Page 380 - Caldera Volcanism Analysis, Modelling and Response

Facilitating Dike Intrusions into Ring-Faults 355

Bosworth et al., 2003), and thereby influence ring-dike intrusions. This means that
ring-dikes may be emplaced in association with both magma chamber pressure
changes and extrinsic processes. In this paper, the conditions under which ring-
fractures may open to facilitate ring-dikes will be further explored and summarized.
This work uses a set of boundary element models that address the question of where
and under which circumstances a ring-fracture is subject to opening, and thus
examines the geometric possibility of ring-dikes. The first models are simple, using
spherical magma chambers and cylindrical ring-fractures. More complex models
are then designed in order to understand the effects of ellipsoidal and sill-shaped
chambers, and to test how extrinsic activities, such as peripheral radial dikes or
earthquakes, can affect the locations and patterns of subsequent ring-dikes.
Natural ring-dikes strongly compare to the patterns described herein (see Section 4).
This paper intends to provide a general overview of ring-dike formation using
numerical models, with the goal of stimulating successive studies at key locations
elsewhere.

2. Modeling Method

Numerical models are performed in a three-dimensional linear elastic half-
space medium, using a boundary element code (Crouch and Starfield, 1983;
Becker, 1992; Thomas, 1993). The modeling method is based on the analytical
solutions for angular dislocations in isotropic half- and full space (Comninou and
Dundurs, 1975), and has already been used in various studies concerning the
development of stress in volcanoes (e.g., Walter et al., 2005; Walter and Amelung,
2006). Using combinations of angular dislocations, polygonal (triangular) boundary
elements are made that together can describe complex three-dimensional objects.
This allows finite magma chambers and ring-faults of various dimensions to be
considered. Boundary conditions are defined as tractions or displacements at
the center of each element. Linear equations are solved in order to calculate
displacement distributions along faults, dikes, and magma chambers. For a more
detailed description, see Thomas (1993).
This study considers (i) a deflating magma chamber of various geometries
(spherical, oblate spheroid, ellipsoid), (ii) a subvertical ring-fault surrounding the
magma chamber (spherical, elliptical), (iii) freely slipping faults that may be
reactivated during magma chamber evacuation, and (iv) dike intrusion and faulting
in the periphery of the ring-fault.
The boundary element method was validated by comparing it with the
analytical solution of a spheroid source (Yang et al., 1988); results agree within a few
percentage for the studied range of geometries. The type of loading as shown in this
paper is pressure change at the magma chamber by 10 MPa (depressurization). If
other types of loading were applied, they are specified below. A Young’s modulus of
E ¼ 70 GPa and a Poisson’s ratio of v ¼ 0.25 were assigned that were typical values
for the shallow crust (Turcotte and Schubert, 2002). Varying these material
properties can affect the magnitude of the results, but the patterns remain similar.