Omori, cutoff and rate-state decay fits to 2011-2018 gave similar 2019-2024 errors in 22 Tohoku-activated cells (JMA M3.5+, depth 60 km or less); no tail shape was clearly better

Question: after the 2011 Mw 9.0 Tohoku-Oki earthquake, can 13 years of data separate a power-law (Omori-Utsu) aftershock tail from an exponential (rate-state, Dieterich 1994) tail by forecast skill? Method: we used the JMA unified hypocenter catalog for 1998-2024 in 1 x 1 degree cells at 34-42 N, 138-146 E (depth 60 km or less, M 3.5 or more). The 1998-2011 rate is the old baseline. We fitted five decay models to day 10 to 2018-12-31 by Poisson likelihood: Omori to the old baseline, Omori with an exponential cutoff, one-step rate-state, and Omori and rate-state toward a free new level. Then we forecast the 2019-2024 count in each cell. Result: in 22 activated cells (days 10-365 rate 5 or more times the baseline), the mean absolute log error was 0.39-0.48 for the five decay models, 0.56 for the old baseline and 0.52 for persistence of the last three years. The rate-state minus Omori difference was +0.03 (95% block-bootstrap interval -0.08 to +0.16). Its interval included zero in all six variants (median baseline, M 3.0+, fit to 2015, M 6.5 windows masked). The cutoff gave a small gain (0.01-0.07) that was clear only in the masked variants. A free new level improved training fits (median 0.75 times the old baseline) but not held-out forecasts. All decay models forecast too many events (log bias -0.20 to -0.35). The largest errors came from a cell in the high-slip area at 0.04 times its old rate in 2022-2024 and from the 2021-2022 M7.3-7.4 Fukushima-oki events, not from the tail shape. Limitations: few dependent cells, Poisson likelihood ignores clustering, the baseline choice changes the errors more than the tail shape, and the 8-14 year horizon cannot test decades-long tails.

Tohoku-Oki 2011 · aftershock decay · Omori-Utsu law · rate-and-state friction · aftershock duration · forecast test · JMA catalog · seismic quiescence · background seismicity · null result