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Conceptual and numerical models of ring-fault formation

Agust Gudmundsson

Department of Earth Sciences, Royal Holloway University of London, UK ()

Abstract

Most ring faults of collapse calderas are primarily shear fractures the initiation and development of which depends on the state of stress in the host rock. The state of stress in a volcano is controlled by the loading conditions, such as magma-chamber geometry and pressure, but also by the mechanical properties of its rock units and structures (such as existing contacts, faults, and joints). Ring-fault formation is thus essentially a problem in rock physics. Field observations show that some ring faults are dip-slip, whereas others are partly faults (shear fractures) and partly ring dykes (extension fractures). Although slip on existing ring faults is much more common in basaltic edifices (shield volcanoes) than in true composite volcanoes, in both types of volcanoes most caldera unrest periods do not result in ring-fault slip. Here I present new conceptual and numerical models of caldera formation in volcanoes with shallow spherical (circular) or sill-like (oblate ellipsoidal) magma chambers. In the layered models, the host rock above the chamber is composed of 30 comparatively thin layers with stiffnesses (Young’s moduli) alternating between 1 GPa to 100 GPa. The chamber itself is located in a single, thick layer. The crustal segment hosting the chamber is either 20 km or 40 km wide but has a constant thickness of 20 km. The loading conditions considered are: (1) a crustal segment subject to 5 MPa tension; (2) crustal segment subject to excess magmatic pressure of 10 MPa at the bottom (doming of the volcanic field containing the chamber); (3) a combination of tension and doming; and (4) chamber subject to underpressure (negative excess pressure) of 5 MPa. The main results are as follows: (1) Excess pressure and underpressure in a chamber normally favour dyke injection rather than ring-fault formation. (2) For doming or tension, a spherical magma chamber favours dyke injection except when the layer hosting the chamber is very soft (10 GPa) or one with recent dyke injections, in which case the surface stress field favours ring-fault formation. (3) For a sill-like chamber in a 20-km wide crustal segment, a ring-fault can be generated by either tension or tension and doming; for a 40-km wide segment, doming alone is sufficient to generate a ring fault. (4) Since individual layers in a volcano may develop different local stresses, stress-field homogenisation through all the layers between the chamber and the surface is a necessary condition for ring-fault formation. (5) Because the mechanical properties of the layers that constitute basaltic edifices are more uniform than those that constitute true composite volcanoes, it follows that stress-field homogenisation, and thus ring-fault formation or slip, is more commonly reached in basaltic edifices than in composite volcanoes. (6) Both for basaltic edifices and composite volcanoes, the stress fields most likely to initiate ring faults are those generated around sill-like chambers subject to tension, doming, or both.

Keywords. Collapse calderas, rock properties, magma chambers, crustal stresses, composite volcanoes, basaltic edifices

1. Introduction

Many caldera collapses are associated with violent, explosive eruptions which can devastate large and densely populated areas. Collapse-caldera formation, and slip on existing ring faults, is therefore not only of academic interest, but also of great concern to human society. Typical collapse calderas are commonly many kilometres in diameter and with vertical displacement (subsidence) from several hundred metres to several kilometres (Fig. 1).

The ring faults of collapse calderas are rock fractures; the magma chambers from which most of them develop are rock cavities (Fig. 1). The initiation and development of any rock fracture depends on the state of stress in the host rock. The state of stress in a volcano is controlled by the material properties of its rock units and structures, such as existing contacts, faults, and joints, as well as by the loading conditions. In solid mechanics, “loading conditions” normally denote the forces, stresses, or pressures that are applied to a body and external to its material (Benham et al., 1996). Here, “loading conditions” refer to the fluid pressure in the shallow magma chamber, and the tectonic stress applied to the chamber and the associated volcano. The loading conditions thus depend on the tectonic environment and, in particular, the geometry and magma pressure of the chamber. The formation of a ring fault is thus essentially a problem in rock physics; it should not be confused with the separate problem of an ash-flow eruption, even if these are commonly associated.

While eruptions in collapse calderas are very common (Newhall and Dzurisin, 1988), formation of new ring faults or slip on existing ring faults are, in comparison, rare. This applies particularly to slip on ring faults in composite volcanoes (stratovolcanoes); in basaltic edifices or shield volcanoes such as in Hawaii and the Galapagos Islands, slip on existing calderas, often with very small or no eruptions, is more common.

To understand how and when a ring fault develops, and why an existing ring fault slips so infrequently, one must know the state of stress in the host volcano. This implies the knowledge of the rock properties and structures of the volcano. Furthermore, to forecast whether a ring fault is likely to form or slip during a particular unrest period we must have a rough idea of the geometry of the associated magma chamber. Ring-fault formation and slip are mechanical processes that cannot be forecasted solely on the basis of empirical criteria; to develop viable models to assess the probability of ring-fault formation or slip these processes must be understood in mechanical terms.

This paper has three principal purposes. The first is to discuss the general structure and attitude of ring faults. The focus is on summarising field results and to provide a conceptual model of a typical ring fault. The second is to explain the general stress-field conditions for the formation of or slip on existing ring faults. Here the focus is on the results of field studies and numerical models of the stress fields that must be generated so as to trigger ring-fault formation. The third is to use the results of the numerical models to explain why ring-fault formation and slip on existing faults is much more common in basaltic edifices than in composite volcanoes.

2. Ring-fault structure

Traditionally, collapse calderas are defined as circular or moderately elliptical volcanic depressions (Fig. 1) with a diameter exceeding about 1 mile or 1.6 km (Macdonald, 1972). Using this definition, caldera on Earth are from 1.6 km to about 80 km in maximum diameter (Lipman, 2000). The lower limit makes it possible to distinguish morphologically between calderas and pit craters; pit craters exceed 1 km in diameter. Normally, the diameter of a caldera is many times greater than those of any associated vents.

Many calderas are located within volcanic fields, that is, clusters of volcanoes within a limited area all of which are active over a certain period and often have certain compositional characteristics in common. Volcanic fields and the magma-accumulation regions at their bottoms are normally much larger than the diameter of any included magma chamber or caldera (Komuro, 1986; Francis 1993). Well-known volcanic fields include the Galapagos Islands, the Eifel area in Germany (Schmincke, 2004), many regions in Japan (Komuro, 1986), and in the western United States (Steven and Lipman, 1976; Francis, 1993). By extension, large volcanic zones that include many active calderas and other volcanoes may be regarded as elongated volcanic fields.

Some calderas are multiple, that is, consist of two or more adjacent ring faults (Fig. 2). The calderas are then commonly of a different age. When one or more small ring faults occur inside a larger ring fault, the caldera is referred to as nested (Fig. 3). The small ring fault is then normally the younger of the two.

Most calderas are somewhat elliptical in plan view. Although many calderas are close to being circular, few if any are exactly of that ideal shape; many more are elliptical while some have nearly rectangular boundaries (Acocella et al., 2003, 2004; Holohan et al., 2005; Spinks et al., 2005). Some collapse calderas are very elongated and similar to grabens (Aguirre-Diaz, Labarthe-Hernadez, 2003; Aguirra-Diaz et al., 2005). These observations, together with general mechanical considerations, suggest that many calderas – at least normal-fault calderas (Gudmundsson, 1998a) – and grabens form a spectrum of fault-generated structures. At one end of the spectrum there are circular collapse calderas, at the other end narrow and long grabens (Fig. 4). In this paper I shall use the term “ring fault” to refer to the boundary faults of a collapse caldera irrespective of its actual shape in plan view.

Most ring faults are subvertical dip-slip faults (Figs. 1, 3 and 4). Some studies indicate outward-dipping ring faults (Williams et al., 1970; Branney, 1995; Cole et al., 2005), but many more indicate vertical or inward-dipping faults (Macdonald, 1972; Filson et al., 1973; Aramaki, 1984; Lipman, 1984, 1997, 2000; Newhall and Dzurisin, 1988; Gudmundsson, 1998a; Geshi et al., 2002).

The well-documented collapse on the Fernandina Caldera in the Galapagos Islands in 1968, for instance, occurred on a ring fault dipping inward at about 80° (Simkin and Howard, 1970). Also, the collapse of the Miyakejima Caldera in Japan in 2000 was primarily on an inward-dipping ring fault (Geshi et al., 2002). All funnel-shaped calderas must, by definition, dip inwards (Aramaki, 1984; Lipman, 1997; Cole et al., 2005). Ring faults in Iceland are either close to vertical or dip steeply inwards. Many ring faults are occupied by dykes, most of which are vertical or dip steeply inwards (Oftedahl, 1953; Almond, 1977).

Shear fractures such as ring faults make certain angles with the directions (trajectories) of the principal stresses. For dip slip faults, the angle between the fault plane and the direction of the maximum principal compressive stress, s1, is commonly 10-30°. In areas with comparatively flat surfaces, the near-surface maximum compressive principal stress is close to vertical and the intermediate and minimum compressive stresses, s2 and s3, respectively, close to horizontal. A shallow magma chamber, however, generates a local stress field where, depending on the magma-chamber shape, crustal properties, and loading conditions, the principal stresses may be inclined, even in homogeneous, isotropic crustal segments (Gudmundsson, 1998b).

When composite volcanoes are modelled so that the layers and contacts may have widely different mechanical properties and the magma chamber may be of various shapes, the trajectories of the principal stresses may vary abruptly from one layer to the next (Gudmundsson, 2006). Faults, joints, and other discontinuities may also affect the ring-fault dips since the faults tend to develop along suitably orientated weaknesses, particularly joints. The dip of a ring fault, as that of any dip-slip fault (Fig. 5), may thus vary from one layer to the next (Fig. 6). It follows that a ring-fault may dip inward in one layer, outward in the next, and be vertical in the third. In a composite volcano the local dips of a ring fault, measured in different outcrops along the fault plane, may be highly variable and thus cannot to be used as a basis for general mechanical models on ring-fault formation.

3. Magma-chamber geometry

Most or all ring faults are associated with comparatively shallow crustal magma chambers (Figs. 1, 3, 4, 6). Field studies indicate that many shallow magma chambers, at least during the end stages of their evolution, are of a shape surprisingly close to that of an ideal ellipsoid (Gudmundsson, 2006). Consider, for instance, the felsic (granophyre/granite) Slaufrudalur pluton in Southeast Iceland (Figs. 7, 8). The pluton is about 8 km long, with a maximum width of 2 km, a cross-sectional area of about 15 km2, and an exposed volume of about 10 km3. The total volume is likely to be considerably greater. It is the second largest pluton in Iceland. The trend of the pluton coincides with the strike of the lavas in the pile within which it formed.

The Slaufrudalur pluton acted as a magma chamber. This is indicated by many dykes that cut through its roof, many of which are less than one metre thick, but some of which reach a thickness of about 10 m (Fig. 8). They are of the same composition as the granophyre in the pluton itself (Cargill et al., 1928).

Not only is the roof of the chamber exceptionally well exposed, but so are its walls (Fig. 8). The roof, made of basaltic lava flows, makes a sharp contact with the pluton. The magma-chamber formation was forceful, as is indicated by the general change in the dip of the adjacent lava pile. For example, over a short distance of a few kilometres, the dip of the lava pile changes from 16-18°NW to 10°E at the eastern margin of the Slaufrudalur pluton. The general dip of the lava pile in Southeast Iceland is to the northwest, but near the Slaufrudalur pluton the dips are away from the pluton: for example 10°E at its eastern margin and 22-25°N at its northern margin. In a vertical section the pluton has the shape of an elongate dome which reaches an altitude of 700 m.

The formation of the Slaufrudalur magma chamber was primarily through repeated injections of tens-of-metres thick sill-like bodies on top of each other (Cargill et al., 1928; Beswick, 1965). At present, the sills dip 5-10°NE, which is similar to that of the regional lava pile hosting the pluton. The space for the magma chamber was partly generated by uplift and tilting of the host rock, as indicated by the away-dipping lava pile. Part of the space, however, may have been generated by subsidence or downbending of the floor under the sill-like intrusions. The Slaufrudalur pluton may be the uppermost part of a much larger magma chamber, a chamber that is presumably mostly of gabbro and acted as a source to a central (composite) volcano.