Correction to: Earth Planets Space (2021) 73:122 https://doi.org/10.1186/s40623-021-01439-8

Following publication of the original article (Tanioka et al. 2021), the authors reported an error in the third reference.

The original reference was:

Kano M, Miyazaki S, Ishikawa Y, Hirahara K (2020) Adjoint-based direct data assimilation of GNSS time series for optimizing frictional parameters and predicting postseismic deformation following the 2003 Tokachi-oki earthquake. Earth Planets Space 72:156. https://doi.org/10.1186/s40623-020-01293-0

The correct reference should be:

Kano M, Miyazaki S, Ishikawa Y, Hirahara K (2020) Adjoint-based direct data assimilation of GNSS time series for optimizing frictional parameters and predicting postseismic deformation following the 2003 Tokachi-oki earthquake. Earth Planets Space 72:159. https://doi.org/10.1186/s40623-020-01293-0

The original article (Tanioka et al. 2021) has been updated.