Page 358 - Caldera Volcanism Analysis, Modelling and Response

Magma-Chamber Geometry, Fluid Transport, Local Stresses and Rock Behaviour 333

base of the crustal segment, resulting in a very small (centimetres) upward (concave)
bending or doming of the crustal segment hosting the chamber and (4) magmatic
underpressure, that is, negative excess pressure in the chamber. All the models are
two-dimensional, so that a spherical chamber is modelled as a circle and a sill-like
chamber as a flat ‘tunnel-shaped’ through crack (Gudmundsson, 2000b). The two-
dimensional model results, however, have been compared with three-dimensional
analytical (Tsuchida and Nakahara, 1970; Tsuchida et al., 1982) and numerical
models. While the magnitudes of the stresses differ between the two- and
three-dimensional models, the geometries of the local stress fields are generally
similar.
The numerical models in this paper derive from recent studies using the finite-
element programme ANSYS (Gudmundsson, 2007; Gudmundsson and Nilsen,
2006). The finite-element method is described by Zienkiewicz (1977), the ANSYS
programme by Logan (2002) and the ANSYS homepage (www.ansys.com). The
finite-element method is also discussed in the context of rock-mechanics problems
by Jing and Hudson (2002).
In some of the numerical models, the rock stiffnesses used are from laboratory
tests (Carmichael, 1989; Afrouz, 1992; Bell, 2000; Myrvang, 2001); in other models,
the stiffnesses are modified from laboratory tests using information on in situ rock
properties (Farmer, 1983; Priest, 1993; Scho ¨n, 2004). The boundary conditions
used are derived from geological and geophysical field studies (cf. Gudmundsson,
2006). I consider first magma chambers of circular (spherical) shape and then of
sill-like (oblate ellipsoidal) shape.
The stress field around a circular magma chamber in a homogeneous, isotropic
crust and subject to various types of loading is unlikely to trigger ring-fault
initiation (Gudmundsson, 1998a; Gudmundsson and Nilsen, 2006). When the
loading is internal excess magmatic pressure (in excess of the lithostatic stress or
pressure), the maximum surface tensile and shear stresses occur at the point directly
above the centre of the chamber. When the chamber is subject to underpressure,
that is, negative excess pressure, the surface shear stress peaks above the centre of the
chamber. Neither stress field is suitable for ring-fault formation. Similarly, when the
crustal segment hosting the chamber is subject to either external horizontal tension
or doming pressure at its lower margin (due to magma accumulation), the
maximum tensile and shear stress at the margin of the chamber occur at the point
next to the free surface and thus not at a suitable location for ring-fault or ring-
dyke formation.
In all these models, magma-chamber rupture is most likely to result in dyke or
sheet injection (Figure 13) rather than ring-fault formation. The models assume,
however, that the crustal segment hosting the chamber is homogeneous and
isotropic, an assumption that is normally unrealistic for composite volcanoes and rift
zones. Circular magma chambers located in layered crustal segments generate
different stress fields, some of which may be suitable for ring-fault formation.
In order to test this possibility, many numerical models were made of a circular
chamber in a layered crustal segment, a volcanic zone, 20 km thick and 40 km wide,
the chamber itself supplying magma to the associated composite volcano. The
upper part of the crustal segment is composed of 30 layers, each 100 m thick and