Glacial rebound and relative sea-level variations: a new appraisal

Abstract

Late Pleistocene and Holocene changes in sea-level at technically stable shorelines contain information on the melting history of the ice sheets and on the response of the Earth to changes in surface loads on time scales of 104yr. Some separation of parameters defining the ice loads and the Earth's response can be achieved by examining sea-level change at different sites around the world and at different epochs. This paper examines the mathematical requirements for obtaining satisfactory solutions for the sea-level equation rather than emphasizing results for the Earth's response to the surface loads. an examination of the equation expressing the sea-level variation on a viscoelastic earth indicates that careful consideration needs to be given to both the definition of the ice load and the geometry of the redistributed water load if geophysically significant Earth-response parameters are to be deduced from observations of relative sea-level. the spectrum of the 5° × 5° area-mean description of the ice load, widely used in glacial rebound studies, contains significant power at high degrees (n > 30) and can result in substantial spatial variations in sea-level unless a thick lithosphere is introduced in the Earth's response function. A smoothed 1°× 1° description of the ice model avoids these high-degree oscillations in relative sea-level and produces satisfactory sea-level results without requiring a thick lithosphere. At far field sites, the Holocene sea-levels are sensitive to the Earth's response to the meltwater loading in the vicinity of the site and a high-degree spatial resolution of coastline geometry is required to model the mantle flow driven by the differential loading about the site. At some sites convergence of the solution to the sea-level equation is not obtained, even when the solution is expanded to degree 180. Convergent solutions at lower degrees can be achieved by introducing earth models with a moderately thick lithosphere. If high-resolution ice and meltwater load models are not used then the tendency will be to overestimate the effective elastic thickness of the lithosphere. Estimates of mantle viscosity are also of questionable value if these high resolution models are not used. A preliminary examination of sea-levels at sites in both the near- and far-field places an upper limit of about 50–80 km on the effective lithospheric thickness. These sea-level observations are also consistent with an upper mantle viscosity of about 1021 Pas with a lower mantle viscosity in the range of 1021−1023Pa s.