  We present a first principles method for calculating the inelastic electron
tunneling spectroscopy (IETS) on gated graphene. We reproduce experiments on
pristine graphene and point out the importance of including several phonon
modes to correctly estimate the local doping from IETS. We demonstrate how the
IETS of typical imperfections in graphene can yield characteristic fingerprints
revealing e.g. adsorbate species or local buckling. Our results show how care
is needed when interpreting STM images of defects due to suppression of the
elastic tunneling on graphene.
