Page 359 - Caldera Volcanism Analysis, Modelling and Response

334 Agust Gudmundsson

alternating in stiffness (Young’s modulus) between 1 GPa (soft layers) and 100 GPa
(stiff layers). Many sedimentary and pyroclastic layers in Iceland and other volcanic
areas have thicknesses of about 100 m, and so do many pahoehoe lava flows
(Gudmundsson, 2006). The circular chamber itself, 4 km in diameter and with a
top at 3 km depth, is located in a soft layer with a stiffness of 10 GPa. The rest of
the crustal segment, down to its bottom, is a moderately stiff layer of 40 GPa,
typical for many rift-zone segments (Gudmundsson, 2006). At the bottom of the
rift zone, there is a magma reservoir, that is, a dome-shaped ‘notch’, with a width of
16 km and thus similar to the width of a typical volcanic system in Iceland
(Gudmundsson, 2000a). The reservoir has an ‘amplitude’ or height (vertical
dimension) of 2 km.
In the models below, when the loading is ‘doming’, it means that the deep-
seated reservoir is subject to magmatic excess pressure of 10 MPa. But when the
loading is through horizontal tension, there is no excess pressure in the deep-seated
reservoir (the reservoir being in lithostatic equilibrium with its host rock). Then the
applied horizontal tensile stress is 5 MPa, a figure that is similar to the maximum in
situ tensile strength of most solid rocks (Haimson and Rummel, 1982; Schultz,
1995; Amadei and Stephansson, 1997).
Horizontal tension (Figure 14) and doming (Figure 15) generally yield similar
results. For horizontal tension (Figure 14), the maximum tensile stress s 3 at the
margin of the magma chamber is about 5 MPa, whereas at the free surface above the
chamber s 3 shows two peaks of 15 MPa. Similarly, the von Mises (octahedral) shear
stress t at the margin of the chamber reaches about 4 MPa, but at the free surface
above the chamber t shows two peaks of about 13 MPa.

Doming stress (pressure) at the base of the crustal segment generates tensile s 3
and shear t stresses at the surface that both peak above the margins of the chamber;
s 3 reaches about 25 MPa and t about 22 MPa (Figure 15). At the margin of the
chamber, these same stresses reach maximum values of about 14 and 12 MPa,
respectively.
In both models (Figures 14 and 15), the conditions for ring-fault formation at
the free surface and at shallow depths are thus likely to be reached before the
condition of rupture of the chamber itself. Tensile surface stresses of 15–25 MPa
would normally not be reached in nature. However, because they are so much
higher than the tensile stresses at the chamber margin, ring-fault formation rather
than dyke injection from the chamber is favoured.
The results for a circular chamber in a layered crustal segment indicate that
when the chamber is located in a soft layer, such as a soft sedimentary or pyroclastic
unit, horizontal tensile stress or doming pressure may trigger ring-fault formation.
For other loading conditions and layering, however, a circular chamber is normally
unlikely to trigger ring-fault formation. Numerous numerical models indicate that
the magma-chamber geometry most likely to initiate ring faults is sill-like (oblate
ellipsoidal) (Gudmundsson, 1998a; Gudmundsson and Nilsen, 2006).
The results for a sill-like magma chamber in a homogeneous, isotropic crust are
well known and may be summarised as follows (Gudmundsson, 1998a, 2007;
Gudmundsson and Nilsen, 2006). A chamber that is subject to internal magmatic
excess pressure as the only loading is unlikely to trigger ring-fault formation