Additional file 1 of Spatiotemporal functional modeling of postseismic deformations after the 2011 Tohoku-Oki earthquake
Creators: name: Fujiwara, Satoshi
name: Tobita, Mikio
name: Ozawa, Shinzaburo
Publisher: name: figshare
Year: 2022
Subjects: subject: Biophysics
subject: 29999 Physical Sciences not elsewhere classified
subject: FOS: Physical sciences
subject: Molecular Biology
subject: Neuroscience
subject: Physiology
subject: FOS: Biological sciences
subject: Biotechnology
subject: 80699 Information Systems not elsewhere classified
subject: FOS: Computer and information sciences
subject: 19999 Mathematical Sciences not elsewhere classified
subject: FOS: Mathematics
subject: Cancer
subject: 111714 Mental Health
subject: FOS: Health sciences
subject: Hematology

description: Additional file 1: Fig. S1. Observed and predicted postseismic deformation using the functional model. Deformation is depicted for the four stations of a Minase, b Miyako, c Yamoto, and d Choshi (Fig. 1). The three components of east–west (EW), north–south (NS), and up–down (UD) are drawn for each station from the day after the earthquake to 2026.5. Black dots represent daily observations. Dashed lines represent the time series of predicted values for each fitting period (2.0, 3.9, 5.8, and 8.9 years). Fig. S2. Difference in the fitting period. a 2.0-year model of the short-period logarithmic term in Eq. (1), b 3.9-year model of the short-period logarithmic term in Eq. (1), c a minus b. Values for each term represent three years after the earthquake (March 11, 2014), with the values immediately after the earthquake set to zero. Fig. S3. Residuals between the observed values and the 3.9-year model. Each component of a east–west (EW), b north–south (NS), and c up–down (UD) is drawn for the Minase, Miyako, Yamoto, and Choshi stations (Fig. 1). Gray dots represent the residuals of the 3.9-year model based on Eq. (1). Black dots represent the residuals of the predicted values by adding a linear deformation term after 2015 to the 3.9-year model based on Eqs. (3) and (4). Light blue, straight lines represent the fittings to the gray dots from December 2015 to December 2020. Fig. S4. Observed and predicted postseismic deformation. Deformation is depicted for the four stations of a Minase, b Miyako, c Yamoto, and d Choshi (shown in Fig.1). The three components of east–west (EW), north–south (NS), and up–down (UD) are drawn for each station from the day after the earthquake to 2026.5. Gray dots represent the daily observations used for the fitting period of the 3.9-year model. Black dots represent the daily observations during the prediction period. Red lines represent the predicted values based on Eqs. (3) and (4) other lines represent specific terms in Eqs. (3) and (4) (see text). Fig. S5. Residuals of the functional models with different fitting periods. Residuals are depicted for the four stations of a Minase, b Miyako, c Yamoto, and d Choshi (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 residual 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]. Fig. S6. Ratio of the spatial function for different time constants. a Blue line represents the total length of short-period logarithmic term in Eq. (1) for the time function with the time constant of the 3.9-year model. Red line represents the total length with the time constant of the 2.0-year model. Pink line represents the ratio of the total length for the 2.0-year to the 3.9-year model. Light green line represents the average of the ratios. As the ratios become unstable as the value of the total length becomes smaller, they are sorted by the total length obtained for the 3.9-year model. Therefore, the average calculation is performed sequentially starting from one with the larger length for each component, and is terminated when the standard deviation of the average value becomes markedly larger (shown as the area defined by the light green line). b Same as a for the long-period logarithmic term in Eq. (1). c Same as a for the exponential term in Eq. (1). Fig. S7. Checkerboard resolution test result of geodetic inversion used in this study. a Synthetic slip on the plate surface. b Inverted slip from the synthetic data of synthetic slip with Gaussian error of 1 cm for horizontal components and 5 cm for vertical components.