Page 5 - Sea-level change_2004

ARTICLE IN PRESS
K. Lambeck, A. Purcell / Quaternary Science Reviews 24 (2005) 1969–1988 1973

mantle viscosity distribution with depth is approximated 3. Model predictions across the Mediterranean basin
by a small number of layers. The elastic parameters,
including compressibility and density, vary with depth 3.1. Sea level on a rigid earth
according to seismic data. Phase boundaries are
assumednot to respond on the time scales of the glacial Without deformation of the solid earth, the sea-level
cycles and comparisons of model predictions based on function is determined by the gravity of the surface load
this assumption with results in which the phase of ice andredistributedmeltwater such that the sea-
boundaries adjust instantaneously to the change in surface remains at constant gravitational potential. Fig.
pressure do not indicate that this distinction is 1a illustrates this contribution at 12 ka BP (it is zero at
important in terms of producing parameters that 6.8 ka as in this model there is no further change in the
describe the rebound (Johnston et al., 1997). For the ice history from this time to the present) for the iterative
models considered here a three-layered mantle is solution of Eq. (1) in which the mantle viscosity has
adopted comprising an elastic lithosphere of effective been set to an infinitely large value. The pattern is a
thickness H 1 , an upper mantle of average effective quasi-uniform gradient across the region with levels
viscosity Z um extending from the base of the lithosphere above the esl value of 54 m for this epoch. This is the
to the 670 km seismic discontinuity, and a lower mantle result of the broadzone that develops around each of
of effective viscosity Z lm extending to the core-mantle the northern hemisphere ice sheets in which the sea
boundary. Tests for mantle models with a greater degree surface is deflected upwards by the gravitational
of layering show that such simple models capture most attraction of the ice. The North American influence is
of the reboundsignal. seen mainly as a NW–SE slope of about 3.5 m from the
Lateral variability in mantle viscosity, as well as in Golfe du Lion (France) to Egypt whereas the Scandi-
lithospheric thickness is ignored. This is on the grounds navian signal is a predominantly N–S gradient of about
that there is no observational database that would be 0.5 m from Trieste to the Gulf of Sirte (Libya) and
satisfactory for inversion for both the ice-model together they form the broadpattern shown in Fig. 1a.
parameters and the depth-lateral distribution of viscos- (By 12 ka BP the percentage reduction in ice volume of
ity. However, regional inversions of sea-level data Scandinavia has been greater than for North America,
do indicate that there may be some lateral variability and despite the greater distance to it, the North
in effective upper-mantle viscosity in a range of American ice loaddominates the signal. At the time of
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10 Pa s for the South Pacific mantle to the LGM, the gradients are more comparable, 9 m for
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5–6 10 Pa s for the mantle beneath North America. the NW–SE slope towards North America and 7.5 m
This provides one of the rationales for carrying out for the N–S slope towards Scandinavia.) The small
regional solutions, rather than a single global ‘wiggles’ in the contours in Fig. 1a at the land–water
solution, on the basis that much of the regional boundaries, such as across Italy or the Aegean Sea or
deformation recorded is more indicative of the mantle the larger ones across the coast of North Africa, are the
rheology beneath the loaded area than of the result of the changing gravitational attraction between
mantle beyondthis region. A number of solutions water andlandas sea level rises. The Antarctic influence
indicate that representative values for the upper-mantle is predominantly the constant equivalent sea level for
viscosity beneath continental margins andaway from the epoch.
the cratonic cores of Scandinavia and North America,
and including the Mediterranean, are in the range 3.2. Glacio-isostatic contributions
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(2–4) 10 Pa s (e.g. Lambeck andNakada, 1990;
Lambeck andBard, 2000; Lambeck et al., 2004a). The Figs. 1b andc illustrate the glacio-isostatic contribu-
lower-mantle viscosity is reasonably well constrainedby tions to relative sea level at 12 ka BP from the individual
sea-level data from far-field sites because the wavelength ice sheets over northern Europe andNorth America,
of the water loads, defined by the ocean basins, is equal respectively, andthe signal is primarily due to the
or greater than the depth of the mantle. Also, the time change in deformation of the planet between 12 ka and
dependence of the inertia tensor of the planet, as the present rather than to the change in direct
recorded in the orbital perturbation spectrum of close gravitational potential of the ice sheet. The result is a
earth satellites or in the planetary rotation, provide concentric pattern of subsidence of the broad uplift zone
goodconstraints on lower-mantle viscosity (e.g. Kauf- createdduring the time of ice growth aroundeach of the
mann andLambeck, 2002) andwe adopt values of ice sheets. Also illustrated(Fig. 1d) is the contribution
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(5–20) 10 Pa s. Effective values for the elastic thick- from the Alpine deglaciation for the same epoch and
ness of 50–80 km also appear to be appropriate. within the marine environment, this contribution is
Independent solutions for mantle rheology give similar significant only in the northern Adriatic and Gulf of
results (e.g. Mitrovica, 1996; Mitrovica andForte, 1997; Genoa areas, reaching 4–5 m at 12 ka BP and1–1.2 m at
Milne et al., 2001). 6 ka BP.