabilistic Metric Spaces”. ISBN 0-444-00666-4, North-Holland Series in Probability and Applied Mathematics. https://www.academia.edu/26211504/B_Schweizer_A_Sklar_Probabilistic_metric_spaces_Elsevier_North_Holland_New_York_1983_pdf
Denuit M and Lambert P (2005). “Constraints on concordance measures in bivariate discrete data”. Journal of Multivariate Analysis, 93(1): 40-57. https://doi.org/10.1016/j.jmva.2004.01.004 DOI: https://doi.org/10.1016/j.jmva.2004.01.004
Trivedi P and Zimmer D (2007). “Copula modeling: an introduction for practitioners”. Foundations and Trends in Econometrics, 1(1): 1-111. http://dx.doi.org/10.1561/0800000005 DOI: https://doi.org/10.1561/0800000005
Hofert M, Kojadinovic I, Mächler M and Yan J (2019). “Elements of copula modeling with R”. ISBN 978-3-319-89634-2. Springer. https://doi.org/10.1007/978-3-319-89635-9 DOI: https://doi.org/10.1007/978-3-319-89635-9
Stevens WL (1950). “Fiducial Limits of the parameter of a discontinuous distribution”. Biometrika 37: 117–129. https://doi.org/10.1093/biomet/37.1-2.117 DOI: https://doi.org/10.1093/biomet/37.1-2.117
Rizal J, Gunawan AY, Indratno SW and Meilano I (2021). “The application of Copula continuous extension technique for bivariate discrete data: A case study on dependence modeling of seismicity data”. Mathematical Modelling of Engineering Problems, 8(5): 793-804. https://doi.org/10.18280/mmep.080516 DOI: https://doi.org/10.18280/mmep.080516
Dempster AP, Laird NM and Rubin DB (1977). “Maximum likelihood from incomplete data via the EM algorithm”. Journal of the Royal Statistical Society: Series B (Methodological), 39(1): 1-22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x DOI: https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
Nasri BR, Rémillard BN and Thioub MY (2020). “Goodness‐of‐fit for regime‐switching copula models with application to option pricing”. Canadian Journal of Statistics, 48(1): 79-96. https://doi.org/10.1002/cjs.11534 DOI: https://doi.org/10.1002/cjs.11534
Thioub MY, Nasri BR, Pieugueu R and Rémillard BN (2020). “Package HMMcopula”. https://cran.r-project.org/web/packages/HMMcopula/HMMcopula.pdf
Forney GD (1973). “The viterbi algorithm”. Proceedings of the IEEE, 61(3): 268-278. https://doi.org/10.1109/PROC.1973.9030 DOI: https://doi.org/10.1109/PROC.1973.9030
Zhang L and Singh VP (2019). “Copulas and their applications in water resources engineering” page 62-122, Online ISBN 9781108565103, Cambridge University Press. https://doi.org/10.1017/9781108565103.004 DOI: https://doi.org/10.1017/9781108565103
Patton AJ (2012). “A review of copula models for economic time series”. Journal of Multivariate Analysis, 110: 4-18. https://doi.org/10.1016/j.jmva.2012.02.021 DOI: https://doi.org/10.1016/j.jmva.2012.02.021
Bárdossy A and Li J (2008). “Geostatistical interpolation using copulas”. Water Resources Research, 44(7): 1-15. https://doi.org/10.1029/2007wr006115 DOI: https://doi.org/10.1029/2007WR006115
Kazianka, H., & Pilz, J. (2010). “Spatial interpolation using copula-based geostatistical models”. In GeoENV VII–Geostatistics for Environmental Applications, Springer Dordrecht, 16: 307-319. https://doi.org/10.1007/978-90-481-2322-3_27 DOI: https://doi.org/10.1007/978-90-481-2322-3_27
Genest C, Gendron M and Bourdeau-Brien M (2009a). “The advent of copulas in finance”. The European Journal of Finance, 15(7-8): 609-618. https://doi.org/10.1080/13518470802604457 DOI: https://doi.org/10.1080/13518470802604457
Aas K (2016). “Pair-copula constructions for financial applications: A review”. Econometrics, 4(4): 1-15. https://doi.org/10.3390/econometrics4040043 DOI: https://doi.org/10.3390/econometrics4040043
Sklar A (1959). “Functions de repartition an dimensions et leurs marges”. Publications de l’Institut de Statistique de l’Universite de Paris, 8: 229-231. https://ci.nii.ac.jp/naid/10011938360
Angus JE (1994). “The probability integral transform and related results”. SIAM Review, 36(4): 652-654. https://doi.org/10.1137/1036146 DOI: https://doi.org/10.1137/1036146
Joe H and Xu JJ (1996). “The Estimation Method of Inference Functions for Margins for Multivariate Models”. Technical Report 166, Department of Statistics, University of British Columbia, 22pp. https://dx.doi.org/10.14288/1.0225985
Fermanian JD and Scaillet O (2005). “Some statistical pitfalls in copula modelling for financical applications”, E. Klein (Ed.), Capital Formation, Gouvernance and Banking, 1-24. https://doi.org/10.2139/ssrn.558981 DOI: https://doi.org/10.2139/ssrn.558981
Genest C and Nešlehová J (2007). “A primer on copulas for count data”. ASTIN Bulletin: The Journal of the IAA, 37(2): 475-515. https://doi.org/10.2143/ast.37.2.2024077 DOI: https://doi.org/10.1017/S0515036100014963
Heinen A and Rengifo E (2007). “Multivariate autoregressive modeling of time series count data using copulas”. Journal of Empirical Finance, 14(4): 564-583. https://doi.org/10.1016/j.jempfin.2006.07.004 DOI: https://doi.org/10.1016/j.jempfin.2006.07.004
Nikoloulopoulos AK (2013). “On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood”. Journal of Statistical Planning and Inference, 143(11): 1923-1937. https://doi.org/10.1016/j.jspi.2013.06.015 DOI: https://doi.org/10.1016/j.jspi.2013.06.015
Inouye DI, Yang E, Allen GI and Ravikumar P (2017). “A review of multivariate distributions for count data derived from the Poisson distribution”. Wiley Interdisciplinary Reviews: Computational Statistics, 9(3): e1398. https://doi.org/10.1002/wics.1398 DOI: https://doi.org/10.1002/wics.1398
van Stiphout T, Zhuang J and Marsan D (2012). “Seismicity declustering”. Community Online Resource for Statistical Seismicity Analysis, 10(1): 1-25. https://doi.org/10.5078/corssa-52382934
Mignan A and Woessner J (2012). “Estimating the magnitude of completeness for earthquake catalogs”. Community Online Resource for Statistical Seismicity Analysis, 1-45. https://doi.org/10.5078/corssa-00180805
Wiemer S (2001). “A software package to analyze seismicity: ZMAP”, Seismological Research Letters, 72(3): 373-382. https://doi.org/10.1785/gssrl.72.3.373 DOI: https://doi.org/10.1785/gssrl.72.3.373
Reasenberg P (1985). “Second‐order moment of central California seismicity, 1969–1982”. Journal of Geophysical Research: Solid Earth, 90(B7): 5479-5495. https://doi.org/10.1029/jb090ib07p05479 DOI: https://doi.org/10.1029/JB090iB07p05479
Woessner J and Wiemer S (2005). “Assessing the quality of earthquake catalogues: Estimating the magnitude of completeness and its uncertainty”. Bulletin of the Seismological Society of America, 95(2): 684-698. https://doi.org/10.1785/0120040007 DOI: https://doi.org/10.1785/0120040007
Schorlemmer D and Woessner J (2008). “Probability of detecting an earthquake”. Bulletin of the Seismological Society of America, 98(5): 2103-2117. https://doi.org/10.1785/0120070105 DOI: https://doi.org/10.1785/0120070105
Ljung GM and Box GE (1978). “On a measure of lack of fit in time series models”. Biometrika, 65(2): 297-303. https://doi.org/10.1093/biomet/65.2.297 DOI: https://doi.org/10.1093/biomet/65.2.297
Schwarz G (1978). “Estimating the dimension of a model”. The Annals of Statistics, 6(2): 461-464. https://doi.org/10.1214/aos/1176344136 DOI: https://doi.org/10.1214/aos/1176344136
Kruskal WH (1958). “Ordinal measures of association”. Journal of the American Statistical Association, 53(284): 814-861. https://doi.org/10.1080/01621459.1958.10501481 DOI: https://doi.org/10.1080/01621459.1958.10501481
Bücher A, Kojadinovic I, Rohmer T and Segers J (2014). “Detecting changes in cross-sectional dependence in multivariate time series”. Journal of Multivariate Analysis, 132: 111-128. https://doi.org/10.1016/j.jmva.2014.07.012 DOI: https://doi.org/10.1016/j.jmva.2014.07.012
Csörgö M and Horváth L (1997). “Limit Theorems in Change-Point Analysis”. ISBN 978-0-471-95522-1, Chichester: Wiley. https://www.wiley.com/en-us/Limit+Theorems+in+Change+Point+Analysis-p-9780471955221
Gombay E and Horváth L (1999). “Change‐points and bootstrap”. Environmetrics: The official Journal of the International Environmetrics Society, 10(6): 725-736. https://doi.org/10.1002/(sici)1099-095x(199911/12)10:6%3C725::aid-env387%3E3.0.co;2-k DOI: https://doi.org/10.1002/(SICI)1099-095X(199911/12)10:6<725::AID-ENV387>3.0.CO;2-K
Genest C and Rémillard B (2004). “Test of independence and randomness based on the empirical copula process”. Test, 13(2): 335-369. https://doi.org/10.1007/bf02595777 DOI: https://doi.org/10.1007/BF02595777
Genest C, Rémillard B and Beaudoin D (2009b). “Goodness-of-fit tests for copulas: A review and a power study”. Insurance: Mathematics and Economics, 44(2): 199-213. https://doi.org/10.1016/j.insmatheco.2007.10.005 DOI: https://doi.org/10.1016/j.insmatheco.2007.10.005
Kojadinovic I and Yan J (2011). “Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process”. Annals of the Institute of Statistical Mathematics, 63(2): 347-373. https://doi.org/10.1007/s10463-009-0257-x DOI: https://doi.org/10.1007/s10463-009-0257-x
