Page 276 - Caldera Volcanism Analysis, Modelling and Response

A Review on Collapse Caldera Modelling 251

cohesion and internal friction coefficient of the chamber roof, the ring-fault dip
angle, the magma chamber’s thickness, and on the depth at which the magma
chamber is located (Figure 7). Values predicted for f are quite variable, depending
on the model and on the parameters above, and may vary from a few to as much as
60–70 vol.%. In shallow silicic reservoirs, for instance, most magma is expected
to be oversaturated with volatiles, and hence the fraction of compressible
magma (above the exsolution level) is larger. It follows that, the rest being equal,
in order to achieve a certain pressure drop more magma needs to be withdrawn
from shallower reservoirs than from deeper reservoirs. For the same reason,
a magma chamber with a vertical gradient in volatile contents has a lower value
of f compared to that of a homogeneous chamber. The influence of the chamber
vertical extent (thickness) is also relevant, as pressure decreases faster with increasing
thickness. Sill-like chambers, therefore, have a value of f lower than that of dyke-
like chambers if the rest of the parameters remain the same. Magma chambers
with the same aspect ratio but different geometries (cylindrical or ellipsoidal)
present similar results.
An obvious important limitation of these models is their assumption that
collapse occurs after critical decompression, without considering the evolution of
the stress field around the chamber. This evolution dictates if collapse faults can
form or reactivate for a particular chamber geometry and ambient conditions.
A second less evident drawback is that these models assume implicitly that magma
can continue to flow out even if the chamber pressure decreases below lithostatic
value by several megapascals. In the case of volatile-rich magma, this can be justified
by the presence of gas bubbles, which drive the ascent of magma through
the conduit, such that the bulk density of the rising magma column may become
much lower than the bulk density of the surrounding medium. As a result, parts
of the chamber can have a pressure exceeding the pressure caused by the magma

Figure 7 Examples of model geometries applied to numerical models. (A) 2-D rectangular
magma chamber used by Mart|¤ et al. (2000) for the eruptive phase. (B) System considered by
Roche and Druitt (2001). q r , country rock of density; h, potential vertical or outward-dipping
ring fault of angle; A, B, magma chamber axis; d, magma chamber depth; F w ,weight of the
roof; F p , upward force on the roof exerted by the magma; F s , resisting upward shear force on
the potential ring fault; he, magma chamber horizontal extent; P m , £uid reservoir pressure;
ve, magma chamber vertical extent; Z, displacement.