  Exotic compact objects refer to a wide class of black hole alternatives or
effective models to describe phenomenologically quantum gravitational effects
on the horizon scale. In this work we show how the knowledge of the
quasi-normal mode spectrum of non-rotating wormhole models can be used to
reconstruct the effective potential that appears in the perturbation equations.
From this it is further possible to obtain the parameters that characterize the
specific wormhole model, which in this paper was chosen to be the one by Damour
and Solodukhin. We also address the question whether one can distinguish such
type of wormholes from ultra compact stars, if only the quasi-normal mode
spectrum is known. We have proven that this is not possible by using the
trapped modes only, but requires additional information.
  The here presented inverse method is an extension of work that has previously
been developed and applied to the oscillation spectra of ultra compact stars
and gravastars. However, it is not limited to the study of exotic compact
objects, but applicable to symmetric double barrier potentials that appear in
one-dimensional wave equations. Therefore we think it can be of interest for
other fields too.
