Tables for the deformation of an Earth model by surface mass distributions

The surface displacements of a spherical earth model consisting of a homogeneous elastic shell enclosing a fluid core are given in the case that the deforming forces arise from a mass distribution of constant thickness over a single spherical surface cap of arbitrary size. A simple method is also given for the computation of the displacements for which the deforming forces arise from any surface mass distribution. In practice such loads are associated with geological structures, ice loads, snow caps, changing atmospheric pressure, and ocean tides. Values of the surface displacements are listed for various values of the radius of the cap and for values of the elastic parameters which correspond to a simplified representation of Bullen's [1947] model. The density and thickness of the mass over the caps has been chosen to give a mean pressure of 106 dynes/cm2 over the surface. But displacements for other densities and thicknesses can easily be obtained from the tables, which can also be used for other values of the elastic parameters in the core and mantle, provided that Poisson's ratio in the mantle is kept equal to 0.28.