MacNeil, F. Stearns
Postglacial Trangression
Sea Level Change and Its Effect on Reef Growth
Solution Unconformities
Subsidence Hypothesis of Reef Development
Thickness of Holocene Reefs
GLACIO-HYDRO ISOSTASY
Kurt Lambeck
The Australian National University, Canberra ACT,
Australia
Synonyms
Eustatic sea level; Glacial rebound; Postglacial sea level
Definition
Glacio-hydro isostasy refers to the earth’s response to
changes in surface ice and water loading during glacial
cycles. During the growth of an ice sheet, the crust is
loaded in the areas of glaciation and the crust beneath
and near the ice sheet subsides. During the decay phase
of an ice sheet, the crust is unloaded and rebounds. This
is the glacio-isostasy component. But as water is extracted
from, or added into, the oceans during ice growth and
decay, the oceanic crust also responds to the changing
water load. This response is called the hydro isostasy.
The two combined components, not uncoupled, are
referred to as glacio-hydro isostasy.
Introduction
The glacio-hydro isostatic effect is manifested in geological, geophysical, and geodetic observations. It is seen in
the geological record as a complex spatial and temporal
pattern of raised shorelines (Figure 1) in areas of former
glaciation (primarily the glacio-isostatic signal) as well
as along coastlines far from the former ice margins (primarily the hydro-isostatic signal). It is also seen in geodetic observations: as displacements of the crust, both
vertical and horizontal; as sea-level change in tide gauge
and satellite altimeter data; as changes in gravity measured
by surface instrumentation and by satellite sensors and
orbital perturbations; and as anomalies in the earth’s rotation. It has implications for understanding sea-level
change, paleogeographic reconstructions of coastal environments, archaeology, the stress state of the crust, and
the computation of precise satellite orbits.
Models for glacio-hydro isostasy
A zero-order description for isostatic response to loading
is a model of local response of a crust–lithosphere that is
unable to support shear stresses and that overlies a fluid
mantle of zero viscosity. An ice load of H m thick and of
density r i would displace the crust beneath it by
ÀHr i /r mantle or $25–30% of the thickness of the ice or
water load. This model ignores the strength of the essentially elastic crust–lithosphere as well as the viscosity of
the mantle, but it provides a useful order of magnitude
estimate of the maximum displacement that may occur.
Thus, beneath large ice sheets, the maximum crustal displacement may approach a kilometer and the seafloor
within ocean basins may be displaced by 30–40 m for
a globally averaged sea-level change of $120 m.
An improved model is one of regional isostasy in which
the load is supported by an elastic crust–lithosphere layer
that overlies a zero viscosity mantle. For loads of horizontal dimensions much greater than the lithospheric thickness, the displacement at the center is nearly equal to
that predicted by the local model but at the edge of the load
it is only about one half of this amount because the load is
partly supported by the flexural strength of the lithosphere. Thus, along continental margins, the hydroisostatic signal may reach 15–20 m for the above global
sea-level change of $120 m. But this is still only an order
of magnitude estimate and to fully describe the global pattern of sea-level change, more physically realistic models,
that involve the mantle viscosity, are required.
Realistic models of the glacio-hydro-isostatic phenomenon include the following features:
Physically realistic representation of the planet’s
response function, or rheology, to surface loading on
timescales of thousands of years. The observational evidence indicates that the earth is still responding today to
the unloading of the last great ice sheets such that the
model requires elastic as well as viscous elements in
the response function. For both mathematical expediency and because it provides a satisfactory explanation
of the observational evidence, a linear viscoelastic
response is usually assumed. Both depth and lateral variability in the rheology needs to be considered.
A realistic description of the evolution of the ice sheets
during the full glacial cycle. A detailed description of
the individual ice sheets is required (on a 0.5
grid
and preferably smaller) for the evaluation of the
glacio-isostatic component, but for the hydro-isostatic
component it is the total rate at which water is added
or removed from the oceans that is the significant
requirement.
A detailed description of the ocean basin to ensure that
meltwater from the ice sheets is properly distributed.
This distribution has to satisfy the requirement that the
ocean surface is an equipotential surface at all times
and that the ice–water mass is conserved. Through time,
the ocean basin deforms, the shorelines migrate and the
ice sheets displace water on the shelves. The ocean
basin deforms in response to both the ice and water
loads and this introduces a coupling between the glacioand hydro-components of the isostatic response.
The ability to compute the deformation and the mass
distribution of the earth–ocean–ice system through time
and to relate this to the observational evidence for
GLACIO-HYDRO ISOSTASY
491
Postglacial Trangression
Sea Level Change and Its Effect on Reef Growth
Solution Unconformities
Subsidence Hypothesis of Reef Development
Thickness of Holocene Reefs
GLACIO-HYDRO ISOSTASY
Kurt Lambeck
The Australian National University, Canberra ACT,
Australia
Synonyms
Eustatic sea level; Glacial rebound; Postglacial sea level
Definition
Glacio-hydro isostasy refers to the earth’s response to
changes in surface ice and water loading during glacial
cycles. During the growth of an ice sheet, the crust is
loaded in the areas of glaciation and the crust beneath
and near the ice sheet subsides. During the decay phase
of an ice sheet, the crust is unloaded and rebounds. This
is the glacio-isostasy component. But as water is extracted
from, or added into, the oceans during ice growth and
decay, the oceanic crust also responds to the changing
water load. This response is called the hydro isostasy.
The two combined components, not uncoupled, are
referred to as glacio-hydro isostasy.
Introduction
The glacio-hydro isostatic effect is manifested in geological, geophysical, and geodetic observations. It is seen in
the geological record as a complex spatial and temporal
pattern of raised shorelines (Figure 1) in areas of former
glaciation (primarily the glacio-isostatic signal) as well
as along coastlines far from the former ice margins (primarily the hydro-isostatic signal). It is also seen in geodetic observations: as displacements of the crust, both
vertical and horizontal; as sea-level change in tide gauge
and satellite altimeter data; as changes in gravity measured
by surface instrumentation and by satellite sensors and
orbital perturbations; and as anomalies in the earth’s rotation. It has implications for understanding sea-level
change, paleogeographic reconstructions of coastal environments, archaeology, the stress state of the crust, and
the computation of precise satellite orbits.
Models for glacio-hydro isostasy
A zero-order description for isostatic response to loading
is a model of local response of a crust–lithosphere that is
unable to support shear stresses and that overlies a fluid
mantle of zero viscosity. An ice load of H m thick and of
density r i would displace the crust beneath it by
ÀHr i /r mantle or $25–30% of the thickness of the ice or
water load. This model ignores the strength of the essentially elastic crust–lithosphere as well as the viscosity of
the mantle, but it provides a useful order of magnitude
estimate of the maximum displacement that may occur.
Thus, beneath large ice sheets, the maximum crustal displacement may approach a kilometer and the seafloor
within ocean basins may be displaced by 30–40 m for
a globally averaged sea-level change of $120 m.
An improved model is one of regional isostasy in which
the load is supported by an elastic crust–lithosphere layer
that overlies a zero viscosity mantle. For loads of horizontal dimensions much greater than the lithospheric thickness, the displacement at the center is nearly equal to
that predicted by the local model but at the edge of the load
it is only about one half of this amount because the load is
partly supported by the flexural strength of the lithosphere. Thus, along continental margins, the hydroisostatic signal may reach 15–20 m for the above global
sea-level change of $120 m. But this is still only an order
of magnitude estimate and to fully describe the global pattern of sea-level change, more physically realistic models,
that involve the mantle viscosity, are required.
Realistic models of the glacio-hydro-isostatic phenomenon include the following features:
Physically realistic representation of the planet’s
response function, or rheology, to surface loading on
timescales of thousands of years. The observational evidence indicates that the earth is still responding today to
the unloading of the last great ice sheets such that the
model requires elastic as well as viscous elements in
the response function. For both mathematical expediency and because it provides a satisfactory explanation
of the observational evidence, a linear viscoelastic
response is usually assumed. Both depth and lateral variability in the rheology needs to be considered.
A realistic description of the evolution of the ice sheets
during the full glacial cycle. A detailed description of
the individual ice sheets is required (on a 0.5
grid
and preferably smaller) for the evaluation of the
glacio-isostatic component, but for the hydro-isostatic
component it is the total rate at which water is added
or removed from the oceans that is the significant
requirement.
A detailed description of the ocean basin to ensure that
meltwater from the ice sheets is properly distributed.
This distribution has to satisfy the requirement that the
ocean surface is an equipotential surface at all times
and that the ice–water mass is conserved. Through time,
the ocean basin deforms, the shorelines migrate and the
ice sheets displace water on the shelves. The ocean
basin deforms in response to both the ice and water
loads and this introduces a coupling between the glacioand hydro-components of the isostatic response.
The ability to compute the deformation and the mass
distribution of the earth–ocean–ice system through time
and to relate this to the observational evidence for
GLACIO-HYDRO ISOSTASY
491