Page 367 - Caldera Volcanism Analysis, Modelling and Response

342 Agust Gudmundsson

pressure becomes zero or, in fact, in the underpressure model negative. This
problem follows from Equations (1)–(4) and was discussed in the context of these
equations. When dealing with petroleum reservoirs and hydraulic fractures injected
from drill holes, it is normally assumed that the fluid must have pressure in excess of
the minimum principal compressive stress to keep the hydraulic fracture open at its
contact with the drill hole (Valko and Economides, 1995; Charlez, 1997; Yew,
1997). By contrast, in the underpressure model, the dyke fractures are supposed to
remain open when the magma pressure is less than the minimum principal
compressive stress. It remains to be explained how magma chambers can behave in
this way and under what conditions.
A second problem, not mentioned by Gudmundsson and Nilsen (2006), is the
shear stress generated in the roof of a supposed-to-be empty magma chamber. For a
chamber with a top at the depth of 4–5 km, for example, an empty cavity at the
chamber top would result in a shear stress of at least 50–60 MPa. By contrast, the in
situ shear strength, twice the tensile strength, is likely to be about 10 MPa or less. In
fact, driving shear stresses (stress drops) in most earthquakes are 1–10 MPa (Scholz,
1990). So the following question must be answered: how can the rocks sustain the
shear stresses necessary for an empty cavity to form at many kilometres depth?
Perhaps, the most serious problem for the underpressure model, from a general
volcanological point of view, is the poor correlation between collapse (caldera)
volume and combined volumes of extrusive and intrusive material leaving the
chamber during the caldera eruption. For calderas in basaltic edifices the volume
correspondence is normally poor (Walker, 1988). In fact, the two best-documented
large caldera collapses in recent decades, that of Fernandina in Galapagos in 1968
(Filson et al., 1973; Munro and Rowland, 1996) and that of Miyakejima in Japan in
2000 (Geshi et al., 2002) had hardly any eruptions at all. And even if dykes were
associated with the volcano-tectonic events leading to these collapses, realistic dyke-
volume estimates are only fractions of the collapse volumes.
There exist many other careful estimates showing similar lack of volume
correspondence (Smith, 1979; Williams and McBirney, 1979). An interesting aspect
of the lack of volume correspondence is that not only do many calderas subside
without significant eruption or intrusion, but there are also several large-volume
explosive eruptions that show no major ring-fault slip at the eruption site (Lavallee
et al., 2006). For example, an explosive eruption at 1600 AD of the Huaynaputina
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volcano in Peru produced about 11 km DRE of eruptive materials and unspecified
volume of intrusive materials. This large explosive eruption was associated with two
small collapse structures, one about 1 km and the other about 0.6 km in diameter
(and thus too small to be really classified as calderas), with a combined volume of
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0.043 km or about 0.4% of the eruptive volume (Lavallee et al., 2006).
The examples of lack of volume correspondence serve to illustrate the point that
there is clearly no critical eruptive/intrusive volume depending on the size of the
chamber that can be regarded as a threshold for ring-fault formation or slip.
Hundreds of eruptions and dyke injections occur in volcanoes worldwide every
century, and of greatly varying volumes, but very few result in ring-fault formation
or slip on existing ring faults. In terms of purely empirical theories of caldera
formation, such as the underpressure model, it is not easy to account for the rarity