Modelling the Relation between Gravity and Vertical Displacement Change Rates in Formerly Glaciated Areas

In formerly glaciated areas, the rate of change of surface gravity, g-dot, and vertical deformation rate of the solid surface, u-dot, are two observables that contribute information on glacial isostatic adjustment (GIA). The main purpose of this presentation is to investigate the predicted relation between g-dot and u-dot in previously glaciated areas with the aim to determine if such a relation can provide additional insight to the physics of this process and also improved constraints on model parameters. We use the normal mode approach for one dimensional earth models and solutions of the sea level equation with time-dependent coastline geometry.

Numerical predictions of g-dot and u-dot are computed for Laurentia, Fennoscandia and the British Isles respectively, using six different earth models. Within each region a linear trend is then fitted using the relation g-dot = C · u-dot + g₀-dot. Estimated values of C and g₀-dot differ more between the regions than between different earth models within each region. For Fennoscandia, C ≈ 0.163 µGal/mm and for Laurentia C ≈ 0.152 µGal/mm. Maximum residuals between the linear trend and spatially varying model predictions of are 0.04 µGal/yr in Fennoscandia and 0.17 µGal/yr in Laurentia. For the British Isles the results are harder to interpret, mainly since this region is located on the zero uplift isoline of Fennoscandia. In addition, we study the temporal variation of the relation since the last glacial maximum till present-day.

The temporal and spatial variation of the relation between g-dot and u-dot can be explained by (i) the elastic and viscous proportions of the total signal and (ii) the spectral composition of the regional signal. Additional local effects, such as the Newtonian attraction and elastic deformation from local sea level changes, are examined in a case study for six stations in the Nordic absolute gravity network. The influence of these local effects on the relation between g-dot and u-dot is negligible except for extreme locations close to the sea.