The conditional probability of earthquake occurrence and the next large earthquake in Tokyo, Japan

Abstract

The use of probability distribution ofrecurrence times as described by theexponential, Weibull and Rayleihgprobability densities form the core of theprobabilistic seismic prediction analysispresented in this paper. Using these threeprobabilistic models we derive threeformulas to calculate the conditionalprobability P(Δt|t) than an earthquakeevent will occur in the time interval (t, t+ Δt), provide that it has not occurredin the elapsed time t since the last largeearthquake (M ≥ 6.4) in the Tokyo area.This paper proposes a new method toestimate the time interval Δt foroccurrence of a new large earthquake inTokyo area. This time interval is measuredafter the elapsed time (t) since the lastlarge earthquake. To do this we use thethree formulas for the conditionalprobability P(Δt|t) and the criterionof the maximum conditional probability ofearthquake occurrence.Using a list of historical earthquakeswhich have occurred in the Tokyo area asgiven by Usami (1976, pp. 235–243), wefound that: (1) Using the exponentialmodel, it is estimated that a highlydamaging earthquake magnitude M ≥ 6.4, mayoccur before the year 2009.50, orequivalently before June 2009; (2) Usingthe Weibull model, it is estimated that thedamaging earthquake (M ≥ 6.4) may occurbefore the year 2129.80, or equivalentlybefore October 2129.