Jökull - 01.12.1989, Page 18

solution to the heat-flow equation with the above
boundary conditions
T(z,t)
T2 +
(Ti-T2)
2
erf
h-z
V2kT
+ 2erf
z
V2kF
- erf
h+z
V2kF
(4)
Here T is temperature at time t and depth z meas-
ured down from the upper surface of the intrusion. h
is the thickness of the intrusion and T, and T2 are
respectively the initial temperature values of the
intrusion and the surroundings. erf is Gauss error
function and k is the coefficient of thermal
difíusivity. A value of k=20 m2/year for basalt is
used (Cermák and Rybach, 1982).
The heat left in the sill-like body and the rocks
below it at any given time t can be estimated by
integrating T(z,t) with respect to z from z=0 down to
where T(z,t) = T2. These calculations indicate that a
10 m thick sill has lost 80% of its heat through its
upper surface after about 5 years from its formation
and 90% after 15-20 years. For a 20 m thick sill
80% is lost after 20 years and 90% after 50 years.
These results of the model must by treated with cau-
tion, as it may be unrealistic that no warming up of
the rocks above the sill takes place while it is still
molten or very hot. Furthermore, the role of convec-
tion in heat transport may be underestimated once
the intrusion is solidifled. However, the results
clearly indicate that the contribution of shallow
intrusions to the power of a geothermal area
becomes negligible within few decades from their
formation.
Eruptions are known to have occurred in Gríms-
vötn in 1867, 1873, 1883, 1922, 1934, 1938 and
1983, and are considered likely in 1861, 1892 and
1903 (Þórarinsson, 1974; Jóhannesson, 1983;
Bjömsson, 1988). The 1983 eruption was consider-
ably smaller than the other eruptions and would
probably not have been detected without the local
seismic monitoring network (Einarsson and Brands-
dóttir, 1984). It is possible that minor eruptions
occurred in 1945 and 1954 (Áskelsson, 1959; Jó-
hannesson, 1983). In the period 1860-1940, 6-9
eruptions occur in the area or one eruption every
9-13 years. Since 1940, 1-3 very minor eruptions
have occurred over a 50 years interval. It is there-
fore possible that part of the base heat flux observed
in the period 1860-1976 was derived from shallow
intrusions and lava flows erupted onto the caldera
floor. The observed drop in thermal power of the
area could be caused by the reduced eruption fre-
quency since 1940, as the heat from lava flows and
intrusions has been exhausted. If this is true, the
geothermal power observed at present reflects the
energy drawn from more deeply seated magma
bodies by hydrothermal convection.
CONCLUSIONS
The results of the 1987 seismic reflection survey
have been presented and an interpretation presented
and discussed. It is believed that the following con-
clusions are supported by the data:
1. The ice shelf covering the subglacial lake is 240-
260 m thick and the thickness of the water layer is
40-90 m.
2. The area of the subglacial lake in June 1987 was
10 km2 and the volume of water stored in the lake
was 0.5 km3.
3. The area of the main caldera in Grímsvötn is
about 20 km2. The elevation of the caldera floor is
1060-1200 m a.s.l. The caldera floor dips slightly
towards north and the deepest part is under the
northern caldera wall.
4. The caldera floor can be divided into two separate
areas. The deeper northern and eastem parts are
covered with sediments but the southem part is
covered with lava flows.
5. Comparison with earlier seismic surveys (1955)
suggests, that the ice shelf was 120-150 m thick at
that time, i.e. about 100 m less than at present.
6. The caldera infill is believed to be made up of a
pile of lava flows and sediments, with a minimum
thickness of 100-150 m. The lava flows seem to
have been erupted in the southem part of the cal-
dera, but the sediments have accumulated in the
northem part.
7. The existence of the lava flows suggests that the
thermal effects of eruptions within the caldera
16 JÖKULL, No. 39, 1989