Earth Planets Space, Vol. 64 (No. 7), pp. e17-e20, 2012
Masajiro Imoto and Hiroyuki Fujiwara
National Research Institute for Earth Science and Disaster Prevention, 3-1 Ten-nodai, Tsukuba, Ibaraki 305-0006, Japan
(Received March 30, 2012; Revised June 14, 2012; Accepted June 17, 2012; Online published August 16, 2012)
We attempt to estimate the long-term probability of a Magnitude (M) 8 earthquake along the Sagami Trough in the Kanto subduction zone, central Japan. A Brownian passage time model is applied to sets of historical earthquakes identified in previous studies. An optimal model is obtained by the maximum likelihood method for each data set. The optimal parameters are not well constrained since each data set includes a small number of earthquakes. To obtain reliable probabilities, two weighting methods are introduced. First, we apply the weighted log-likelihood method, where the model parameters are estimated from the log-likelihood function, summed up with each log-likelihood weighted in proportion to the reliability of the data set. Second, probabilities are estimated as the weighted average of every alternative model. The weight of each model represents the normalized relative likelihood of the model. The probabilities of the weighted log-likelihood function are within the ranges of those obtained for each set. In averaging the proposed sequence and over probable parameter values, the probability of an M 8 earthquake occurring in the next 30 years is estimated to be 2.0 to 4.6%, depending on the cutoff value of the weight.
Key words: Brownian passage time model, weighted log-likelihood method, Kanto, M 8 earthquake, Japan.