  We explore the possible observational signatures of different types of kink
modes (horizontal and vertical oscillations in their fundamental mode and
second harmonic) that may arise in coronal loops, with the aim of determining
how well the individual modes can be uniquely identified from time series of
images. A simple, purely geometrical model is constructed to describe the
different types of kink-mode oscillations. These are then `observed' from a
given direction. In particular, we employ the 3D geometrical parameters of 14
TRACE loops of transverse oscillations to try to identify the correct observed
wave mode. We find that for many combinations of viewing and loop geometry it
is not straightforward to distinguish between at least two types of kink modes
just using time series of images. We also considered Doppler signatures and
find that these can help obtain unique identifications of the oscillation modes
when employed in combination with imaging. We then compare the modeled spatial
signatures with the observations of 14 TRACE loops. We find that out of three
oscillations previously identified as fundamental horizontal mode oscillations,
two cases appear to be fundamental vertical mode oscillations (but possibly
combined with the fundamental horizontal mode), and one case appears to be a
combination of the fundamental vertical and horizontal modes, while in three
cases it is not possible to clearly distinguish between the fundamental mode
and the second-harmonic of the horizontal oscillation. In five other cases it
is not possible to clearly distinguish between a fundamental horizontal mode
and the second-harmonic of a vertical mode.
