  We present a detailed phenomenological analysis of the production of a
Standard Model Higgs boson in association with up to three jets. We consider
the gluon fusion channel using an effective theory in the large top-quark mass
limit. Higgs boson production in gluon fusion constitutes an irreducible
background to the vector boson fusion (VBF) process; hence the precise
knowledge of its characteristics is a prerequisite for any measurement in the
VBF channel. The calculation is carried out at next-to-leading order (NLO) in
QCD in a fully automated way by combining the two programs GoSam and Sherpa. We
present numerical results for a large variety of observables for both standard
cuts and VBF selection cuts. We find that for all jet multiplicities the NLO
corrections are sizeable. This is particularly true in the presence of
kinematic selections enhancing the VBF topology, which are based on vetoing
additional jet activity. In this case, precise predictions for the background
can be made using our calculation by taking the difference between the
inclusive H+2 jets and the inclusive H+3 jets result.
