important to note that this process is important also on longer time scales when it comes to interpreting interglacial
sea levels in terms of differences in ice volumes relative
today (Lambeck et al. 2012; Raymo et al. 2011. First, the
response to the glacial history immediately before the
interglacial will determine the nature of the interglacial
sea-level function in the same way as the LGM determined
the character of Holocene sea levels. Second, the observation of the past interglacial sea levels are with respect to
present sea-level which is still evolving in response to
the last glacial loading-unloading phase. This latter part
can be predicted with some confidence from analyses of
the recent interval, but the accuracy of the first part will
be very much limited by the knowledge of ice extent during the earlier glacial maxima. Hence, estimates of the differences in ice volumes between present and earlier
interglacials remain uncertain.
Summary
Glacio-hydro isostasy is an important physical process
describing the Earth-ocean response to changes in ice
sheets during glacial cycles. It is a global phenomenon
and operates long after the surface loads have stabilized.
It manifests itself in a wide range of geophysical and geological observations of which the most important is
sea-level change. Observations of the isostatic response
provide an important input for understanding the evolution of past ice sheets and ocean volumes.
Bibliography
Cathles, L. A., 1975. The Viscosity of the Earth’s Mantle. Princeton:
Princeton University Press, p. 403.
Čížková, H., van den Berg, A. P., Spakman, W., and Matyska, C.,
2012. The viscosity of the Earth’s lower mantle inferred from
sinking speed of subducted lithosphere. Physics of the Earth
and Planetary Interiors, 200–201, 56–62.
Farrell, W. E., and Clark, J. A., 1976. On post-glacial sea level. Geophysical Journal of the Royal Astronomical Society, 46,
647–667.
Fleming, K., and Lambeck, K., 2004. Constraints on the Greenland
ice sheet since the last glacial maximum from observations of
sea-level change and glacial-rebound modelling. Quaternary
Science Reviews, 23, 1053–1077.
Heiskanen, H., and Vening-Meinesz, F. A., 1958. The Earth and Its
Gravity Field. New York: McGraw-Hill, p. 470.
Lambeck, K., and Chappell, J., 2001. Sea level change through the
last glacial cycle. Science, 292, 679–686.
Lambeck, K., Purcell, A., Zhao, J., and Svensson, N.-O., 2010. The
Scandinavian ice sheet: from MIS4 to the end of the Last Glacial
Maximum. Boreas, 39, 410–435.
Lambeck, K., Purcell, A., and Dutton, A., 2012. The anatomy of
interglacial sea levels. The relationship between sea levels and
ice volumes during the Last Interglacial. Earth and Planetary
Science Letters, 315–316, 4–11.
Mitrovica, J. X., and Forte, A. M., 2004. A new inference of mantle
viscosity based upon joint inversion of convection and glacial
isostatic adjustment. Earth and Planetary Science Letters, 225,
177–189.
Mitrovica, J. X., and Milne, G. A., 2003. On post-glacial sea level:
I. General theory. Geophysical Journal International, 154,
253–267.
Paulson, A., Zhong, S., and Wahr, J., 2007. Limitations on the inversion for mantle viscosity from postglacial rebound. Geophysical
Journal International, 168, 1195–1209.
Peltier, W. R., 1974. The impulse response of a Maxwell Earth.
Reviews of Geophysics, 12, 649–669.
Peltier, W. R., 2004. Global glacial isostasy and the surface of the
Ice-Age Earth: the ICE-5G (VM2) model and GRACE. Annual
Reviews in Earth and Planetary Science, 32, 111–149.
Raymo, M., Mitrovica, J. X., O’Leary, M. J., DeConto, R. M., and
Hearty, P. J., 2011. Departures from eustasy in Pliocene
sea-level records. Nature Geoscience, 4, 328–332.
Watts, A. B., 2001. Isostasy and Flexure of the Lithosphere. Cambridge: Cambridge University Press.
Whitehouse, P. L., Bentley, M. J., and Le Brocq, A. M., 2012.
A deglacial model for Antarctica. Quaternary Science Reviews,
32, 1–24.
Cross-references
Relative Sea-level (RSL) Cycle
Sea-Level
GRAVITY FIELD
Udo Barckhausen and Ingo Heyde
Federal Institute for Geosciences and Natural Resources,
Hannover, Germany
Definition
The gravity field in marine geosciences is the gravitational
force that the Earth’s mass exerts on objects on or near its
surface.
Introduction
The basic principle for the Earth’s gravity field in classical
mechanics is Newton’s law of universal gravitation. It
states that every massive body exerts an attractive force
on all other massive objects. The force is proportional to
the product of the bodies’ masses and inversely proportional to the square of the distance between them. For
extended bodies like the Earth, their mass can be assumed
to be concentrated as a point mass in their center (strictly
this is only true for spheres with a symmetrical mass distribution). In geophysics, Newton’s law is used in the form
K ¼ G
mM
r 2 r
0
where G ¼ 6:672
∗ 10
À11 Nm
2 kg
À2 is the gravitational
constant, m the mass of a body on or near Earth’s surface,
M Earth’s mass, r the distance between m and the Earth’s
center, and r
0 the unit vector giving the direction from m to
the Earth’s center.
Since the Earth is rotating, centrifugal acceleration has
to be taken into account when calculating resulting
gravity:
z ¼ O
2 R cos j
GRAVITY FIELD
299
sea levels in terms of differences in ice volumes relative
today (Lambeck et al. 2012; Raymo et al. 2011. First, the
response to the glacial history immediately before the
interglacial will determine the nature of the interglacial
sea-level function in the same way as the LGM determined
the character of Holocene sea levels. Second, the observation of the past interglacial sea levels are with respect to
present sea-level which is still evolving in response to
the last glacial loading-unloading phase. This latter part
can be predicted with some confidence from analyses of
the recent interval, but the accuracy of the first part will
be very much limited by the knowledge of ice extent during the earlier glacial maxima. Hence, estimates of the differences in ice volumes between present and earlier
interglacials remain uncertain.
Summary
Glacio-hydro isostasy is an important physical process
describing the Earth-ocean response to changes in ice
sheets during glacial cycles. It is a global phenomenon
and operates long after the surface loads have stabilized.
It manifests itself in a wide range of geophysical and geological observations of which the most important is
sea-level change. Observations of the isostatic response
provide an important input for understanding the evolution of past ice sheets and ocean volumes.
Bibliography
Cathles, L. A., 1975. The Viscosity of the Earth’s Mantle. Princeton:
Princeton University Press, p. 403.
Čížková, H., van den Berg, A. P., Spakman, W., and Matyska, C.,
2012. The viscosity of the Earth’s lower mantle inferred from
sinking speed of subducted lithosphere. Physics of the Earth
and Planetary Interiors, 200–201, 56–62.
Farrell, W. E., and Clark, J. A., 1976. On post-glacial sea level. Geophysical Journal of the Royal Astronomical Society, 46,
647–667.
Fleming, K., and Lambeck, K., 2004. Constraints on the Greenland
ice sheet since the last glacial maximum from observations of
sea-level change and glacial-rebound modelling. Quaternary
Science Reviews, 23, 1053–1077.
Heiskanen, H., and Vening-Meinesz, F. A., 1958. The Earth and Its
Gravity Field. New York: McGraw-Hill, p. 470.
Lambeck, K., and Chappell, J., 2001. Sea level change through the
last glacial cycle. Science, 292, 679–686.
Lambeck, K., Purcell, A., Zhao, J., and Svensson, N.-O., 2010. The
Scandinavian ice sheet: from MIS4 to the end of the Last Glacial
Maximum. Boreas, 39, 410–435.
Lambeck, K., Purcell, A., and Dutton, A., 2012. The anatomy of
interglacial sea levels. The relationship between sea levels and
ice volumes during the Last Interglacial. Earth and Planetary
Science Letters, 315–316, 4–11.
Mitrovica, J. X., and Forte, A. M., 2004. A new inference of mantle
viscosity based upon joint inversion of convection and glacial
isostatic adjustment. Earth and Planetary Science Letters, 225,
177–189.
Mitrovica, J. X., and Milne, G. A., 2003. On post-glacial sea level:
I. General theory. Geophysical Journal International, 154,
253–267.
Paulson, A., Zhong, S., and Wahr, J., 2007. Limitations on the inversion for mantle viscosity from postglacial rebound. Geophysical
Journal International, 168, 1195–1209.
Peltier, W. R., 1974. The impulse response of a Maxwell Earth.
Reviews of Geophysics, 12, 649–669.
Peltier, W. R., 2004. Global glacial isostasy and the surface of the
Ice-Age Earth: the ICE-5G (VM2) model and GRACE. Annual
Reviews in Earth and Planetary Science, 32, 111–149.
Raymo, M., Mitrovica, J. X., O’Leary, M. J., DeConto, R. M., and
Hearty, P. J., 2011. Departures from eustasy in Pliocene
sea-level records. Nature Geoscience, 4, 328–332.
Watts, A. B., 2001. Isostasy and Flexure of the Lithosphere. Cambridge: Cambridge University Press.
Whitehouse, P. L., Bentley, M. J., and Le Brocq, A. M., 2012.
A deglacial model for Antarctica. Quaternary Science Reviews,
32, 1–24.
Cross-references
Relative Sea-level (RSL) Cycle
Sea-Level
GRAVITY FIELD
Udo Barckhausen and Ingo Heyde
Federal Institute for Geosciences and Natural Resources,
Hannover, Germany
Definition
The gravity field in marine geosciences is the gravitational
force that the Earth’s mass exerts on objects on or near its
surface.
Introduction
The basic principle for the Earth’s gravity field in classical
mechanics is Newton’s law of universal gravitation. It
states that every massive body exerts an attractive force
on all other massive objects. The force is proportional to
the product of the bodies’ masses and inversely proportional to the square of the distance between them. For
extended bodies like the Earth, their mass can be assumed
to be concentrated as a point mass in their center (strictly
this is only true for spheres with a symmetrical mass distribution). In geophysics, Newton’s law is used in the form
K ¼ G
mM
r 2 r
0
where G ¼ 6:672
∗ 10
À11 Nm
2 kg
À2 is the gravitational
constant, m the mass of a body on or near Earth’s surface,
M Earth’s mass, r the distance between m and the Earth’s
center, and r
0 the unit vector giving the direction from m to
the Earth’s center.
Since the Earth is rotating, centrifugal acceleration has
to be taken into account when calculating resulting
gravity:
z ¼ O
2 R cos j
GRAVITY FIELD
299