  In this paper, we categorize non-rotating black hole spacetimes based on
their pole structure and in each of these categories we determine whether the
WKB approximation is a valid approximation for calculating the asymptotic
quasinormal modes. We show that Schwarzschild black holes with the Gauss-Bonnet
correction belong to the category in which the WKB approximation is invalid for
calculating these modes. In this context, we further discuss and clarify some
of the ambiguity in the literature surrounding the validity conditions provided
for the WKB approximation.
