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Facilitating Dike Intrusions into Ring-Faults                        367


             views show that maximum opening occurs at the part of the ring-fault that is closest
             to the dike (Figure 9C). This suggests that ring-dike intrusion might occur at the
             segment of the ring-fault that is closest to the radial dike intrusion in the periphery
             of the caldera. Accordingly, a dipping dike would lead to ring-dike formation that
             obliquely propagates upwards.




                  4. Discussion

                  This paper uses numerical models to (i) describe deformation around a
             depressurized magma chamber and test how local structures can affect this
             displacement, (ii) describe the potential of opening a ring-fault in order to examine
             the location at which potential dike intrusions occur, and (iii) describe how
             processes external to the caldera, such as an earthquake or radial intrusion, affect the
             location of a ring-dike intrusion.
                The models are simplified and assume a homogeneous elastic material. Volcanoes,
             especially caldera volcanoes that experience a high degree of fracturing and
             hydrothermal weakening, may have a time-dependent viscoelastic rheology (New-
             man et al., 2001) and rock-strength values that vary by as much as several orders of
             magnitude (Wattersetal.,2000). The variations in material may be lateral (due to
             fracturing, dikes, alteration) or vertical (due to lithologic layering, increasing
             confining pressure). Thus, the development of a stress field and the deformation
             pattern may be influenced by such heterogeneities (e.g., Manconi et al., 2007;
             Gudmundsson, 2006). One may speculate, for instance, that the amount of ground
             displacement in a deflating or inflating caldera basin can be amplified by rock types
             that have a lower modulus of elasticity. Likewise, the effect of external processes, such
             as earthquakes or dike intrusion in the periphery of the volcano, may have an effect on
             caldera systems. The models used in this study assume that the intrusion of ring-dikes
             as subvertical extensional fractures (mode I) is governed by opening perpendicular
             to a ring-fault. This generally agrees with historical caldera activity, where
             displacement often occurs along near-vertical ring-faults (Newhall and Dzurisin,
             1988). However, it must be noted that this is a simplification of more complex
             geometries, as some historical caldera ring-faults have shear fractures that dip slightly
             inward (Darwin caldera) or outward (Rabaul caldera), the latter also approximating
             the findings of previous seminal work (Anderson, 1936, 1937). Some (probably most)
             dike intrusions intrude in a mixed-mode mechanism, including opening (mode I)
             but also strike-slip shear (mode II) and dip-slip shear (mode III) dislocation, which is
             not considered in the models presented here. Nevertheless, important conclusions can
             be drawn from these models, as shown by comparisons to natural caldera systems.
                The models imply that a ring-dike forms in a uniform circular way only when
             the magma chamber is uniform, perfectly spherical, and not influenced by regional
             or external structures or deformation fields. Most other numerical models suggest
             that a potential ring-dike is more likely to intrude only partially into a ring-fault.
             Likewise, typical ring-dikes found in nature show such complexities, where in
             combination with the models summarized here, external influences can be assessed.
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