Page 30 - Caldera Volcanism Analysis, Modelling and Response

Residence Times of Silicic Magmas Associated with Calderas 5

Figure 1 Location of the caldera systems discussed in the manuscript.The sizes of the circles
are roughly proportional to the di¡erence in caldera diameters.

some simple thermal and mechanical calculations of magma reservoirs. Section 5
summarizes the main findings of the manuscript.

2. Methods for Obtaining Time Constraints
of Magmatic Processes

2.1. Radioactive isotopes
The age determination is based on radioactive decay laws which state that the rate
of spontaneous decay of an unstable radioactive parent is proportional to the
number of parent atoms. One can obtain an age if: (1) the initial number of
daughter atoms since the system’s closure is known, and (2) the system that is dated
(e.g., mineral, phases or rock associations) has remained closed to additions or losses
of parent and daughter atoms (e.g., Faure and Mensing, 2004). In analogy to the
chemical diffusion approach described below, the first requirement is related to the
initial conditions of the system, and the second to the boundary conditions and
because of its importance it is discussed below in some detail.
The advent of in-situ analytical techniques enabled multiple isotope determina-
tions for age purposes in a single crystal using secondary ion mass spectrometry
(SIMS), although thermal ionisation mass spectrometry (TIMS) on bulk materials
(single crystal or not) are more commonly used. A good example of the power of
SIMS is the possibility to obtain isochrons from multiple in situ analyses of single
zircon crystals (Lowenstern et al., 2000). Details about the dating methods and
radioactive systems used to obtain time scales of magmatic process can be found
in McDougall and Harrison (1999), Condomines et al. (2003), Turner et al. (2003)
and Dickin (2005).