The study of glacial isostatic adjustment (GIA) is gaining an increasingly important role within the geophysical community. Understanding the response of the Earth to loading is crucial in various contexts, ranging from the interpretation of modern satellite geodetic measurements (e.g. GRACE and GOCE) to the projections of future sea level trends in response to climate change. Modern modelling approaches to GIA are based on various techniques that range from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, we do not have a suitably large set of agreed numerical results through which the methods may be validated; a community benchmark data set would clearly be valuable. Following the example of the mantle convection community, here we present, for the first time, the results of a benchmark study of codes designed to model GIA. This has taken place within a collaboration facilitated through European Cooperation in Science and Technology (COST) Action ES0701. The approaches benchmarked are based on significantly different codes and different techniques. The test computations are based on models with spherical symmetry and Maxwell rheology and include inputs from different methods and solution techniques: viscoelastic normal modes, spectral-finite elements and finite elements. The tests involve the loading and tidal Love numbers and their relaxation spectra, the deformation and gravity variations driven by surface loads characterized by simple geometry and time history and the rotational fluctuations in response to glacial unloading. In spite of the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the participants
Summary The Fennoscandian relaxation‐time spectrum (RTS), first derived by McConnell (1968), is a classic data set in studies of glacial isostatic adjustment (GIA). We outline a new method for estimating an RTS from a set of strandline data, which is based on a damped least‐squares solution for spherical harmonic coefficients associated with the strandline heights. In contrast to the Hankel transform approach outlined by McConnell (1968), the method does not require interpolation or extrapolation of the data, nor does it use the assumption that peripheral deformations are zero. We begin by applying the new approach to a suite of synthetic strandlines. These synthetic calculations quantify the effect on the RTS estimates of the common assumptions of free‐decay uplift, an axisymmetric Fennoscandian deformation field, and the uncertainty introduced by limited spatial and temporal sampling of this field. Recently, the accuracy of the Sauramo (1958) strandline data upon which the McConnell (1968) RTS was based has been questioned (Wolf 1996); accordingly, we apply our new approach to a set of more robust strandline data published by Donner (1964, 1969, 1980, 1995) to compute a revised RTS for Fennoscandia. At high harmonic degrees (above 50), our new RTS is characterized by weak constraints, whereas McConnell’s (1968) RTS suggests a significant reduction in relaxation times relative to the values at low degrees. This reduction was the basis for McConnell’s (1968) inference of an elastic lithosphere. In contrast to this, we conclude that the trend is an artefact of the observational data set he adopted. At lower degrees, McConnell’s (1968) relaxation‐time estimates lie at the lower end of the range implied by the present analysis. To complete our study, we apply the techniques of linearized Bayesian inference to invert our newly derived RTS for mantle viscosity. We find that the RTS provides an estimate of ~ 5 × 1020 Pa s for the volumetric mean viscosity in a region extending from the base of the lithosphere to about 550 km depth. Target regions which extend from the transition zone to ~ 1200 km depth are less well constrained; however, the average viscosity from the base of the lithosphere to 1200 km depth is consistent with the classic Haskell (1935) value of 1021 Pa s for mantle viscosity. Finally, we demonstrate that viscosity models within the class inferred by Mitrovica & Forte (1997) from joint inversions of postglacial relaxation times associated with GIA and mantle convection observables simultaneously fit the revised Fennoscandian RTS.
We consider a chemically and entropically stratified, compressible, rotating fluid planet and study gravitational-viscoelastic perturbations of a hydrostatic initial state. Using the Lagrangian formulation, we first derive the incremental field equations and continuity conditions governing the perturbations. Following this, we deduce the asymptotes to the equations for short and long times after the onset of the perturbations. The short-time asymptotic equations are referred to as the incremental field equations and continuity conditions of generalized elastodynamics. They include the equations of conventional elastodynamics as zeroth-order approximations. The long-time asymptotic equations agree with the incremental field equations and continuity conditions of Newtonian-viscous fluid dynamics. In particular, the incremental thermodynamic pressure appearing in the long-time asymptote to the incremental constitutive equation satisfies the appropriate incremental state equation. Finally, we introduce the generalized incremental incompressibility condition. Based on it, we derive approximate incremental field equations for gravitational-viscoelastic perturbations of isochemical, isentropic and compressible regions.
S U M M A R YWe investigate the effects of lateral heterogeneities in the upper mantle on the calculation of postglacial land uplift. For the model calculations we use a commercial finiteelement code, which enables us to solve the equations governing a layered, isotropic, incompressible, Maxwell-viscoelastic half-space with laterally varying layer thicknesses and physical properties. Following previous investigations performed by Sabadini, Yuen & Portney (1986) and Gasperini & Sabadini (1989), we extend their results using a more realistic loading history and different earth models. We then focus our attention on the question whether lateral heterogeneities in the upper mantle can be modelled correctly using a set of homogeneous earth models. To this end, a comparison of model calculations using both laterally homogeneous and heterogeneous earth models is performed.We find that lateral heterogeneities in the upper mantle significantly influence the calculated postglacial land uplift. The resolving power of relative sea-level observations for the prescribed lateral heterogeneities used in this study is mainly focused on observations around the load margin and outside the glaciated areas, where differences in predicted land uplift between individual models are large enough to be resolved by observations.We can qualitatively determine lateral heterogeneities in the upper mantle using a set of laterally homogeneous earth models, if the geological structure, for example a continental margin, is known. However, in order to infer the correct values of lithospheric thickness and asthenospheric viscosity, we need to use laterally heterogeneous models.
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