Glacial-Isostatic Adjustment-I. The Forward Problem

Abstract

The isostatic adjustment of a radially stratified visco-elastic spheroid is treated using space-time Green functions for the associated surface mass load boundary value problem. These impulse response functions are convolved with a Heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t = 0 and allowed to remain on the surface. The resulting ' Heaviside Green functions ' can be employed to simulate al! of the important signatures of glacial isostatic adjustment. Given a space-time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins, these source terms are simply convolved with the Heaviside Green function appropriate to a specific response signature. A realistic model of the spatial distribution of the main late Pleistocene ice loads and of their temporal disintegration is constructed. The response of two visco-elastic earth models is computed and compared to a global set of relaxation data (relative sea-level curves). On the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded. In addition, clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the Laurentide ice sheet. Such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness. Further extensions of the calculation are suggested.

On the reconstruction of palaeo-ice sheets: Recent advances and future challenges

“…Pure 'GIAbased' reconstructions invoke iterative tuning of ice load chronologies to fit relevant GIA data, subject to geologically-inferred ice margin chronologies (e.g. Peltier and Andrews, 1976). Traditionally, the GIA-based method was largely reliant on relative sea level (RSL) data, which have no coverage for the large regions of palaeo-ice sheets that are presently ice covered and/or were not exposed to post-glacial submarine conditions.…”

On the origins of Earth rotation anomalies: New insights on the basis of both “paleogeodetic” data and Gravity Recovery and Climate Experiment (GRACE) data

“…Such predictions are made by solving an integral equation that I have come to refer to as the sea level equation (SLE). A primitive version of the SLE was first solved by Clark et al [1978] and Peltier et al [1978], based on the work of Peltier [1974Peltier [ , 1976, Peltier and Andrews [1976], and Farrell and Clark [1976]. Given a history of continental ice sheet thickness variations I(q, l, t), solution of the SLE delivers the space-and time-dependent field S(q, l, t) which represents the variation of the level of the sea relative to the continuously deforming surface of the solid Earth.…”

Modelling of the GIA-induced surface gravity change over Fennoscandia

“…[30,5,34,31,43,44,45], that is, the normal mode method for a spherical, non-rotating, laterally homogenous, viscoelastic Earth as an extension of the work of [19,20] and [13] who considered an elastic body only. The sea level variations are found by solving the Sea Level Equation, originally introduced by [12].…”

“…Based on the assumption of isostatic equilibrium at Latest Glacial Maximum (LGM), the surface vertical displacement u and gravity change ∆g, since the assumed isostatic equilibrium at LGM, is found by convolving appropriate Green's functions G in time and space, with a function L of the temporal and spacial evolution of the loading of the Earth [34] (with notation from [36]),…”

“…The theoretical foundation is based on the theory introduced by [30,34] for a spherical, non-rotating, laterally homogenous, viscoelastic, Maxwell Earth and the solution of the Sea Level Equation, originally introduced by [12], with time-dependent coastline geometry. The ice history is de ned by the ice model ICE-5G.…”