著者

Tokuji Utsu Yosihiko Ogata Ritsuko S Matsu'ura

出版者

The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan

雑誌

Journal of Physics of the Earth (ISSN:00223743)

巻号頁・発行日

vol.43, no.1, pp.1-33, 1995 (Released:2009-04-30)

参考文献数

139

被引用文献数

587 958

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The Omori formula n(t)=K(t+c)-1 and its modified form n(t)=K(t+c)-P have been successfully applied to many aftershock sequences since the former was proposed just 100 years ago. This paper summarizes studies using these formulae. The problems of fitting these formulae and related point process models to observational data are discussed mainly. Studies published during the last 1/3 century confirmed that the modified Omori formula generally provides an appropriate representation of the temporal variation of aftershock activity. Although no systematic dependence of the index p has been found on the magnitude of the main shock and on the lowest limit of magnitude above which aftershocks are counted, this index (usually p = 0.9-1.5) differs from sequence to. sequence. This variability may be related to the tectonic condition of the region such as structural heterogeneity, stress, and temperature, but it is not clear which factor is most significant in controlling the p value. The constant c is a controversial quantity. It is strongly influenced by incomplete detection of small aftershocks in the early stage of sequence. Careful analyses indicate that c is positive at least for some sequences. Point process models for the temporal pattern of shallow seismicity must include the existence of aftershocks, most suitably expressed by the modified Omori law. Among such models, the ETAS model seems to best represent the main features of seismicity with only five parameters. An anomalous decrease in aftershock activity below the level predicted by the modified Omori formula sometimes precedes a large aftershock. An anomalous decrease in seismic activity of a region below the level predicted by the ETAS model is sometimes followed by a large earthquake in the same or in a neighboring region.

著者

Tokuji UTSU

出版者

The Seismological Society of Japan, The Volcanological Society of Japan , The Geodetic Society of Japan

雑誌

Journal of Physics of the Earth (ISSN:00223743)

巻号頁・発行日

vol.14, no.2, pp.37-40, 1966 (Released:2009-04-30)

参考文献数

6

被引用文献数

68 153

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The probability density function for the value of b in the formula logn(M)=a-bM estimated by the author's method has been obtained in an exact form. This function leads to a simple method to test the statistical significance of the difference between two b-values. Application of this method to SUYEHIRO'S data on foreshocks and aftershocks of the great Chilean earthquake of 1960 indicates a significant difference in b-value between the foreshocks and the aftershocks at the 98% confidence level.