  Weak vector boson scattering (VBS) at the LHC provides an excellent source of
information on the structure of quartic gauge couplings and possible effects of
physics beyond the SM in electroweak symmetry breaking. Parameterizing
deviations from the SM within an effective field theory at tree level, the
dimension-8 operators, which are needed for sufficiently general modeling, lead
to unphysical enhancements of cross sections within the accessible energy range
of the LHC. Preservation of unitarity limits is needed for phenomenological
studies of the $VVjj$ events which signify VBS. Here we develop a numerical
unitarization scheme for the full off-shell VBS processes and apply it to
same-sign $W$ scattering, i.e. processes like $qq\to qqW^+W^+$. The scheme is
implemented within the Monte Carlo program VBFNLO, including leptonic decay of
the weak bosons and NLO QCD corrections. Distributions differentiating between
higher dimensional operators are discussed.
