  We use microlocal radial estimates to prove the full limiting absorption
principle for $P$, a self-adjoint 0th order pseudodifferential operator
satisfying hyperbolic dynamical assumptions as of Colin de Verdi\`ere and
Saint-Raymond. We define the scattering matrix for $P-\omega$ with generic
$\omega \in \mathbb R$ and show that the scattering matrix extends to a unitary
operator on appropriate $L^2$ spaces. After conjugation with natural reference
operators, the scattering matrix becomes a $0$th order Fourier integral
operator with a canonical relation associated to the bicharacteristics of
$P-\omega$. The operator $P$ gives a microlocal model of internal waves in
stratified fluids as illustrated in the paper of Colin de Verdi\`ere and
Saint-Raymond.
