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A Power-Law Function for Earthquake Interarrival Time and Magnitude

British Geological Survey
West Mains Road
Edinburgh EH9 3LA
UK
R.Musson{at}bgs.ac.uk
(R.M.W.M.)
Laboratory of Geophysics
University of Thessaloniki
Mail Box 352-1
GR-540 06 Thessaloniki
Greece
tsapanos{at}geo.auth.gr
(T.T.)
Department of Mathematics
Statistics and Operation Research Branch
Aristotle University of Thessaloniki
GR-540 06 Thessaloniki
Greece
(C.T.N.)

Manuscript received 10 January 2000.

The question of time-dependent seismic hazard models is still an open one. While most hazard studies assume stationarity of seismicity, there has been some debate on the relative merits of Poissonian and non-Poissonian recurrence models, and opinions about the viability of the seismic gap hypothesis also vary. Previous attempts to treat seismic hazard as time-dependent have, however, concentrated on large earthquakes, which do not always control the hazard at a site. In this study, earthquake interarrival times are studied for several regions in Japan and Greece. It is found that a lognormal distribution provides a good model and that seismicity can be represented by the equation ln IAT = a + b M ± c where ln IAT is the log interarrival time of earthquakes exceeding magnitude M and a, b, and c are regional constants. This power law is clearly related to the normal Gutenberg-Richter magnitude-frequency law, but actually contains more information. This law provides a basis for time-dependent seismic hazard analysis in which the whole earthquake catalog is used, rather than just the largest events. A question still remains as to whether c (the standard deviation) is significantly dependent on magnitude.