Fig. 9

Residuals of the functional models with different fitting periods. Residuals are depicted for the four stations of a Kaminokuni, b Kawai, c Nadachi, and d Shizugawa (Fig. 1). Residuals of the three components of east–west (EW), north–south (NS), and up–down (UD) are drawn for each station from the day after the 2011 Tohoku-Oki earthquake to 2026.5. As a reference value, we use the 3.9-year model (the spatial functions with the fitting period of 3.9 years and the time constants of the 3.9-year model [S3.9T3.9]). Blue lines represent the residuals of the time series for the spatial functions with the fitting period of 2.0 years and the time constants of the 2.0-year model [S2.0T2.0]. Green lines represent the residuals of the time series for the spatial functions with the fitting period of 2.0 years and the time constants of the 3.9-year model [S2.0T3.9]. Red lines represent the residuals of the time series for the spatial functions with the fitting period of 3.9 years and the time constants of the 2.0-year model [S3.9T2.0]