Seismicity analysis through point-process modeling: A review

Pure and Applied Geophysics

Volumn 155, Issue 2-4, 1999, Pages 471-507

  Ogata, Yosihiko ^a  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Causal relationship; ETAS model; Modified Omori formula; Relative quiescence; Seasonality of seismicity; Space time models

Indexed keywords

EARTHQUAKE PREDICTION; EARTHQUAKE RECURRENCE; MAXIMUM LIKELIHOOD ANALYSIS; SEISMICITY;

EID: 0032752981     PISSN: 00334553     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000240050275     Document Type: Article

References (107)

1. AKAIKE, H. (1974), A New Look at the Statistical Model Identification, IEEE Trans. Autom. Control 19, 716-723.
2. AKAIKE, H., On entropy maximization principle. In Applications of Statistics (ed. Krishnaiah, P. R.) (North-Holland, Amsterdam 1977) pp. 27-41.
3. AKAIKE, H., OZAKI, T., ISHIGURO, M., OGATA, Y., KITAGAWA, G., TAMURA, Y. H., ARAHATA, E., KATSURA, K., and TAMURA, Y. (1984), Time Series Analysis and Control Program Package, TIMSAC-84, The Institute of Statistical Mathematics, Tokyo.
4. AKI, K. (1956), A Review of Statistical Seismology, Zisin (J. Seismol. Soc. Japan), Ser. 2, 8, 205-228, in Japanese.
5. BERMAN, M., and TURNER, T. R. (1992), Approximating Point-process Likelihoods, Applied Statist. (J. Roy. Statist. Soc. C) 41, 31-38.
6. BRILLINGER, D. (1988), Some Statistical Methods for Random Process Data from Seismology and Neurophysiology, The 1983 Wold Memorial Lectures, Ann. Statist. 16, 1-54.
7. Cox, D., and LEWIS, P. A. W., The Statistical Analysis of Series Events (Methuen, London 1966).
8. CREAMER, F. H., and KISSLINGER, C. (1993), The Relation between Temperature and the Omori Decay Parameter for Aftershock Sequences near Japan, EOS, 74, 43, Supplement, p. 417.
9. DALEY, D. J., and VERE-JONES, D., A summary of the theory of point processes. In Stochastic Point Processes: Statistical Analysis, Theory and Appplications (ed. Lewis, P. A. W.) (Wiley, New York 1972).
10. DE NATALE, G., MUSMECI, F., and ZOLLO, A. (1988), A Linear Intensity Model to Investigate the Causal Relation between Calabrian and North-Aegean Earthquake Sequences, Geophys. J. 95, 285-293.
11. FISHER, N., Statistical Analysis of Circular Data (Cambridge University Press, Cambridge 1993).
12. FLETCHER, R., and POWELL, M. J. D. (1963), A Rapidly Convergent Method for Minimization, Comput. J. 6, 163-168.
13. GUO, Z., and OGATA, Y. (1995), Correlation between Characteristic Parameters of Aftershock Distributions in Time, Space and Magnitude, Geophys. Res. Lett. 22, 993-996.
14. Guo, Z., and OGATA, Y. (1997), Statistical Relations between the Parameters of Aftershocks in Time, Space and Magnitude, J. Geophys. Res. 102 (B2), 2857-2873.
15. HABERMANN, R. E. (1983), Teleseismic Detection in the Aleutian Island Arc, J. Geophys. Res. 88, 5056-5064.
16. HABERMANN, R. E. (1988), Precursory Seismic Quiescence: Past, Present, and Future, Pure appl. geophys. 126, 279-318.
17. HAWKES, A. G. (1971), Point Spectra of Some Mutually Exciting Point Processes, J. Roy. Statist. Soc. B33, 438-443.
18. HAWKES, A. G., and ADAMOPOULOS, L. (1973), Cluster Models for Earthquakes-Regional Comparisons, Bulletin of the International Statistical Institute 45, Book 3, 454-461.
19. HAWKES, A. G., and OAKES, D. A. (1974), A Cluster Process Representation of Self-exciting Process, J. Appl. Probab. 11, 493-503.
20. IMOTO, M., MAEDA, K., and YOSHIDA, A. (1999). Use of statistical Models to Analyze Periodic Seismicity Observed for Clusters in the Kanto Region, Central Japan, this volume.
21. ISHAM, V., and WESTCOTT, M. (1979), A self-correcting Point Process, Stoc. Proc. Appl. 8, 335-348.
22. KAGAN, Y. Y. (1991), Likelihood Analysis of Earthquake Catalogues, J. Geophys. Res. 106, 135-148.
23. KAGAN, Y. Y. (1992a), Correlations of Earthquake Focal Mechanisms, Geophys. J. Int. 110, 305-320.
24. KAGAN, Y. Y. (1992b), On the Geometry of an Earthquake Fault System, PEPI 71, 15-35.
25. KAGAN, Y. Y., and KNOPOFF, L. (1978), Statistical Study of the Occurrence of Shallow Earthquake, Geophys. J. R. Astron. Soc. 55, 67-86.
26. KAGAN, Y. Y., and KNOPOFF, L. (1980), Spatial Distribution of Earthquakes: The Two-point Correlation Function, Geophys. J. R. Astron. Soc. 62, 303-320.
27. KAGAN, Y. Y., and KNOPOFF, L. (1985), The first-order Statistical Moment of the Seismic Moment Tensor, Geophys. J. R. Astron. Soc. 81, 429-444.
28. KAGAN, Y. Y., and JACKSON, D. D. (1998), Spatial Aftershock Distribution: Effect of Normal Stress, J. Geophys. Res. 103, 24,453-24,465.
29. KAWASUMI, H. (1970), Proofs of 69 Year Periodicity and Imminence of Destructive Earthquakes in Southern Kwanto District and Problems in the Countermeasures Thereof, Chigaku Zasshi (J. Geography) 79(3), 115-138, in Japanese.
30. KENDALL, D. G. (1949), Stochastic Processes and Population Growth, J. Roy. Statist. Soc. 11, 230-264.
31. KISSLINGER, C., and JONES, L. M. (1991), Properties of Aftershocks in Southern California, J. Geophys. Res. 96, 11,947-11,958.
32. KITAGAWA, G., and AKAIKE, H. (1978), A Procedure for the Modeling of Non-stationary Time Series, Ann. Inst. Statist. Math. 30, 351-363.
33. KUTOYANTS, Yu. A. (1979), Local Asymptotic Normality for Processes of Poisson Type, Izvest. Akad. Arm. Nauk. Ser. Matematika 14, 3-20.
34. KUTOYANTS, Yu. A. (1982), Multidimensional Parameter Estimation of the Intensity Function of Inhomogeneous Poisson Processes, Probl. Control Inf. Theory 11 (4), 325-334.
35. LEWIS, P. A. W. (1970), Remarks on the Theory, Computation and Application of the Spectral Analysis of Series of Events, J. Sound Vib. 12, 353-375.
36. LEWIS, P. A. W., and SHEDLER, G. S. (1979). Simulation of Non-homogeneous Poisson Processes by Thinning, Naval Res. Logistics Quart. 26, 403-413.
37. LIPTZER and SHIRYAEV, Statistics of Random Processes (Springer-Verlag, Berlin 1978).
38. LIU, J., CHEN, Y., SHI, Y., and VERE-JONES, D. (1999), Coupled Stress Release Model for Time-dependent Seismicity, this volume.
39. MA, LI, and VERE-JONES, D. (1997), Application of M 8 and Lin-Lin Algorithms to New Zealand Earthquake Data, N.Z. J. Geol. Geophys. 40, 77-89.
40. MATSUMURA, K. (1986), On Regional Characteristics of Seasonal Variation of Shallow Earthquake Activities in the World, Bull. Disas. Prev. Inst., Kyoto Univ. 36, 43-98.
41. MATSU'URA, R. S. (1986), Precursory Quiescence and Recovery of Aftershock Activities before Some Large Aftershocks, Bull. Earthq. Res. Inst. Univ. Tokyo 61, 1-65.
42. MACLEAN, C. J. (1974), Estimation and Testing of an Exponential Polynomial Rate Function within the Non-stationary Poisson Process, Biometrika 61, 81-86.
43. MOGI, K. (1962), On the Time Distribution of Aftershocks Accompanying the Recent Major Earthquakes in and near Japan, Bull. Earthq. Res. Inst. Univ. of Tokyo 40, 107-124.
44. MOGI, K. (1973), Relationship between Deep and Shallow Seismicity in the Western Pacific Region, Tectonophysics 17, 1-22.
45. MUSMECI, F., and VERE-JONES, D. (1992), A space-time Clustering Model for Historical Earthquakes, Ann. Inst. Statist. Math. 44, 1-11.
46. NISHIZAWA, O., LEI, X., and NAGATO, T., Hazard function analysis of seismo-electric signals in Greece. In Electromagnetic Phenomena Related to Earthquake Prediction (eds. Hayakawa, M., and Fujinawa, Y.) (Terra Publishing Company, Tokyo 1994) pp. 459-474.
47. OHTAKE, M. (1980), Earthquake Prediction Based on the Seismic Gap with Special Item to the Oaxaca, Mexico Earthquake (in Japanese with English summary), Report of the National Research Center for Disaster Prevention 23, 65-110.
48. OGATA, Y. (1978), Asymptotic Behaviour of the Maximum Likelihood Estimators for the Stationary Point Processes, Ann. Inst. Statist. Math. A 30, 243-261.
49. OGATA, Y. (1981), On Lewis' Simulation Method for Point Processes, IEEE Trans. Inform. Theory IT-30, 23-31.
50. OGATA, Y. (1983a), Estimation of the Parameters in the Modified Omori Formula for Aftershock Frequencies by the Maximum Likelihood Procedure, J. Phys. Earth 31, 115-124.
51. OGATA, Y. (1983b), Likelihood Analysis of Point Processes and its Applications to Seismological Data, Bull. Int. Statist. Inst. 50, Book 2, 943-961.
52. OGATA, Y. (1985), Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, Research Memo. (Technical report), No. 288, Inst. Statist. Math., Tokyo.
53. OGATA, Y. (1987), Long term dependence of earthquake occurrences and statistical models for standard seismic activity, In Suri Zisin Gaku (Mathematical Seismology) II (ed. Saito, M.) (Cooperative Research Report 3, Inst. Statist. Math., Tokyo 1987) pp. 115-124 (in Japanese).
54. OGATA, Y. (1988), Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, J. Amer. Statist. Assoc. 83, 9-27.
55. OGATA, Y. (1989), Statistical Model for Standard Seismicity and Detection of Anomalies by Residual Analysis for Point Process, Tectonophysics 169, 1-16.
56. OGATA, Y. (1992), Detection of Precursory Relative Quiescence before Great Earthquakes through a Statistical Model, J. Geophys. Res. 97, 19,845-19,871.
57. OGATA, Y. (1993), Space-time Modeling of Earthquake Occurrences, Bull. Int. Statist. Inst. 55, Contributed papers, Book 2, 249-250.
58. OGATA, Y. (1998a), Quiescence Relative to the ETAS Model, Zisin (J. Seismol. Soc. Japan), Ser. 2, 10, 35-45 (in Japanese with English summary).
59. OGATA, Y. (1998b), Space-time Point-process Models for Earthquake Occurrences, Ann. Inst. Math. Statist. 50, 379-402.
60. OGATA, Y., and AKAIKE, H. (1982), On Linear Intensity Models for Mixed Doubly Stochastic Poisson and Self-exciting Point Processes, J. Royal Statist. Soc. B 44, 102-107.
61. OGATA, Y., AKAIKE, H., and KATSURA, K. (1982), The Application of Linear Intensity Models to the Investigation of Causal Relations between a Point Process and Another Stochastic Process, Ann. Inst. Statist. Math. 34B, 373-387.
62. OGATA, Y., and SHIMAZAKI, K. (1984), Transition from Aftershock to Normal Activity, Bull. Seismol. Soc. Am. 74, 1757-1765.
63. OGATA, Y., and VERE-JONES, D. (1984), Inference for Earthquake Models: A Self-correcting Model, Stoch. Processes Appl. 17, 337-347.
64. OGATA, Y., and KATSURA, K. (1986), Point-process Model with Linearly Parameterized Intensity for the Application to Earthquake Data, J. Appl. Probab. 23A, 291-310.
65. OGATA, Y., and KATSURA, K. (1988), Likelihood Analysis of Spatial Inhomogeneity for Marked Point Patterns, Ann. Inst. Statist. Math. 40, 29-40.
66. OGATA, Y., and ABE, K. (1991), Some Statistical Features of Long-term Variation of the Global and Regional Seismic Activity, Int. Statist. Rev. 59, 139-161.
67. OGATA, Y., IMOTO, M., and KATSURA, K. (1991), Three-dimensional Spatial Variation of b Values of Magnitude Frequency Distribution beneath the Kanto District, Japan, Geophys. J. Int. 10, 135-146.
68. OGATA, Y., and KATSURA, K. (1991), Maximum Likelihood Estimates of the Fractal Dimension for Spatial Patterns, Biometrika 78, 463-467.
69. OGATA, Y., and KATSURA, K. (1993), Analysis of Temporal and Spatial Heterogeneity of Magnitude Frequency Distribution Inferred from Earthquake Catalogues, Geophys. J. Int. 113, 727-738.
70. OGATA, Y., MATSU'URA, R. S., and KATSURA, K. (1993), Fast Likelihood Computation of Epidemic Type Aftershock-sequence Model, Geophys. Res. Lett. 20(19), 2143-2146.
71. OGATA, Y., UTSU, T., and KATSURA, K. (1995), Statistical Features of Foreshocks in Comparison with other Earthquake Clusters, Geophys. J. Int. 121, 233-254.
72. OGATA, Y., UTSU, T., and KATSURA, K. (1996), Statistical Discrimination of Foreshocks from other Earthquake Clusters, Geophys. J. Int. 127, 17-30.
73. OIKE, K. (1977), On the Relation between Rainfall and the Occurrence of Earthquakes, Bull Disas. Prev. Res. Inst. 20 (B1), 35-45 (in Japanese).
74. OMORI, F. (1894), On the Aftershocks of Earthquake, J. Coll. Sci. Imp. Univ. Tokyo 7, 111-200.
75. OZAKI, T. (1978), Maximum Likelihood Estimation of Hawkes' Self-exciting Point Processes, Ann. Inst. Stat. Math. 30, 145-155.
76. OZAKI, T., and TONG, H. (1975), On the Filling of Non-stationary Auto-regressive Models in Time Series Analysis, Proceeding of the 8-th Hawaii Intern. Conf. on System Science, Western Periodical Company.
77. PAPANGELOU, F. (1972), Integrability of Expected Increments of Point Processes and Related Random Change of Scale, Trans. Amer. Math. Soc. 165, 483-506.
78. RAMSELAAR, P. A. (1990), The Mean Behaviour of the Ogata Earthquake Process, Master's Thesis, Dept. Math., Univ. Utrecht.
79. REASENBERG, P. A. (1985), Second-order Moment of Central California Seismicity, J. Geophys. Res. 90, 5479-5493.
80. REASENBERG, P. A. (1994), Computer Programs ASPAR, GSAS and APROB for the Statistical Modeling of Aftershock Sequences and Estimation of Aftershock Hazard, U.S.G.S. Open File Report 94-221.
81. REASENBERG, P. A., and MATTHEWS, M. V. (1988), Precursory Seismic Quiescence: A Preliminary Assessment of the Hypothesis, Pure appl. geophys. 126, 373-406.
82. REASENBERG, P. A., and JONES, L. M. (1989), Earthquake Hazard after a Mainshock in California, Science 243, 1173-1176.
83. REASENBERG, P. A., and JONES, L. M. (1990), California Aftershock Hazard Forecast, Science 247, 345-346.
84. REASENBERG, P. A., and JONES, L. M. (1994), Earthquake Aftershocks: Update, Science 265, 1251-1252.
85. RUBIN, I. (1972), Regular Point Processes and their Detection, IEEE Trans. Inform. Theory IT-18, 547-557.
86. RATHBUN, S. L. (1993), Modeling Marked spatio-temporal Point Patterns, Bull. Int. Statist. Inst. 55, Book 2, 379-396.
87. SHIMAZAKI, K. (1971), On Periodicity of Earthquake Occurrences, Kagaku (Natural Sciences) 41, Iwanami Publ. Co., Tokyo, 688-689 (in Japanese).
88. SCHUSTER, A. (1897), On Lunar and Solar Periodicities of Earthquakes, Proc. Roy. Soc. 61, 455-465.
89. UTSU, T. (1957), Magnitude of Earthquakes and Occurrence of their Aftershocks, Zisin (J. Seismol. Soc. Japan), Ser. 2 10, 35-45 (in Japanese with English summary).
90. UTSU, T. (1961), A Statistical Study on the Occurrence of Aftershocks, Geophys. Mag. 30, 521-605.
91. UTSU, T. (1969), Aftershocks and Earthquake Statistics (I): Some Parameters which Characterize an Aftershock Sequence and their Interaction, J. Faculty Sci., Hokkaido Univ., Ser. VIII 3, 129-195.
92. UTSU, T. (1970), Aftershocks and Earthquake Statistics (II): Further Investigation of Aftershocks and other Earthquakes Sequence Based on a New Classification of Earthquake Sequences, J. Faculty Sci., Hokkaido Univ., Ser. VII 3, 379-441.
93. USTU, T. (1971), Aftershocks and Earthquake Statistics (III): Analyses of the Distribution of Earthquakes in Magnitude, Time, and Space with Special Consideration to Clustering Characteristics to Earthquake Occurrence (1), J. Faculty Sci., Hokkaido Univ., Ser. VIII 3, 379-441.
94. UTSU, T. (1975), Correlation between Shallow Earthquakes in Kwanto Region and Intermediate Earthquakes in Hida Region, Central Japan, Zisin (J. Seismol. Soc., Japan) Ser. 2 (28), 303-311 (in Japanese).
95. UTSU, T., and SEKI, A. (1955), Relation between the Area of Aftershock Region and the Energy of the Mainshock, Zisin (J. Seismol. Soc. Japan), Ser. 2, ii 7, 233-240 (in Japanese).
96. UTSU, T., OGATA, Y., and MATSU'URA, R. S. (1995), The Centenary of the Omori Formula for a Decay Law of the Aftershock Activity, J. Phys. Earth 43, 1-33.
97. UTSU, T., and OGATA, Y. (1997), Statistical analysis of seismicity. In Algorithms for Earthquake Statistics and Prediction, IASPEI Software Library 6, 13-94, International Association of Seismology and Physics of the Earth's Interior in collaboration with the Seismological Society of America.
98. VERE-JONES, D. (1970), Stochastic Models for Earthquake Occurrence (with discussion), J. Roy. Stat. Soc. B 32, 1-62.
99. VERE-JONES, D. (1978), Earthquake Prediction - A Statistician's View, J. Phys. Earth 26, 129-146.
100. VERE-JoNES, D. (1985), The Detection and Estimation of Periodicities in Point Process Data, Technical Report, ISOR, Victoria Univ. of Wellington.
101. 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, N.Z. J. Geol. Geophys. 9, 251-284.
102. VERE-JONES, D., and OGATA, Y. (1984), On the Moments of a Self-correcting Process, J. Appl. Probab. 21, 335-352.
103. VERE-JONES, D., and OZAKI, T. (1982), Some Examples of Statistical Estimation Applied to Earthquake Data, 1. Cyclic Poisson and Self-exciting Models, Ann. Inst. Statist. Math. 34B, 189-207.
104. WYSS, M., and HABERMANN, R. E. (1988), Precursory Seismic Quiescence, Pure appl. geophys. 126, 319-332.
105. YAMANAKA, Y., and SHIMAZAKI, K. (1990), Scaling Relationship between the Number of Aftershocks and the Size of the Mainshock, J. Phys. Earth 38, 305-324.
106. YOSHIDA, A. (1994), Re-examination of the Correlation between Earthquakes in Kanto Region and Intermediate-depth Earthquakes in Hida Region, Central Japan, Chigaku Zasshi (J. Geography) 103 (3), 201-206 (in Japanese).
107. ZHAO, Z., MATSUMURA, K., and OIKE, K. (1989), Precursory Change of Aftershock Activity before Large Aftershock: A Case Study for Recent Earthquakes in China, J. Phys. Earth 37, 155-177.