Weyl formulae for some singular metrics with application to acoustic modes in gas giants

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...

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Published inarXiv.org
Main Authors de Verdìère, Yves Colin, Dietze, Charlotte, de Hoop, Maarten V, Trélat, Emmanuel
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.06.2024
Subjects
Acoustic propagation
Acoustic waves
Gas giant planets
Inverse problems
Operators (mathematics)
Riemann manifold
Spectrum analysis
Wave propagation
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Summary: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.
ISSN:2331-8422