  In this paper, it is shown that for any closed orientable $3$-manifold with
positive simplicial volume, the growth of the Seifert volume of its finite
covers is faster than the linear rate. In particular, each closed orientable
$3$-manifold with positive simplicial volume has virtually positive Seifert
volume. The result reveals certain fundamental difference between the
representation volume of the hyperbolic type and the Seifert type. The proof is
based on developments and reactions of recent results on virtual domination and
on virtual representation volumes of $3$-manifolds.
