Jökull - 01.12.1953, Page 5

ent accuracy. This depth may at each place be
considered as the sum of three or four quanti-
ties.
1. Height of highest shore-line above present
sea level.
2. Rise of the country before the formation
of the highest shore-line.
3. Rise of general sea-level since the formation
of the highest shore-line.
4. Future rise öf the land until equilibrium
is attained.
The last contribution may probably be ne-
glected in Iceland. No 1 is observable, but
No 2 and No 3 must be calculated on the basis
of the otherwise found viscosity of the sub-
stratum and the rate of melting of the glaciers
in late Glacial times.
Rather complete data, including absolute
dating, will be necessary if satisfactory accuracy
is to be attained. —
During the present inquiry I have worked
out a method to calulate the depression produ-
ced by a given ice load, by various values of
crustal thickness, and it seems worth while to
present this method here, as it is both easy to
use and generally applicable. The method is
based on the solution of H. Hertz (6) of the
depression of an infinte floating plate under
a point force. By dividing the ice sheet into
narrow vertical columns whose weights are
considered as point forces, we can use Hertz’
solution and sum up the depressions produced
at a chosen point P by the individual columns.
In practice the procedure is as follows.
On transparent paper are drawn concentric
circles with radii: /2 l, l, 3/2 l, 2 l, 3 l, 4 l, and 8
l. The zone from V2 l to i! is divided by radii in-
to 4 equal parts, while each outer zone is divided
by radii into 8 equal parts. We thus get 45 com-
partments. The length l depends on T, the
thickness of the elastic crust, as shown in table I.
TABLE I.
T (km) l (km)
10 23.6
20 39.7
30 54
40 67
50 79
/ m2 E T3 \1/.
I is defined by Z = ( ---------------- ) ' 4
y 12 (m2 — 1) G d J
where
m = coefficient of Poisson = 4,1.
E = modulus of elasticity = 106 kg/cm2.
These values are accepted after Vening Meinesz
(7), who bases them on B. Gutenberg.
T = thickness of the rigid elastic crust.
G = 981 cm/sec2
d = density of plastic substratum, assumed to
be 3.00. Where the density of ice appears in the
calculations later the value 0,9 is used.
We now place the transparent paper on a map
of the glacier, with the cénter of the circles at
the chosen point P, and estimate the average
thickness of the ice in each of the 45 compart-
ments. A compartment with the ice thickness
H gives a contribution h to the depression at P
Then h/H is found in table II.
TABLE II.
Zone h/H
0 - V2/ 0,0276
1 /2l- l 0,01683
l- 3/2 l 0,00956
3/2 i- 21 0,00844
21- 31 0,01041
31- 41 0,0022
41- 8 l - 0,0054
Examples: 1000 m ice thickness in the central
compartment gives a depression of 27.6 m. 1000
m thickness in one compartment in the zone 2 l
— 3 l gives a depression of 10,41 m. 1000 m
thickness in one compartment in the zone 4 l —
8 l gives a rise of 5,4 m.
At last the contributions of the various com-
partments are summed up, remembering that
thé sign for the outermost zone is negative.
As a test of the table we find for a very large
ice sheet of constant thickness 1000 m a depressi-
on of 297 m. It is easily seen that the correct
value is 300 m. The difference of 3 m is caused
by the neglect of the area outside 8 l, which
usually will be unimportant. When drawing
the circles on the transparent paper the scale
of the map to be used must naturally be taken
into account.
Further it will be clear that the depression
found in this way refers to equilibrium condi-
tions, i. e. it means the fully developed depress-
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