On the spectrum of the earth.

We introduce an appropriate form and present an analysis of the elastic-gravitational system of equations describing the free oscillations of a rotating earth. We highlight the complications associated with the presence of an outer core. We discuss basic properties, including energy estimates, well-posedness, extraction of the elastic wave equation and a characterization and computation of the spectrum. We show how physics constrains the essential spectrum. We conclude with the analysis of an inverse problem for a spherically symmetric model (PREM) and give, via a trace formula, a spectral rigidity result. We will also show some recent observations. Joint research with S. Holman, J. Ilmavirta, S. Jimbo, G. Nakamura, H. Pham and J. Shi.


This talk is part of a Inverse Problem half-day : https://www-ljk.imag.fr/membres/Faouzi.Triki/projetANR/sem1.pdf