Time-domain approach to linearized rotational response of a three-dimensional viscoelastic earth model induced by glacial-isostatic adjustment: I. Inertia-tensor perturbations

Abstract

For a spherically symmetric viscoelastic earth model, the movement of the rotation vector due to surface and internal mass redistribution during the Pleistocene glaciation cycle has conventionally been computed in the Laplace-transform domain. The method involves multiplication of the Laplace transforms of the second-degree surface-load and tidal-load Love numbers with the time evolution of the surface load followed by inverse Laplace transformation into the time domain. The recently developed spectral finite-element method solves the field equations governing glacial-isostatic adjustment (GIA) directly in the time domain and, thus, eliminates the need of applying the Laplace-domain method. The new method offers the possibility to model the GIA-induced rotational response of the Earth by time integration of the linearized Liouville equation. The theory presented here derives the temporal perturbation of the inertia tensor, required to be specified in the Liouville equation, from time variations of the second-degree gravitational-potential coefficients by the MacCullagh's formulae. This extends the conventional approach based on the second-degree load Love numbers to general 3-D viscoelastic earth models. The verification of the theory of the GIA-induced rotational response of the Earth is performed by using two alternative approaches of computing the perturbation of the inertia tensor: a direct numerical integration and the Laplace-domain method. The time-domain solution of both the GIA and the induced rotational response of the Earth is readily combined with a time-domain solution of the sea level equation with a time-varying shoreline geometry. In a follow-up paper, we derive the theory for the case when GIA-induced perturbations in the centrifugal force affect not only the distribution of sea water, but also deformations and gravitational-potential perturbations of the Earth.