Deformation of an Earth model by surface pressures

The surface displacements of a spherical earth model consisting of a homogeneous elastic shell enclosing a fluid core are considered, when the surface stress consists of a uniform pressure over equal antipodal circular caps and is zero elsewhere. On the earth, local loads are generally associated with geological structures, ice loads, or the ocean tides. In the present theory, the gravitational effects arising from the deformations are not included—such effects are small when the radius of the loaded area is small. Values of the surface displacements are listed for four values of the radius of the pressure cap, and for values of the elastic constants which correspond to a simplified representation of Bullen's [1947] model. In the shell the elastic constants λ2 and μ2 are 14/11×1012 and 1012, respectively, corresponding to a Poisson's ratio of 0.28. The value of the outer radius of the shell, r2, is 6.371×108 cm; the inner radius, r1 is 0.545r2. Within the core, μ1 = 0, and λ1 μ2−1 = 8. The computed results are easily modified for other values of λ1 and μ2 provided the value of Poisson's ratio in the shell remains unchanged. The geophysical implications of the results are discussed.