Perturbation theory for the stress tensor in the Moon's body with tidal effects taken into account

V. P. Pavlov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 195-205

Résumé

On the basis of the seismic data from the Apollo project, we show that one can use linear elasticity theory to process these data, which yields information on the mechanical parameters of the Moon's body with an accuracy of 10%. Within this theory, we obtain a theoretical formula for the dependence of pressure on depth in the Moon's body in the presence of tidal effects. We also derive theoretical dependence of the variations of the free energy density due to tidal effects on latitude and depth. In all these formulas the contribution of shear stresses is taken into account. It turns out that the main contribution is made by the Earth tides. Estimates for the dissipation of the energy of tidal oscillations show that this energy is certainly enough to explain where the energy released in deep focus moonquakes comes from.