[S-SS04] Earthquake prediction and forecast

[SSS04-P03] Comments on the Brownian Passage Time model for recurrent earthquakes with uncertain origin times

*Masajiro Imoto¹, Nobuyuki Morikawa¹, Hiroyuki Fujiwara¹ (1.National Research Institute for Earth Science and Disaster Resilience)

Keywords:Great earthquake, Japan Trench, Probability, Inverse Gaussian distribution, Uncertain origin times

Five recurrent great earthquakes along the Japan Trench off Tohoku (Tohoku-oki−type earthquakes) are reported through studies of tsunami deposits (Earthquake Research Committee; ERC report, 2019). For recurrent earthquakes with uncertain origin times, Ogata (JGR, 1999) formulated the likelihood function in a multiproduct form of a probability density function integrated with respect to origin times over uncertain intervals (ERC report, 2001). The ERC report (2019) estimates the long-term probability of a Tohoku-oki−type earthquake by using a method different from Ogata's. For the sake of comparison, we applied Ogata's formula with the Brownian Passage Time distribution to this earthquake sequence. This revealed that Ogata's formula leads to an extraordinarily small value, at most 0.03, for the shape parameter. A detailed calculation showed that sequences of lower likelihood, relatively larger shape parameters, are less weighted (even by orders of magnitude), and that sequences including the Keicho-Sanriku of the 1611 historical earthquake, one of two candidates for the fourth event, play no crucial role in the maximum likelihood estimation. This must be contrary to the idea that both historical earthquakes, Kyotoku of 1454 and Keichou-Sanriku, are listed with equal possibilities. Accordingly, Ogata's formula could not give a representative model parameter over all possible sequences.