Thermoelastic deformations of the Earth's lithosphere: A mathematical model (Q1072791)

We examine the problem of the thermoelastic deformation of a spherical Earth with constant elastic parameters heated from within by the spontaneous decay of radiogenic elements. The problem consists of the simultaneous solution of the Navier-Stokes equation and the heat conduction equation. We reach an integrodifferential equation which we solve by means of the Laplace transform and the Green function approach. We obtain analytic solutions for the temperature distribution and radial deformation as infinite series of functions of the radial distance and time, depending also on a sequence of eigenvalues. We provide particular solutions for the case when the two specific heats \(C_ p\) and \(C_ v\) are approximately equal. We believe that our analytic results are applicable to the study of the oceanic lithosphere deformations. Our approach could be successfully applied to ascertain the deformation according to other regimes of internal heating.