Let $\mathscr{X}$ be a $dlt$-model of $X$ over $\mathscr{C}$, let $\mathscr{Y}$ be a proper $snc$-model of $X$ over $\mathscr{C}$ and let $h:\mathscr{Y}\to\mathscr{X}$ be a morphism of $\mathscr{C}$-models. Denote by $\Delta$ the log pullback of $(\mathscr{X}_{s})_{\mathrm{red}}$ to $\mathscr{Y}$. If we set

$$S=\{x\in\mathrm{Sk}(\mathscr{Y})\,|\,v_{x}(\Delta)=v_{x}((\mathscr{Y}_{s})_{\mathrm{red}})\}$$

then $\mathrm{Sk}(\mathscr{X})=S$.