Abstract
An existing magma chamber is normally a necessary condition for the
generation of a large volcanic edifice. Most magma chambers form
through repeated magma injections, commonly sills, and gradually
expand and change their shapes. Highly irregular magma-chamber shapes
are thermo-mechanically unstable; common long-term equilibrium shapes
are comparatively smooth and approximate those of ellipsoids of revolution.
Some chambers, particularly small and sill-like, may be totally molten.
Most chambers, however, are only partially molten, the main part
of the chamber being crystal mush, a porous material. During an eruption,
magma is drawn from the crystal mush towards a molten zone beneath
the lower end of the feeder dyke. Magma transport to the feeder dyke,
however, depends on the chamber's internal structure; in particular
on whether the chamber contains pressure compartments that are, to
a degree, isolated from other compartments. It is only during large
drops in the hydraulic potential beneath the feeder dyke that other
compartments become likely to supply magma to the erupting compartment,
thereby contributing to its excess pressure (the pressure needed
to rupture a magma chamber) and the duration of the eruption. Simple
analytical models suggest that during a typical eruption, the excess-pressure
in the chamber decreases exponentially. This result applies to a
magma chamber that (a) is homogeneous and totally fluid (contains
no compartments), (b) is not subject to significant replenishment
(inflow of new magma into the chamber) during the eruption, and (c)
contains magma where exsolution of gas has no significant effect
on the excess pressure. For a chamber consisting of pressure compartments,
the exponential excess-pressure decline applies primarily to a single
erupting compartment. When more than one compartment contributes
magma to the eruption, the excess pressure may decline much more
slowly and irregularly. Excess pressure is normally similar to the
in-situ tensile strength of the host rock, 0.5-9 MPa. These in-situ
strength estimates are based on hydraulic fracture measurements in
drill-holes worldwide down to crustal depths of about 9 km. These
measurements do not support some recent magma-chamber stress models
that predict (a) extra gravity-related wall-parallel stresses at
the boundaries of magma chambers and (b) magma-chamber excess pressures
prior to rupture of as much as hundreds of mega-pascals, particularly
at great depths. General stress models of magma chambers are of two
main types: analytical and numerical. Earlier analytical models were
based on a nucleus-of-strain source (a 'point pressure source') for
the magma chamber, and have been very useful for rough estimates
of magma-chamber depths from surface deformation during unrest periods.
More recent models assume the magma chamber to be axisymmetric ellipsoids
or, in two-dimensions, ellipses of various shapes. Nearly all these
models use the excess pressure in the chamber as the only loading
(since lithostatic stress effects are then automatically taken into
account), assume the chamber to be totally molten, and predict similar
local stress fields. The predicted stress fields are generally in
agreement with the world-wide stress measurements in drill-holes
and, in particular, with the in-situ tensile-strength estimates.
Recent numerical models consider magma-chambers of various (ideal)
shapes and sizes in relation to their depths below the Earth's surface.
They also take into account crustal heterogeneities and anisotropies;
in particular the effects of the effects of a nearby free surface
and horizontal and inclined (dipping) mechanical layering. The results
show that the free surface may have strong effects on the local stresses
if the chamber is comparatively close to the surface. The mechanical
layering, however, may have even stronger effects. For realistic
layering, and other heterogeneities, the numerical models predict
complex local stresses around magma chambers, with implications for
dyke paths, dyke arrest, and ring-fault formation.
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