  We analyse three public cosmic shear surveys; the Kilo-Degree Survey
(KiDS-450), the Dark Energy Survey (DES-SV) and the Canada France Hawaii
Telescope Lensing Survey (CFHTLenS). Adopting the COSEBIs statistic to cleanly
and completely separate the lensing E-modes from the non-lensing B-modes, we
detect B-modes in KiDS-450 and CFHTLenS at the level of about 2.7 $\sigma$. For
DES- SV we detect B-modes at the level of 2.8 $\sigma$ in a non-tomographic
analysis, increasing to a 5.5 $\sigma$ B-mode detection in a tomographic
analysis. In order to understand the origin of these detected B-modes we
measure the B-mode signature of a range of different simulated systematics
including PSF leakage, random but correlated PSF modelling errors, camera-based
additive shear bias and photometric redshift selection bias. We show that any
correlation between photometric-noise and the relative orientation of the
galaxy to the point-spread-function leads to an ellipticity selection bias in
tomographic analyses. This work therefore introduces a new systematic for
future lensing surveys to consider. We find that the B-modes in DES-SV appear
similar to a superposition of the B-mode signatures from all of the systematics
simulated. The KiDS-450 and CFHTLenS B-mode measurements show features that are
consistent with a repeating additive shear bias.
