Coupling the spectral element method with a modal solution for elastic wave propagation in global earth models

The equilibrium form of the Earth is generally computed using a hydrostatic theory that assumes a rotating, inviscid planet. We compute the perturbation to this equilibrium form due to the presence of a thin elastic lithospheric shell using viscoelastic Love number theory. The thin shell acts to reduce the flattening of the equilibrium form relative to the value obtained from the traditional hydrostatic calculation. Our results indicate that current estimates of the excess non-hydrostatic flattening of the Earth, defined as the discrepancy between the observed and hydrostatic forms, may therefore be underestimating the actual departure of the observed form from its equilibrium state. This conclusion may be important for viscous flow models of mantle convection, which are commonly constrained to fit the non-hydrostatic flattening. For completeness, we also adopt the Love number formulation to estimate the excess flattening associated with the gradual slowing of the Earthʹs rotation. Our predictions of the fossil rotational bulge confirm the widespread view that this effect is small for reasonable mantle viscosity profiles.