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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