S U M M A R YThe great majority of postglacial rebound computations carried out during the last three decades assumed a purely linear rheological relation for the mantle. Experimental data on high-temperature creep deformation and modelling of other tectonic processes, however, might also support the existence of non-linear creep mechanisms. We addressed postglacial rebound in North America through an axially symmetric finite-element model with a composite (linear plus non-linear) mantle rheology. In such a formulation, the transition stress σ T governs the balance between linear and non-linear creep components, while the term σ B , added to the effective shear stress, accounts for the background (ambient) stress induced by convection and other tectonic processes. By varying σ T and σ B in the ranges 0-10 MPa and 0-5 MPa respectively, we found that composite models fit Relative Sea Level (RSL) variations at 29 North American sites better than the purely linear model. On the basis of the effective shear stress induced in the mantle by glacial forcing (1-3 MPa), our results indicate that power-law creep accounts for the majority of the strain rate.
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...
We describe the implementation of the complete Sea Level Equation (SLE) in a Finite Element (FE) self-gravitating 3D model. The procedure, originally proposed by Wu (2004), consists of iterating the solution of the SLE starting from a non self- gravitating model. At each iteration, the perturbation to the gravitational potential due to the deformation at the density interfaces is determined, and the boundary conditions for the following iteration are modified accordingly. We implemented the computation of the additional loads corresponding to the perturbations induced by glacial and oceanic forcings at the same iteration at which such forcings are applied. This implies an acceleration of the convergence of the iterative process that occurs actually in three to four iterations so that the complete procedure, for a 6,800 elements FE grid, can be run in about two hours of computing time, on a four-core 2.2 GHz Linux workstation. This spherical and self-gravitating FE model can be employed to simulate the deformation of the Earth induced by any kind of load (non necessarily of glacial origin) acting on the surface and/or internally
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