  This paper is motivated by recent works on inverse problems for acoustic wave
propagation in the interior of gas giant planets. In such planets, the speed of
sound is isotropic and tends to zero at the surface. Geometrically, this
corresponds to a Riemannian manifold with boundary whose metric blows up near
the boundary. Here, the spectral analysis of the corresponding Laplace-Beltrami
operator is presented and the Weyl law is derived. The involved exponents
depend on the Hausdorff dimension which, in the supercritical case, is larger
than the topological dimension.
