
form, the surface load is assumed to be underlain by lower-
than-normal densities such that below the crust or lithosphere
the pressures are hydrostatic everywhere. The manner in which
this “compensating” mass is distributed gives rise to different
models of isostasy: Airy, Pratt, or regional. The first two models
are local compensation models in which the compensating mass
is located immediately below the load but in the third model, a
local load is supported regionally. The underlying assumption
in these models is that the surface loads are supported by stresses
within the crust-lithosphere and that the sub-lithospheric mantle
is fluid, an assumption that is operationally effective on long
timescales of many tectonic processes.
Glacial isostasy is concerned with the planet’s response to
the changing surface loads of ice and water during the waxing
and waning of large ice sheets. To a first approximation of local
isostasy, the crust beneath the ice sheet is depressed by the pro-
duct of the ratio of ice and mantle densities and the thickness of
the ice, such that somewhere below the ice-loaded lithosphere
the vertical pressures are constant at constant depth. For a
3 km thick ice cap, this would mean a crustal depression of
about 800 m. On timescales of glacial cycles (10
4
–10
5
years),
the mantle does not behave as a fluid and the load will be partly
supported by viscous stresses in the sub-lithospheric region.
Thus, the initial response to a large ice load will be by elastic
deformation of the entire lithosphere-mantle followed by a
viscous creep as the mantle stresses relax and the load is
increasingly supported by the lithosphere. The local isostatic
depression will be attained as a limit. Likewise, when the ice
sheet is removed, the initial response is elastic followed by a
viscous rebound. The rate at which this occurs will be a func-
tion of the mantle viscosity and observations of this rebound,
in fact, provide the primary evidence for this viscosity.
Large ice sheets have periodically formed on the Earth’s
surface in response to changes in planetary configurations and
the resulting changes in solar insolation (e.g., the Milankovitch
theory). Thus, water mass is withdrawn from the oceans and
localized at high latitudes when large ice sheets form, and more
than 50 10
6
km
3
of water is periodically moved between the
ice sheets and the oceans, resulting in a global lowering of sea
level by 130–150 m. This is the most direct consequence of
glacial isostasy: global fluctuations in sea level that mirror the
growth and decay of ice sheets during the glacial cycles of
the past two million years. The spatial pattern of this sea-level
change is, however, complex. What is observed is that the posi-
tion of past shorelines relative to the present shoreline position
and the crust – which forms the reference surface for the mea-
surement – is itself displaced during the surface-loading cycles.
Moreover, as the Earth deforms and mass is redistributed
around the globe, the gravity field of the planet changes and
surfaces of constant gravitational potential, e.g., the geoid or
sea level in the absence of oceanographic and meteorological
forcing, are modified as well. Thus, the relative sea-level obser-
vation at a locality is a measure of the change in ocean volume,
of the radial deformation of the Earth’s surface under the chan-
ging surface load, and of the change in gravitational potential.
The globally averaged sea-level change resulting from a change
in ice volume is referred to as the ice-volume-equivalent sea-
level change and, in the absence of other processes that change
ocean volume, this corresponds to eustatic sea-level change.
The Earth is presently in an interglacial period and the last
of the large ice sheets over North America and Europe disap-
peared before ~7,000 years ago. The remaining ice sheets
of Greenland and Antarctica also, in a first approximation,
stabilized by about this time. However, while ocean volumes
remained nearly constant during the interglacial period, sea
levels have continued to change as a result of the viscous or
delayed response of the Earth to the removal of the ice load
and the redistribution of the melt water into the oceans. The
amount of this post-glacial change at any location depends on
the relative importance of the different components contribut-
ing to the sea-level change: the crustal deformation under the
changing ice and water load, the changes in gravitational
potential, and the changes in ocean volume. The relative sea
level changes with location and with time and gives rise to
the complex spatial and temporal pattern of sea-level change
that has been observed.
The most obvious deformational effect of the glacial cycles
occurs in the areas of glaciation where, as illustrated above, the
crust may be depressed by hundreds of meters beneath large ice
sheets. However, the removal of water from the ocean basins
also adds to the deformation. The removal of 150 m of water
from an ocean basin would result in a rebound of the ocean
floor, and of islands within the basin, of up to 30–40 m accord-
ing to the local isostatic formulation. Thus, in any rigorous for-
mulation of glacial isostasy the total load of the ice and oceans
needs to be considered.
Sea level is not the only process perturbed by the glacial
cycles. Gravity is time dependent and this can be measured
instrumentally in areas of ongoing rebound. The radial and hor-
izontal changes in position of the crust can also be measured by
space-geodesy methods (the glacial rebound contains a hori-
zontal surface velocity signal as well as the radial signal).
The planetary rotation is modified as the inertia tensor evolves
through time, and the motions of satellites around the planet are
perturbed. All of these signals provide evidence for the Earth’s
viscous response function, but the sea-level signal remains the
most important because it has been preserved in the geological
record, primarily for the period since the last deglaciation and,
in a more fragmentary form, for earlier periods.
If the Earth’s viscosity and elastic structure as well as the
history of the ice sheets are known, then physically consistent
models can be developed that rigorously predict the observed
phenomenon: models that describe the deformation of the
entire planet, that distribute the meltwater in a self-consistent
way into time-dependent and realistic ocean basins, and that
include the effects of the changing water load as well as ice
load. The theory has to be a global one because all parts of
the mantle are affected by the deglaciation of one ice sheet.
This is illustrated in Figure G38 for a simplified model in
which the ice sheet, land mass, and ocean basin are longitude
independent. In this case, a continent-based ice sheet at the
north pole, with dimensions approximating the North American
Ice Sheet, has been rapidly removed and only the rates of man-
tle displacement caused by the changing ice loads are shown
for three epochs, 100 years after the unloading, and 6,000
and 12,000 years later. The deformation extends throughout
the mantle, down to the core-mantle boundary at ~2,900 km
depth, and to the antipodes of the ice cap. The contribution to
this deformation field from the water loading is much smaller
in amplitude and this is shown here only as the radial displace-
ment of the sea surface for three epochs, immediately after
unloading and showing the elastic deformation, and at 6,000
and 12,000 years later. These signals, while relatively small,
are observationally significant and important for estimating
the mantle rheology, particularly at margins far from the former
ice sheets, such as across the antipodal margin illustrated.
GLACIAL ISOSTASY 375