If there are a normed finite-dimensional vector space $(V,\|\raisebox{1.72218pt}{.}\|)$ and a surjective homomorphism $V\otimes_{k}\mathscr{O}_{X}\to L$ such that $h$ is given by $\left\{|\raisebox{1.72218pt}{.}|^{\mathrm{quot}}_{(V,\|\raisebox{1.20552pt}{.}\|)}(x)\right\}_{x\in X^{\mathrm{an}}}$, then $|\raisebox{1.72218pt}{.}|_{h^{n}}(x)=|\raisebox{1.72218pt}{.}|_{h^{n}}^{\mathrm{quot}}(x)$ for all $n\geq 1$.