Elastic Deformations of a Rotating Spheroidal Earth Due to Surface Loads.
NAVAL RESEARCH LAB WASHINGTON DC
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We have developed a differential system of equations for representing the deformations of a rotating elastic Earth which has a spheroidal shape and which is hydrostatically prestressed. Our system is meant to represent a more sophisticated model for the Earths load tide than the ones hereto studied because of the inclusion of rotational terms. In this study, we have assumed that the rotational axis is fixed with respect to the spheroid and that the rotational velocity is constant. We have reached a linearized version of the Navier-Stokes equations consisting of six equations which simultaneously relate three orders of harmonics. We have a boundary-value problem whose solutions must be regular functions of the radial distance in the neighborhood of the center of the configuration and which must also satisfy three other conditions at the free surface varying according to loading conditions. Numerical integration of this differential system requires the knowledge of an Earth model consisting of a density profile and of the elastic parameters as functions of the radial distance. Because of the vanishing of the rigidity, the differential system valid for the liquid outer core shrinks to a system of only four equations discontinuity of some of the variables are to be entertained at the interfaces between the liquid outer core and the solid inner core andor the solid mantle. We briefly discuss the proposed method of numerical solution. Author