  Verifying that sub-mm galaxies (SMGs) are gravitationally lensed requires
time-expensive observations with over-subscribed high-resolution observatories.
Here, we aim to strengthen the evidence of gravitational lensing within the
Herschel Bright Sources (HerBS) by cross-comparing their positions to optical
(SDSS) and near-infrared (VIKING) surveys, in order to search for the
foreground lensing galaxy candidates. Resolved observations of the brightest
HerBS sources have already shown that most are lensed, and a galaxy evolution
model predicts that $\sim$76% of the total HerBS sources are lensed, although
with the SDSS survey we are only able to identify the likely foreground lenses
for 25% of the sources. With the near-infrared VIKING survey, however, we are
able to identify the likely foreground lenses for 57% of the sources, and we
estimate that 82% of the HerBS sources have lenses on the VIKING images even if
we cannot identify the lens in every case. We find that the angular offsets
between lens and Herschel source are larger than that expected if the lensing
is done by individual galaxies. We also find that the fraction of HerBS sources
that are lensed falls with decreasing 500-micron flux density, which is
expected from the galaxy evolution model. Finally, we apply our statistical
VIKING cross-identification to the entire Herschel-ATLAS catalogue, where we
also find that the number of lensed sources falls with decreasing 500-micron
flux density.

Astrophysics of Galaxies