1 Correction to: Progress in Earth and Planetary Science (2021) 8:46 https://doi.org/10.1186/s40645-021-00440-9

Following publication of the original article Nakada et al. (2021), some minor errors were found in the online article:

The first name and last name of all authors were interchanged in the article, the correct authors names should be Satoshi Nakada, Hiroki Haga, Maho Iwaki, Kohji Mabuchi and Noriko Takamura.

The “Results” and “Discussion” of the article were combined to “Results and Discussion” section by the typesetters unfortunately, which is a typesetting error.

In Eq. 12, there is an additional parenthesis which should be removed from the equation, the correct Eq. 12 is shown as follows:

$$\mathrm{cos}\theta ={F}_{B}\sqrt{2\left(\sqrt{1+({F}_{B}/\psi )^{2}}-1\right)}/\psi$$

The original paper has been updated.