Viscoelastic perturbations of the earth: significance of the incremental gravitational force in models of glacial isostasy

The incremental gravitational force (IGF) arises from perturbations of the earth's gravitational potential. In glacial isostasy, its sources are the surficial and internal mass redistributions associated with the growth and decay of the continental ice sheets. We examine the errors caused by the neglect of the IGF using closed-form solutions of the equations governing surface-load induced perturbations of two types of incompressible, spherical-earth models: (1) Maxwellian-viscoelastic mantle enclosed by elastic lithosphere, and (2) Maxwellian-viscoelastic mantle enclosing inviscid core. Calculations in the Legendre domain of the radial surface displacement for these models show that neglecting the IGF causes enhancement of the elastic response and acceleration of the viscous relaxation. In the space domain, these changes entail corresponding modifications of the calculated land adjustment. The magnitude of the error caused by the neglect of the IGF strongly depends on the deglaciation history and load radius adopted. Assuming a typical deglaciation history, the error reaches a maximum of less than 20 m at the end of the deglaciation phase for loads comparable in size to the Canadian or the Fennoscandian ice sheets. We also compare spherical-earth models with IGF and plane-earth models without IGF. Calculations of the radial surface displacement show that the errors due to the neglect of sphericity and the IGF partially compensate each other. Taking the uncertainties of the observational data into account, we conclude that the majority of the Canadian and Fennoscandian glacial-isostatic adjustment data can be modelled with sufficient accuracy using a plane-earth model without IGF.