IERS/GGFC  Special Bureau for Mantle

Glacial Isostatic Adjustment

A Survey of Recent Studies

        The global process of glacial isostatic adjustment (GIA) is the process whereby the Earth's shape and gravitational field are modified in response to the large scale changes in surface mass load that have attended the glaciation and deglaciation of the planetary surface.  The last deglaciation event of the current ice-age began at Last Glacial Maximum (LGM) approximately 21,000 calendar years ago and ended approximately 5000 years ago, by which time the cryosphere had been diminished to approximately its present geographical extent.  Prior to the present Holocene epoch of Earth history, beginning in mid-Pleistocene time approximately 900,000 years ago, the planet  experienced 9 cycles of glaciation and deglaciation, the 100,000 year period of the canonical glacial cycle being characterized by a glaciation phase that lasts approximately 90,000 years and a deglaciation phase that lasts approximately 10,000 years.  At the maximum extent of each of these glacial epochs, sea level was lowered by approximately 120 m in supplying the water of which the great continental ice sheets of the glacial epochs were constructed.

        Interest in studying the response of the planet to these Pleistocene glacial cycles derives primarily from the fact that the geological, geophysical and astronomical data which record them are of such high quality.  Furthermore, these data are almost uniquely capable of providing firm constraints upon the viscoelastic properties of the "solid" interior of the earth.  The rheological model that has most often been employed to invert the data has been the linear viscoelastic Maxwell model with the elastic Lamé parameters of this model (shear modulus, bulk modulas and density) fixed by the constraints of global free oscillation and body wave seismology.  The single remaining parameter of the model, namely the molecular viscosity, is then inferred by fitting the global model of the GIA process to the observations.  Not only do these data significantly constrain Earth rheology, however, they also provide stringent constraints on a wide range of processes related to the internal dynamics of the climate system itself.  A very recent and detailed review of this rapidly expanding body of knowledge can be found in the paper: Peltier, W.R., 1998: Postglacial variations in the level of the sea: implications for climate dynamics and solid earth geophysics, Rev. Geophysics, 36, 603-689.

        Among the most recent advances that have been achieved in this area are those concerning the development of a complete version of the theory that includes the impact of the time dependence of the ocean function upon the adjustment process.  Proper account of this impact has turned out to require implementation of an iterative procedure first discussed in: Peltier; W.R., 1994: Ice age Paleotopography, Science, 265, 195-201; as well as recognition of the occurrence of a non-perturbative effect in the solution of the integral sea level equation which is such as to require recognition of the existence of a surface ice load in the glaciated state that does not explicitly appear in the kernel of the linear perturbation theory based integral sea level equation.  This non-perturbative effect was first pointed out in Peltier, W.R., 1998: Implicit ice in the global theory of glacial isostatic adjustment, Geophys. Res. Lett., 25, 3956-3960.  When the implicit component of the ice load is recognized as having been active in the surface unloading of areas that were initially ice covered but later came to be inundated by the sea, one achieves a much closer agreement with a-priori reconstructions of ice sheet form based upon solution of the equations that govern ice accumulation and flow such as one finds in the glaciological literature (e.g. see L. Tarasov and W.R. Peltier, 1999: Impact of thermomechanical ice sheet coupling on a model of the 100 kyr ice age cycle, J. Geophys. Res., 104, 9517-9545).

        A further influence upon the glacial isostatic adjustment process that has recently been investigated concerns the feedback of the changing rotational state of the planet caused by the glaciation and deglaciation process upon the variations of sea level that occur during the GIA process.  In the paper by B.G. Bills and T.S. James, 1996: Late Quaternary variations in relative sea level due to glacial cycle polar wander, Geophys. Res. Lett., 23, 3023-3026, the authors suggest that this effect would be extremely large, large enough so as to entirely invalidate all previous analyses that had been performed using the "sea level equation" formalism first developed in the work of Peltier (1974; The impulse response of a Maxwell Earth, Rev. Geophys. Space Phys., 12, 649-669), Peltier and Andrews (1976; Glacial isostatic adjustment I: The forward problem, Geophys. J. Roy astr. Soc., 46, 605-646), Peltier (1976; Glacial isostatic adjustment II: The inverse problem, Geophys. J. Roy. Astr. Soc., 46, 669-706) and Farrell and Clark (1976; On postglacial sea level, Geophys. J. Roy. astr. Soc., 46, 647-667).  First solutions of the "sea level equation" for realistic models of surface deglaciation were published by Clark, Farrell and Peltier (1978; Global changes in postglacial sea level: a numerical calculation, Quat. Res., 9, 265-287) and by Peltier, Farrell and Clark (1978; Glacial isostasy and relative sea level: a global finite element model, Tectonophysics, 50, 81-110).  Recent detailed analyses of the issue of rotational feedback on the variations of relative sea level that are induced by the deglaciation process (Milne and Mitrovica, 1996; Geophys. J. Int., 126, F13-F20; Peltier, 1998, Inverse Problems, 14, 441-478; Peltier, 1999, Global and Planetary change, 20, 93-123) have, however, very clearly established that the claim of Bills and James insofar as the strength of the rotational feedback on sea level is concerned was more than an order of magnitude in error.  This influence is in fact sufficiently weak that for almost all purposes it may be safely neglected.

        Recent developments in the formal inference of the radial viscosity structure of the mantle based upon the GIA data are gradually leading to some concensus among the several different groups in which this work is actively pursued.  The application of formal inverse theory to the inference of viscosity depth dependence based upon the simultaneous inversion of the relaxation times that characterize distinct site specific sea level histories from previously glaciated regions, the suite of wavenumber dependent relaxation times that characterize the postglacial recovery of Scandinavia, along with the constraints provided by certain earth rotation observations (non-tidal acceleration and true polar wander speed and direction) have led to a significant refinement of our knowledge of this important transport coefficient.  As first discussed in Peltier and Jiang (1996, Geophys. Res. Lett., 23, 503-506; 1997, Surveys of Geophysics, 18, 239-277) and more recent papers mentioned above it is now clear that the totality of these data require that mantle viscosity increase by approximately  one order of magnitude from an average value near 0.5 x 1021 Pa s in the upper mantle and transition zone to an average value of 2-3 x 1021 Pa s in the lower half of the lower mantle.  The viscosity in this deepest part of the mantle is constrained only by the earth rotation data.  If the modern day global rate of sea level rise (which has a magnitude near 2 mm/yr), is significantly influenced by the melting of polar ice sheets then the rotational data must be decontaminated of this influence prior to employing them together with the glacial isostatic adjustment constraints to infer mantle viscosity.  Allowing for the influence of such contamination requires that the viscosity inferred for the lower half of the lower mantle be increased, depending upon the assumed level of contamination, to a value near 1022 Pa s (see Figure 31 in Peltier 1998, Rev. Geophys., 36, 603-689).

        In connection with the issue of mantle viscosity, there is also considerable interest in the fine structure of the radial profile in the vicinity of the phase transition at 660 km depth in which the mineral Olivine is transformed into a mixture of Perovskite and Magnesiowustite.  In Peltier (1985, J. Geophys. Res., 90, 9411-9421) it was suggested that, if the convective circulation were layered, there should be an anomalously soft layer just above this horizon, and perhaps also an anomalously stiff layer below (an internal lithosphere).  Direct evidence for the presence of such a soft layer has recently been forthcoming through analysis of the aspherical geoid that is supported by the mantle convection process (e.g. see Forte et al., 1993, Geophys. Res. Lett., 20, 225-228).  In Peltier, 1998 (e.g. Rev. Geophys., op.cit., Inverse Problems, op.cit. and Milne et al., 1998, EPSL, 154, 265-278), it is shown that if one simply adds such a soft layer to the otherwise smooth viscosity profile delivered by formal inversion than such models are firmly rejected by the observations.  However, the misfits induced by the presence of the soft layer may be eliminated by increasing the viscosity in the remainder of the overlying transition zone by exploiting the inherent non-uniqueness of the inverse problem (Peltier, 1998, Inverse Problems, 14, 441-478).  It remains unclear as to whether models of this kind are also able to acceptably reconcile the convection timescale constraints, however.  If they were not, this would argue that the soft layer may be a non-Newtonian consequence of the influence of transformational superplasticity associated with the dynamical influence of the phase transition itself.  In this entirely plausible scenario, the soft layer would not exist for the shorter timescale glacial isostatic adjustment process though it would profoundly influence the process of mantle convection.  This issue concerning the Newtonian or non-Newtonian nature of the creep mechanism is one of the great unresolved enigmas that lies at the centre of the ongoing debate concerning mantle geodynamics.  What we are able to conclude at present is that, with the possible exception of the region of the mantle near 660 km depth, the viscosity structure required by the GIA and convection processes are plausibly identical.  To the extent that they can be shown to be identical, we will establish that the governing creep mechanism is Newtonian, otherwise they would be incomprehensible given the enormous disparity in the timescales that characterize these distinct processes.



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Last Updated: April 10, 2000