The relaxation of spherical and flat Maxwell Earth models and effects due to the presence of the lithosphere

The radial surface deflection of a spherical Earth model appropriate to time scales characteristic of glacial loading is compared with the associated halfspace response. For that purpose the analytical solution for a Maxwell sphere surrounded by a thick elastic shell is derived under the assumption of incompressibility. The half-space approximation is deduced as a special case directly from the spherical solution. Comparison of the response spectra, for different thicknesses of the elastic shell, reveals only minor differences. In the spatial domain, the half-space approximation may, nevertheless, diverge significantly from the spherical solution. For a disk load radius R = 800 km (Fennoscandia), the half-space approximation is adequate, whereas it is usually inappropriate if R = 1600 km (Laurentia). The sensitivity of the response to the thickness of the elastic shell is also investigated. For R = 800 km, the surface deflection in the central region below the load is fairly diagnostic of the shell thickness. If R = 1600 km, the peripheral region is more sensitive to this parameter.