Load Numbers, Solid Earth Tides, and Liquid Core Dynamics.

摘要

This report presents in a systematic and rigorous way procedures suitable for the numerical evaluation of the Earth's spheroidal deformations, which most commonly are called the Earth's tides. For this purpose, we: (a) study the Boussinesq theory for the elastic deformations of a flat plate and show how by applying the Boussinesq solution to the tangent plane at a loading point of the spheroidal Earth we can establish the asymptotic behavior of the load numbers (2); (b) elaborate on certain numerical procedures which seem to be best suited for the summation of series once the asymptotic behavior of their coefficients has been ascertained; (c) provide in tabular form the closed form expressions of those infinite series of spherical harmonics which are essential for the numerical evaluation of the Earth's tides; and (d) examine the dynamics of a liquid core for a nonrotating Earth to mathematically prove the existence of a boundary layer at the top of the liquid core. This layer provides a justification for the discontinuous behavior of some of the integration variables at the liquid core/solid mantle interface, and furnishes the proper number of free parameters for satisfying the boundary conditions at the loaded surface. (Author)