Modelling of mantle postglacial relaxation in axisymmetric geometry with a composite rheology and a glacial load interpolated by adjusted spherical harmonics analysis

Abstract

S U M M A R YAlthough studies on glacial isostatic adjustment usually assume a purely linear rheology, we have previously shown that mantle relaxation after the melting of Laurentide ice sheet is better described by a composite rheology including a non-linear term. This modelling is, however, based on axially symmetric geometry and glacial forcing derived from ICE-3G and suffers from a certain amount of arbitrariness in the definition of the ice load. In this work we apply adjusted spherical harmonics analysis to interpolate the ice thicknesses of ICE-3G and ICE-1 glaciological models. This filters out the non-axisymmetric components of the ice load by considering only the zonal terms in the spherical harmonics expansion. The resulting load function is used in finite-element simulation of postglacial rebound to compare composite versus purely linear rheology. Our results confirm that composite rheology can explain relative sea level (RSL) data in North America significantly better than a purely linear rheology. The performance of composite rheology suggests that in future investigations, it may be better to use this more physically realistic creep law for modelling mantle deformation induced by glacial forcing.The modelling of mantle deformation induced by mass redistribution between oceans and ice sheets during glacial cycles (Haskell 1935;Cathles 1975;Peltier & Andrews 1976) is one of the most important tools for inferring the rheological behaviour of the Earth. The majority of postglacial rebound (PGR) studies are conducted assuming a linear viscoelastic rheology for the Earth's mantle, even though there is strong evidence of non-linearity from mineral microphysics (Ranalli 1995). The point here is that if the flow law is linear and the structure of the Earth quite uniform, the problem can be treated by rigorous spectral methods taking advantage of the superposition principle. When some terms of the governing equation are non-linear or the rheological structure is complex (e.g. laterally varying), the superposition of the harmonic responses is no longer applicable. These are the reasons why the first models with a non-Newtonian mantle (Post & Griggs 1973;Brennen 1974;Crough 1977) were based on unrealistic assumptions and their results need to be interpreted with caution. More rigorous solutions of the non-linear case have recently been obtained through finite elements (FE), but only models with non-linear zones in either the upper mantle or the lower mantle performed better than a purely linear reference model (Wu 1999(Wu , 2002, while a uniform non-Newtonian mantle yielded a close but still worse fit to relative sea level (RSL) data than a Newtonian model (Wu 2001). Therefore, a purely non-Newtonian rheology had never appeared to be preferable to a linear creep law. Nevertheless, the observations of traces of deformation due to both diffusion and dislocation creep in laboratory samples suggest that a realistic mantle rheology might be composite, with linear or non-linear creep mechanisms temporarily and local...

Sea levels and uplift rate from composite rheology in glacial isostatic adjustment modeling

“…Gasperini et al (2004) used a flat axisymmetric model and found that composite rheology was able to fit RSL data better than linear rheology. This is confirmed by Dal Forno et al (2005) and Dal Forno and Gasperini (2007).…”

“…Currently, it is not clear how composite rheology behaves for different values of A*, whether the predictions are closer to linear or non-linear rheology, and how predictions using a composite rheology depend on location and time. The answers to these questions can help us relate previous studies of non-linear rheology by Wu (2002) and Wu and Wang (2008) to studies of composite rheology (Gasperini et al, 2004;Giunchi and Spada, 2000;Dal Forno et al, 2005;Dal Forno and Gasperini, 2007). Moreover, present-day uplift rates from composite rheology have not been studied, while a known problem with non-linear rheology is the low uplift rates it provides (e.g.…”

“…Dal Forno et al (2005) and Dal Forno and Gasperini (2007) showed that composite rheology fits the RSL data significantly better than linear and non-linear rheology. However, a global misfit number does not illuminate the temporal and geographic spread of differences in sea level curves, while the RSL behavior at a specific location is sometimes useful to distinguish between linear and non-linear rheology (e.g.…”

“…Finally, self-gravitation and the self-consistent sea-level equation are neglected in previous studies (Giunchi and Spada, 2000;Gasperini et al, 2004;Dal Forno et al, 2005;Dal Forno and Gasperini, 2007). The sea-level can be important at the edge of the former ice sheet, where the ice attracted large amounts of sea water and where also linear and non-linear rheologies behave differently (Wu, 1995).…”

“…Previous studies with composite rheology use a flat Earth geometry (Gasperini et al, 2004;Dal Forno et al, 2005;Dal Forno and Gasperini, 2007) while sphericity can become important for the Laurentide ice sheet especially for RSL data far from its center. Finally, self-gravitation and the self-consistent sea-level equation are neglected in previous studies (Giunchi and Spada, 2000;Gasperini et al, 2004;Dal Forno et al, 2005;Dal Forno and Gasperini, 2007).…”