  A virtual link can be understood as a link in a trivial I-bundle over an
orientable compact surface with genus. A twisted virtual link is a link in a
trivial I-bundle over a not-necessarily orientable compact surface. A twisted
virtual birack is an algebraic structure with axioms derived from the twisted
virtual Reidemeister moves. We extend a method previously used with racks and
biracks to the twisted case to define computable invariants of twisted virtual
links using finite twisted virtual biracks with birack rank $N\ge 1$. As an
application, we classify twist structures on the virtual Hopf link.
