Jökull - 01.12.1980, Side 58

clear that there has been dilation across the
fissure swarms. But, by the very nature of the
fissures grouping into swarms, this dilation is
local and best explained by intrusions. And
this is the model proposed in this paper, i.e. a
magmatic intrusion, to which we will turn
now.
A proposed model
Three possibilities regarding a magmatic
intrusion come into consideration: (1) A
vertical dyke (or dykes), (2) a horizontal sill (or
sills), and (3) a combination of both. The last,
i.e. a complex of dykes and sills, is very
difficult to handle mathematically and test
the results. I therefore decided to examine
only models one and two, in order to find out
whether a simple intrusive model could
explain the Vogar fissure swarm.
A vertical dyke (or dykes)
First we consider the possibility that each
fracture represents a dyke in which the
magma failed to attain the surface. This
model was proposed by Walker (1965) to ex-
plain non-eruptive, postglacial fissures and
faults in Iceland; it has also been proposed by
e.g. Duffield (1975) for the fissure swarms in
Hawaii. It is therefore worth while to examine
this model in some detail.
The main question is: Can the dykes give
rise to the observed fissures and faults on the
surface? Without wishing to maintain dog-
matically that they cannot, I see some diffi-
culties in this explanation. First: we have the
condition for dyke formation:
p><rH + T, (1)
where p is the magma pressure, <rH is the
horizontal stress (perpendicular to the dyke),
and T is the tensile strength of the rock (per-
pendicular to the dyke). If the dyke stops pro-
pagating, as assumed in this hypothesis, then
p<CH+T. The term T is of the order 100
bars, and it is difficult to see how it could be
overcome by the non-propagating dyke. Tak-
ing also into account that dykes do not create
any stress on the free surface immediately
above their upper ends (assuming a uniform
pressure distribution) (Pollard and Holzhausen
1979).
Second: it is by no means clear how the
dykes are supposed to give rise to the faults; in
particular the vertical, closed faults. Usually,
one would expect a dyke to form a right angles
to <r3, i.e. in a principal plane of stress. The
distinctive feature of such a plane is that the
shear stress upon it is zero. Hence, it cannot
possibly become a fault plane. This conclusion
is indeed confirmed by field observations; as a
rule, dykes do not occupy faults, but fissures,
“the walls of which have been merely prised
apart” (Richey 1939). It would therefore be
very surprising if all the faults in the Vogar
fissure swarm were caused, hence occupied, by
dykes.
Next we consider the single dyke model.
Such a model has e.g. been proposed by Koide
and Bhattacharji (1975) for rift valleys. In this
case, the tension fractures, faults and grabens
are supposed to be the result of a general ten-
sion, caused by a single dyke at depth com-
parable to the width of the main graben. As
for the Vogar fissure swarm, this model does
not appear to be very promising. In the first
place, it would be difficult to explain why
many of the faults h'ave reverse inclination,
and why the majority is closed. Both these
factors indicate a more complex stress system
than simple tension. Secondly, the irregularity
of the fissure swarm, both in dilation and ver-
tical displacement, is difficult to correlate to a
single dyke. Thirdly, if the formation of the
fractures has been going on for thousands of
years — which is not clear in the case of the
Vogar fissure swarm, but appears to be the
case in some other swarms in Iceland (Björnsson
et ai. 1977) — then a single dyke is of course
ruled out as an explanation.
The last dyke model we consider, is the one
proposed by Pollard and Holzhausen (1979). In
this model a dyke swarm is again the cause of
the fissure swarm, but the dykes are not sup-
posed to occupy the faults and fissures at the
surface. On the contrary, “just over the dike,
the ground is usually undisturbed, but to
56 JÖKULL 30. ÁR