Page 56 - Fundamentals of Physical Volcanology

9780632054435_4_003.qxd 12/10/2007 12:18PM Page 33

MAGMA MIGRATION 33

larger, respectively, than the average strain rates grows sideways along the boundary, which locally
elsewhere in the mantle where convection is taking increases the average strain rate. Also, the crustal
place without any melting. rocks are cooler than those in the mantle, and
The way in which a rock responds to being therefore closer to their plastic–elastic transition
deformed, i.e., its rheology, depends on its compo- temperature for any given strain rate. Thus both the
sition, its temperature, and the strain rate imposed lower temperature of the overlying rocks and the
on it. If the temperature of a given hot rock is increase in strain rate acting on them will act
kept constant and the strain rate applied to it is together to make the creation of fractures particu-
increased, its response eventually changes from larly likely as a plume head reaches the base of the
that of a very viscous liquid, i.e., a plastic solid, to crust. Note that the increased strain rate applies to
that of a brittle elastic solid. Alternately, keeping the rocks inside the top of the plume as well as to
the strain rate constant and decreasing the temper- the crustal rocks above; thus the process of coales-
ature will also trigger the change from plastic to cence of existing large melt veins into dikes can
elastic behavior and initiate fracturing. Diapirically occur within the plume head itself.
rising masses of rock are always moving from hotter
into cooler surroundings, and so the onset of frac-
turing will occur whenever the rheological bound- 3.4 Dike propagation
ary between the plastic and elastic responses of
the host rocks is crossed, and this is likely to hap- Wherever the change from plastic deformation to
pen at higher temperatures, and therefore at greater brittle fracture of rocks occurs, fractures start to
depths, for larger, more rapidly rising diapiric bod- grow from any feature that can concentrate the
ies than smaller, slower ones. stress – this could be a particularly sharp-cornered
It is very difficult to predict exactly the condi- interface between three crystals as described in
tions under which elastic to plastic transitions in section 2.4.2 or some accidental defect in the inter-
rock behavior will occur in the Earth because it is nal structure of a single mineral grain. As soon as a
hard to simulate mantle conditions in the laborat- fracture forms in the crust above a region contain-
ory. The problem is not so much in producing the ing magma, the liquid will start to flow into the
required temperatures and pressures but in dealing fracture to fill the space created. A major property
with the time scales. If we are prepared to wait one of brittle fractures is that the rate at which the sharp
7
year, that is ∼3 × 10 s, to conduct an experiment tip of the fracture can propagate into the unfrac-

in which a rock sample is deformed by 100%, i.e., tured rock ahead of it is limited only by the speed of
compressed to about half its thickness and double sound in the rock (a sound wave is just a wave of
its cross-sectional area, in a high-pressure, high- deformation of the material in which it is traveling).
temperature apparatus in the laboratory, the average In practice the crack-tip propagation speed is some-
s , which is 30 million
strain rate will be ∼3 × 10 −8 −1 what less than the actual sound speed, but it is still
times faster than in the mantle. Extrapolations on the order of a few kilometers per second, and at
made across this enormous difference in time scale first sight it is tempting to predict that dikes should
are not very reliable. grow at this rate. However, there is a limit to the
However, it is clear that the heads of mantle speed at which magma can flow into a narrow, open-
plumes reaching the base of the overlying crust ing crack. The speed is controlled by the crack width
are particularly likely to cause their host rocks to and the magma viscosity, and also by the widths of
fracture. Two factors combine to cause this. First, a the network of smaller veins that are feeding melt
change in bulk composition occurs, with the crust toward the crack. This magma flow speed will be
being less dense than the mantle in general, includ- very much less than the speed of sound in rock –
ing the hot material in the plume. Thus the plume typically more than a thousand times less. Thus in
buoyancy is lost and the top of the plume ceases practice it is the flow speed of the liquid magma
to rise. The material below it continues to rise, in the narrow veins that determines the speed at
however, and the plume head flattens out and which the dike as a whole can grow upward.