Page 70 - Caldera Volcanism Analysis, Modelling and Response

Residence Times of Silicic Magmas Associated with Calderas 45

growth rates in silicic magmas. They also allow calculating the closure temperatures
of multiple phases and radioactive systems (Figure 2).

4.4. Magma residence times, caldera collapse and the rheology
of the crust

The knowledge of residence times can also contribute to understand the relation
between magma fluxes and rheological behaviour of the crust and thus caldera-
related volcanism. This topic was addressed by Jellinek and DePaolo (2003) using
a visco-elastic model for the crust. Their equations 11 and 12 allow calculating
the time needed to reach a critical overpressure in the elastic and viscous regimes
and also the maximum chamber overpressure. The results from the calculations
3 1
show that the high magma fluxes of ca. 0.01 km y inferred for most large
3
caldera collapse eruptions (W500 km ) require pressurisation times up to the critical
overpressure of decades to hundreds of years (e.g., Figure 4 of Jellinek and DePaolo,
2003). This is several orders of magnitude shorter than most residence times.
Moreover, these high magma fluxes do not allow for the construction of a large
magma volume because the critical overpressure is reached before any significant
amount of magma can be accumulated. The apparent contradiction between the
residence times and the rheological model can be due to several reasons. The model
of Jellinek and DePaolo (2003) contains elastic and viscous behaviour of the crust,
but it does not include damage (e.g., Gray and Monaghan, 2004) or how this might
change with time. The overpressure could be reached by other factors than the
magma influx rate, like the crystallisation and progressive build up of volatiles
(Tait et al., 1989). A much larger uncertainty is probably introduced by using the
mean magma production rates derived from the residence time and volume as if
they would be instantaneous rates. Jellinek and DePaolo (2003) pointed out the
difficulty of building large magma reservoirs that erupt with large periodicities
(ca. 500 ky), and noted that peak intrusion fluxes higher than the average would
be necessary to trigger large caldera-collapse eruptions. Some model calculations
using their equation 8 show that aside from an intrusion peak higher than average,
the increasing volume of the reservoir with time exacerbates this effect even more.
Using linear, exponential or abrupt increases of magma flux rates with time does
not lead to eruption in the frame of the residence times. From this discussion it
is apparent that more feedback between rheological and residence time models is
necessary to understand the processes that lead to eruption of such large volumes
of magma. A main contribution to such an understanding may also arise from studies
of the growth rates of granitoid plutons and their thermal and mechanical effects in
the crust (e.g., Yoshinobu and Girty, 1999; Petford et al., 2000; Gerbi et al., 2004;
ˇ
Glazner et al., 2004; Oberli et al., 2004; Titus et al., 2005; Za ´k and Paterson, 2005).

5. Summary and Conclusions

A review of the data produced in the last 30 years from silicic deposits of major
caldera systems allows to quantify the rates of magmatic differentiation and the mass