Fig. 3

Surface displacement in the Kumamoto area estimated by PSI analysis of ALOS/PALSAR images before the 2016 Kumamoto earthquake (January 7, 2007–March 5, 2011): a transient surface displacement (modeled by the exponential function in Eq. (4)) during the first year from the first SAR image, b magnitude of the seasonal surface displacement (\( \alpha \) in Eq. (4)). c–e examples of time-series displacements, and f Comparison of GNSS observation and the time-series displacement estimated by PSI analysis at the GNSS station of Kumamoto using the GNSS station of Jonan as a reference point. The locations of c–e are in a, and the locations of two GNSS stations are represented as black circles (North: Kumamoto station, South: Jonan station) in a. Colored dots indicate PS pixels, where surface displacements were estimated, and gray dashed lines represent the covered area of the SAR images. Positive sign indicates surface displacement toward satellite direction. Gray lines indicate surface ruptures associated with the 2016 Kumamoto earthquake shown in Fig. 1b (Toda et al. 2016)