  Bar-Natan's Zh-construction associates to each $n$ component virtual link
diagram $L$ an $(n+1)$ component virtual link diagram $Zh(L)$. If $L_0,L_1$ are
equivalent virtual link diagrams, then $Zh(L_0),Zh(L_1)$ are equivalent as
semi-welded links. The importance of the $Zh$-construction is that it unifies
several classical knot invariants with virtual knot invariants. For example,
the generalized Alexander polynomial of a virtual link diagram $L$ is identical
to the usual multi-variable Alexander polynomial of $Zh(L)$. From this it
follows that the generalized Alexander polynomial is a slice obstruction: it
vanishes on any knot concordant to an almost classical knot. Our main result is
a characterization theorem for the $Zh$-construction in terms of almost
classical links. Several consequences of this characterization are explored.
First, we give a purely geometric description of the $Zh$-construction.
Secondly, the $Zh$-construction is used to obtain a simple derivation of the
Dye-Kauffman-Miyazawa polynomial. Lastly, we show that every quandle coloring
invariant and quandle 2-cocycle coloring invariant can be extended to a new
invariant using the $Zh$-construction.
