Jökull - 01.12.1994, Side 34

Fig. 2. A model of the change in thickness of the Vatnajökull
ice cap from 1890-1978. The thickness change is plotted as a
function of distance from the center of a hypothetical circu-
lar ice cap with the same mean radius and maximum thick-
ness as Vatnajökull (Sigmundsson and Einarsson, 1992).
2. mynd. Reiknilíkan til að meta þykktarbreytingar Vatna-
jökuls á tímabilinu 1890-1978. Þykktarbreytingarnar eru
teiknaðar sem fall affjarlœgð frá miðju ímyndaðs, skífulaga
jökuls, sem hefur sama meðallgeisla og hámarksþykkt og
Vatnajökull.
librium uplift beneath the center of the glacier is nearly
4 m, and the curve falls off steeply beyond the glacier
edge. Very little uplift is found at distances greater than
120 km from the center. For the thicker lithosphere the
central uplift is less, only about 2.3 m, but the curve
falls off less steeply. At distances of about 70 km, corre-
sponding to Homafjörður, the uplift is comparable to
that of the thin lithosphere case. Beyond that the uplift
is greater, and is seen out to a distance of 150 km.
The thickness range of 10-20 km for the elastic
layer is chosen here to reflect likely values for the
elastic, brittle part of the crust in Iceland. This thick-
ness can be estimated from the maximum depth of
earthquake hypocenters, below which the crust must
be assumed to deform in a ductile manner. Hypocen-
tral depths larger than 15 km have been found only in
exceptional cases (see e. g. Einarsson, 1991, and
Stefánsson et al., 1993).
lowing the mathematical formulations of Sigmunds-
son (1990) and Sigmundsson and Einarsson (1992).
An Earth model consisting of an elastic plate (litho-
sphere) on top of a Newtonian viscous fluid (astheno-
sphere) is assumed. The main parameters governing
the response of the model are the thickness of the
lithosphere and the viscosity of the asthenosphere.
The viscosity affects the response time of the
model, but not the final shape of the uplift. Fig. 3
shows the uplift rate as a function of distance for differ-
ent viscosity values, 85 years after the onset of unload-
ing. The lithospheric thickness is, for the sake of argu-
ments, assumed to be 10 km. For a viscosity of 1020 Pa
s the rates are of the order of a few mm per year for all
distances. At viscosities of 1019 - 1018 Pa s the rate
reaches 5-16 mm per year at a distance of 70 km from
the glacier center, corresponding to the Homafjörður
lagoon. For still lower viscosities the relaxation time of
the model is short (< 47 years), and most of the move-
ments have already occurred. The uplift rate at the pre-
sent time is therefore low and decreasing.
Lithospheric thickness has a pronounced effect on
the flexural rigidity and thus the shape of the uplift
curve. Fig. 4 shows uplift curves for two values of litho-
sphere thickness, 10 and 20 km, and a fixed value of
viscosity, 1019 Pa s. For a thin lithosphere the final equi-
GPS MEASUREMENTS
GPS geodesy is a powerful method to study
crustal deformation (Larson and Agnew, 1991). Base-
line vectors of tens of kilometers length can be mea-
sured with an accuracy of better than a cm. Deforma-
tion rates of a few mm to a cm per year can thus be
determined by repeated measurements over a reson-
Fig 3. Uplift rate as a function of distance for different vis-
cosity values, 85 years after the onset of unloading. Thinning
rate of the glacier is assumed to be constant during this time,
as shown in Fig. 2 (Sigmundsson and Einarsson, 1992).
3. mynd. Rishraði semfall af fjarlœgð frá jökulmiðju fyrir
mismunandi seigjugildi undirlagsins, 85 árum eftir að fargi
tekur að létta. Gert er ráð fyrir aðfargið léttist með jöfnum
hraða á tímabilinu.
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JOKULL, No. 44