  Seismology of coronal loops using observations of damped transverse
oscillations in combination with results from theoretical models is a tool to
indirectly infer physical parameters in the solar atmospheric plasma. Existing
seismology schemes based on approximations to the period and damping time of
kink oscillations are often used beyond their theoretical range of
applicability. These approximations assume that the variation of density across
the loop is confined to a nonuniform layer much thinner than the radius of the
loop, but the results of the inversion problem often do not satisfy this
preliminary hypothesis. Here, we determine the accuracy of the analytic
approximations to the period and damping time, and its impact on seismology
estimates, when largely nonuniform loops are considered. We find that the
accuracy of the approximations when used beyond their range of applicability is
strongly affected by the form of the density profile across the loop, that is
observationally unknown and so must be arbitrarily imposed as part of the
theoretical model. The error associated with the analytic approximations can be
larger than 50% even for relatively thin nonuniform layers. This error directly
affects the accuracy of approximate seismology estimates compared to actual
numerical inversions. In addition, assuming different density profiles can
produce noncoincident intervals of the seismic variables in inversions of the
same event. The ignorance about the true shape of density variation across the
loop is an important source of error that may dispute the reliability of
parameters seismically inferred assuming an ad hoc density profile.
