Page 263 - Caldera Volcanism Analysis, Modelling and Response

238 J. Martı ´ et al.

2.1. Mining subsidence: an analogue for caldera collapse
An important contribution to the experimental modelling applied to the under-
standing of collapse calderas stems from mining subsidence studies and scaled
experimental models of ground subsidence (Sanford, 1959; Whittaker and Reddish,
1989). A 2-D analysis of mining subsidence allows these authors to define the roof
aspect ratio, the ratio between roof width and roof thickness (Figure 2). They
distinguish between three cases of mining subsidence: subcritical, critical, and
supercritical. The critical aspect ratio is given by:

ðw=2Þ 1
tany ¼ ¼ (1)
h 2R
where y (B351) is the angle of draw, localised between the vertical and the lines
that draw from the edges of the cavity and delimit the collapse depression at surface;
w the roof width and h the roof thickness (depth). For y ¼ 351, the critical value of
R is 0.7. Therefore, the three different cases are: subcritical case (RW0.7) in which
there is a single point of maximum compression located at the centre of the
depression; critical case (R ¼ 0.7) in which there are two points of maximum
compression and a single point of no deformation at the centre; and supercritical case
(Ro0.7) in which there are two points of maximum compression and an
undeformed zone of finite width in between. The model distinguishes between
three different areas: extensional, compressional, and non-deformed (Figure 2). The
width of the marginal deformed zone (extensional and compressional) is constant
for a given y and h, and does not depend on w. For low values of R, there is a central
non-deformed zone bounded by marginal deformed zones. By contrast, for high
values of R the entire depression is affected by surface deformation.
Branney (1995) and Roche et al. (2000) suggested that caldera collapse is
strongly controlled by the relationship between the geometry of the magma
chamber and the thickness of the overlying roof (magma chamber depth), so that
caldera collapse and the resulting caldera structures behave in a similar way to
mining subsidence. Therefore, they propose to apply the concept of roof aspect ratio,
defined as the ratio between magma chamber depth and magma chamber width,
to collapse calderas. The roof aspect ratio concept can be applied to classify caldera
subsidence and, therefore, to interpret the morphological characteristics and
structural features of the different collapse processes reproduced by analogue and
scale models (Acocella, 2008, and references therein). The idea that caldera collapse
and the resulting caldera depressions are strongly controlled by the relationship
between the geometry of the magma chamber and the thickness of the overlaying
roof (magma chamber depth) is also supported by theoretical models (e.g. Folch and
Martı ´, 2004), as we will see later in this paper.

2.2. Main observations
As described in Acocella (2008), experimental models on collapse calderas
may differ depending on the main feature they seek to simulate (Figure 1). Hence,
there are experiments (i) simulating the development of collapse calderas, as a