Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T11:35:34.788Z Has data issue: false hasContentIssue false
  • English
  • Français

Exploratory analysis of earthquake clusters by likelihood-based trigger models

Part of: Geophysics (general) Inference from stochastic processes Geophysics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Yosihiko Ogata
Yosihiko Ogata*
Affiliation:
Institute of Statistical Mathematics, Tokyo
*
1Postal address: Institute of Statistical Mathematics, 4–6–7 Minami-azabu, Minatoku, Tokyo 106, Japan. Email: ogata@ism.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper considers the superposition of modified Omori functions as a conditional intensity function for a point process model used in the exploratory analysis of earthquake clusters. For the examples discussed, the maximum likelihood estimates converge well starting from appropriate initial values even though the number of parameters estimated can be large (though never larger than the number of observations). Three datasets are subjected to different analyses, showing the use of the model to discover and study individual clustering features.

Keywords

AftershocksclustersETAS modelmaximum likelihood estimatesmodified Omori lawtrigger model

MSC classification

Primary: 86A15: Seismology
Secondary: 60G55: Point processes 62M09: Non-Markovian processes
Type
Models and statistics in seismology
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 202 - 212
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Guo, Z. and Ogata, Y. (1997). Statistical relations between the parameters of aftershocks in time, space and magnitude. J. Geophys. Res. 102, 2857–2873.CrossRefGoogle Scholar
Hawkes, A. G. and Adamopoulos, L. (1973). Cluster models for earthquakes–Regional comparisons. Bull. Int. Statist. Inst. 45, Book 3, 454–461.Google Scholar
Hirata, N. et al. (1996). Urgent joint observation of aftershocks of the 1995 Hyogo-Ken-Nanbu earthquake. J. Phys. Earth 44, 317–328.CrossRefGoogle Scholar
Ide, S., Takeo, M. and Yosida, Y. (1996). Source process of the 1995 Kobe earthquake: Determination of spatio-temporal slip distribution by Bayesian modeling. Bull. Seismol. Soc. Amer. 86, 547–566.CrossRefGoogle Scholar
Institute Of Statistical Mathematics and Earthquake Research Institute, University Of Tokyo (1995). Quasi-real-time watch of the aftershock activity change of Hyogoken-Nanbu Earthquake–Prediction of Jan. 25 23h 16m M4.7 aftershock. Report of the Coordinating Committee for Earthquake Prediction 54, ed. Geographical Survey Institute, Ministry of Construction, Japan, 600–607.Google Scholar
Nakamura, M. and Ando, M. (1996). Aftershock distribution of the January 17, 1995 Hyogo-ken Nanbu earthquake determined by the JHD method. J. Phys. Earth 44, 329–335.CrossRefGoogle Scholar
Ogata, Y. (1978). The asymptotic behavior of maximum likelihood estimator of stationary point processes. Ann. Inst. Statist. Math. 30, 243–261.CrossRefGoogle Scholar
Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83, 9–27.CrossRefGoogle Scholar
Ogata, Y. (1992). Detection of precursory relative quiescence before great earthquakes through a statistical model. J. Geophys. Res. 97, 19845–19871.CrossRefGoogle Scholar
Ogata, Y. (2001). Increased probability of large earthquakes near aftershock regions with relative quiescence. J. Geophys. Res. 106, 8729–8744.CrossRefGoogle Scholar
Ogata, Y. and Katsura, K. (1986). Point process model with linearly parameterized intensity for the application to earthquake data. In Essays in Time Series and Allied Processes in Honour of E. J. Hannan (J. Appl. Probab. 23A), eds Gani, J. and Priestly, M. B., Applied Probability Trust, Sheffield, 291–310.Google Scholar
Ogata, Y., Matsu'Ura, R. S. and Katsura, K. (1993). Fast likelihood computation of epidemic type aftershock-sequence model. Geophys. Res. Lett. 20, 2143–2146.CrossRefGoogle Scholar
Richter, C. F. (1958). Elementary Seismology. Freeman, San Francisco.Google Scholar
Seino, M. (1984). Statistical relations among magnitude, number and area of epicentral region, for earthquake clusters. Zisin (2) (J. Seismol. Soc. Japan) 37, 88–98 (in Japanese with English summary and figure captions).Google Scholar
Takahashi, H. and Mori, M. (1973). Quadrature formulas obtained by variable transformation. Numer. Math. 21, 206–219.CrossRefGoogle Scholar
Utsu, T. (1957). Magnitude of earthquakes and occurrence of their aftershocks. Zisin (2) (J. Seismol. Soc. Japan) 10, 35–45 (in Japanese with English summary and figure captions).Google Scholar
Utsu, T. (1969). Aftershocks and earthquake statistics (I): some parameters which characterize an aftershock sequence and their interaction. J. Faculty Sci., Hokkaido Univ., Ser. VII 3, 129–195.Google Scholar
Utsu, T. (1982). Catalog of large earthquakes in the region of Japan from 1885 through 1980. Bull. Earthq. Res. Inst., Univ. Tokyo 57, 401–463 (in Japanese with English summary and figure captions).Google Scholar
Utsu, T. and Seki, A. (1955). Relation between the area of aftershock region and the energy of the main shock. Zisin (2) (J. Seismol. Soc. Japan) 7, 233–240 (in Japanese with English summary).Google Scholar
Vere-Jones, D. (1970). Stochastic models for earthquake occurrence (with discussion). J. Roy. Statist. Soc. Ser. B 32, 1–62.Google Scholar
Vere-Jones, D. and Davies, R. B. (1966). A statistical survey of earthquakes in the main seismic region of New Zealand, Part 2, Time series analyses. New Zealand J. Geol. Geophys. 9, 251–284.CrossRefGoogle Scholar
Yamanaka, Y. and Shimazaki, K. (1990). Scaling relationship between the number of aftershocks and the size of the main shock. J. Phys. Earth 38, 305–324.CrossRefGoogle Scholar