Let $N(D)$ be a regular neighborhood of $D$ in $\Sigma$. Then the smooth part of the hypersurface is $H_{s}^{\mathrm{sm}}:=H_{s}\cap X_{s}(\Sigma\backslash N(D))$, and the rest $H_{s}^{\mathrm{sing}}:=H_{s}\backslash H_{s}^{\mathrm{sm}}$ is singular.