Jökull - 01.12.1980, Side 60

y
Fig. 15. A mathematical presentation of Fig.
14. A mathematical crack occupying the seg-
ment y = 0, -a<x<a, is opened into an elliptic
crack by the uniform pressure PQ. — Mynd 15.
Stærðfrœðileg framsetning á Mynd 14. Stœrðfrœðileg
sprunga, á bilinu y— 0, -a<x<a, opnast yfir í ellipsu,
vegna innri (kviku-) prýstings P0.
The crust of the Reykjanes Peninsula is
composed of basalt lavas and hyaloclastites.
For basalt, reasonable values for E and v are
7X105 bars and 0.2 respectively (Price 1966).
Corresponding values for hyaloclastite are not
known, but u is in any case similar as for
basalt. Farmer (1968) gives an approximation
formula for E when the density of the rock is
known. A number of density measurements on
hyaloclastites from the Reykjanes Peninsula
have been carried out. The most appropriate
value here is 2.4 g/cm3 (Pálsson 1972). The
formula by Farmer is:
E = 0.9 ( p — 2.1) 10r’ bars (4)
where p is the density of the rock. If p is 2.4
g/cm3 then E is 3 X 105 bars, according to the
above formula. The average E value for the
upper 2—3 km of the crust would therefore be
about 5X 105 bars. This is in excellent agree-
ment with the value of E, as estimated from
P-wave velocities in this area (Pálmason 1971).
Hence, I will use this value for E.
From Fig. 4a,b we see that the maximum
width of the main graben in the Vogar area is
about 5 km. Accordingly, we put a = 2.5 km,
and use the above values for E and u . For-
mula (3) then becomes:
_ wmax=P(> (5)
where wmax is in crn and Pu in bars.
Next we must estimate the overpressure, P .
The overpressure is the difference between the
lithostatic pressure and the total magma
pressure. The lithostatic pressure is given by
p R gz, where P R is the density of the rock, g is
the acceleration of gravity, and z is the depth
below surface. If the total magma pressure is
equal to the lithostatic pressure at the magma
source (or magma layer), the overpressure is
given by the formula:
Po=(PR-Pm)gh (6)
where h is the height above that source: or
rather the vertical length of a dyke from that
magma source. Clearly, the overpressure in-
creases with height as long as the density of the
magma is less than the density of the host rock
(assuming the dyke to be directly joined to the
source). As soon as ( PR— Pm) < 0, the over-
pressure decreases with height. Therefore,
other things being equal, the most probabie
place for horizontal intrusion is where
P r= P m> 3-e- where the overpressure is high-
est. If, on the other hand, p R is always larger
than pm then the overpressure increases right
up to the surface.
The depth to the magma source is assumed
to be 25 km. This is similar to the value T
Einarsson (1972) got from the maximum height
of Holocene volcanoes in Iceland. Further-
more, a recent study of seimicity near the vol-
cano Katla in S-Iceland shows that earth-
quakes occur down to depth of 15 — 25 km in
that area (P. Einarsson, personal communi-
cation, 1979). And during the eruption of
Heimaey, 1973, earthquakes occured at depth
of about 20 km (Björnsson and Einarsson 1974).
These figures indicate that the upper mantle,
within the volcanic areas in Iceland, behaves
as brittle down to at least 20—25 km. A
general magma source, contrary to a local
“magma chamber”, must therefore be below
this; and the assumed figure 25 km appears to
be a reasonable value.
The average density of the crust and upper
mantle down to this depth is about 3.0 g/cm3
(.Pálmason 1971). The density of tholeiitic
basalt in the molten state, at a temperature of
58 JÖKULL 30. ÁR