In most active volcanoes, unrest periods with dike injections are much more common than eruptions. While widely recognized, this simple observation has not been satisfactorily explained. Surface deformation in volcanoes is commonly attributed to dikes injected from shallow magma chambers that fail to reach the surface. Field observations of dike tips, many of which are blunt, indicate arrest that is primarily controlled by the local stresses in the layers through which the dikes propagate. Numerical models on the stress fields around magma chambers located in an anisotropic, heterogeneous (layered) crust indicate that, for uniform loading, a layered crust normally develops stress fields that are unfavorable for feeder-dike formation. In particular, the models, together with the field observations, indicate that an essentially homogeneous stress field along the potential pathway of a dike is a necessary condition for its reaching the surface to supply magma to a volcanic eruption.
 Geodetic, seismological, and geochemical observations of active volcanoes indicate that periods of unrest in a volcano are normally much more common than eruptions in the same volcano. Also, that injections of dikes (here the term “dike” includes also inclined sheets) occur during many of the unrest periods that nevertheless do not lead to volcanic eruptions [Gudmundsson, 2002, 2003]. Thus, dike injection is much more common than feeder-dike formation [Harris et al., 2000; Gudmundsson, 2002; Stewart et al., 2003]. This indicates that during many unrest periods the stress situation at, and in the vicinity of, the magma chamber favors dike emplacement while the stress situation away from the chamber favors dike arrest.
 In extinct volcanoes such as the composite (central) volcanoes in Iceland and Tenerife (Canary Islands) many tens of dikes have been observed to terminate vertically in the lava pile. Most dikes do not join extrusive layers (lava flows or pyroclastic flows) but rather end vertically with their tips tapering away or, more commonly, ending bluntly. Many blunt ends, some associated with offset dikes others with arrested dikes [Gudmundsson, 2002, 2003], occur at sharp contacts between layers, suggesting that mechanical rather than thermal conditions are the main factors controlling the offset and, in particular, the arrest of dikes.
 In the past decades geodetic measurements of surface deformation in volcanoes have greatly improved in accuracy and ease of observation. Today routine measurements on many active volcanoes include the use of GPS and SAR [Massonet and Feigl, 1998; Burgmann et al., 2000; Battaglia et al., 2003]. A general inflation of the surface is normally interpreted as being related to pressure increase, and deflation to pressure decrease, in the shallow source chamber of the volcano.
 Recent papers on dike arrest focus mostly on the effects of cooling of magma at the dike tip [e.g., Bolchover and Lister, 1999; Fialko and Rubin, 1999], or are concerned with neutral-buoyancy effects on dikes changing into sills at the crust-mantle boundary [Dahm, 2000]. By contrast, the present paper focuses on the effects of layering at shallow depths in active volcanoes and rift zones on dike propagation and arrest. The first aim of this paper is thus to summarize the main findings concerning arrested dikes. The second aim is to show how variations in mechanical properties of layers (including weak contact layers such as scoria) affect the local stresses in composite volcanoes and rift zones and control dike arrest.
2. Arrested Dikes
 Field studies indicate that most dikes become arrested at some crustal depths and never reach the surface to supply magma to eruptions. For example, studies of dikes in fracture zones and other oceanic depressions indicate that most dikes are non-feeders [Dilek et al., 1998; Karson, 1998; Stewart et al., 2003]. Similarly, in well-exposed ophiolites there is normally an abrupt change from a sheeted dike complex with almost 100% dikes to 10–20% dikes in a 25–100-m-thick transitional layer. This suggests that most dikes in sheeted dike complexes are non-feeders.
 Studies of many thousand late Tertiary and Pleistocene dikes in Iceland and Tenerife (Canary Islands) also indicate that most dikes are non-feeders. Nearly all the dikes seen to end vertically in profiles in these areas do so without being connected to lava flows [Gudmundsson, 2002, 2003].
 Most dikes end either by tapering away or bluntly. When a dike tapers away its thickness gradually decreases toward the tip so that, at the tip, the dike thickness is a small fraction of its normal thickness [Gudmundsson, 2002, 2003]. When a dike ends bluntly the thickness of its tip is generally similar to the normal thickness of the dike. A blunt ending may occur when a dike enters a comparatively soft layer, such as soft pyroclastic rock, or, more commonly, when the dike becomes arrested at a contact between layers.
 The common occurrence of blunt-ended (arrested or offset) dike segments indicates that weak contacts, mechanical contrast between layers, and the associated local stress fields, have dominating effects on dike propagation. In particular, the field results indicate that local stresses within composite volcanoes and rift zones largely determine whether or not an injected dike reaches the surface to feed an eruption.
3. Local Stresses in Volcanoes
 The main factors that determine the local stresses in volcanoes and rift zones are, first, the properties of the associated magma chamber and, second, the properties of the rocks hosting the magma chamber. Many extinct magma chambers (plutons) have shapes similar to prolate ellipsoids with the long axis vertical (or approximately cylindrical bodies), spheres, or oblate ellipsoids with the short axis vertical (or approximately sill-like bodies). For active magma chambers, the volumes are estimated at 5–500 km3 [Chester, 1993] which, for a spherical chamber, would indicate a radius of ∼1–5 km.
 Many numerical and analytical models exist of magma chambers in a homogeneous, isotropic crust and subject to magmatic excess pressure as the only loading [Gudmundsson, 2002] (Figure 1). The results show that the pressure-generated tensile stresses around the chamber falls off rapidly with increasing distance from the chamber, so that the conditions of dike injection next to the chamber are frequently met while the conditions of dike arrest occur at a certain distance. For this reason alone, many volcanic unrest periods with dike injections do not lead to volcanic eruptions because the injected dikes become arrested.
 The probability of dike offset and arrest during periods of volcanic unrest, however, increases when the magma chamber is located in a crust composed of layers with contrasting mechanical properties. Composite volcanoes and rift zones, especially at shallow depths, are normally composed of stiff (high Young's modulus) lava flows (and some pyroclastic flows) that alternate with soft (low Young's modulus) pyroclastic rocks, scorias, and sediments. Most data on the Young's moduli of rocks are based on small-sample laboratory measurements which are known to be commonly 1.5–5 times higher than the common in situ values [Heuze, 1980]. However, this difference generally decreases with depth and confining (overburden) pressure, but increases with the number of fractures trending at right angles to the loading [Priest, 1993]. Here we use the results of laboratory measurements.
 Some layers of basalt and gabbro have Young's moduli as high as 110–130 GPa, whereas volcanic tuffs have Young's moduli as low as 0.05–0.1 GPa [Afrouz, 1992; Bell, 2000]. Poisson's ratios of these rocks have a much narrower range. For example, Poisson's ratio of many basaltic rocks and volcanic tuffs is the same, 0.25 [Bell, 2000].
 To study the effects of crustal layering on local stresses in composite volcanoes on dike arrest, we used the finite-element program ANSYS. A technical description of the finite-element method, and ANSYS in particular, is given by Zienkiewicz , Logan , and the ANSYS homepage (http://www.ansys.com). The focus is on the effects of variation in Young's modulus (stiffness) between layers in composite volcanoes and rift zones; Poisson's ratio is taken as a constant, 0.25, in all the models. Layer stiffness varies between 1 GPa and 100 GPa. Although this is a very large variation in stiffness, it is still well within the limits indicated above. We consider the soft layers (1 GPa) as representing unconsolidated tuffs and late Pleistocene or early Holocene sediments, whereas the stiff layers (100 GPa) represent basaltic and intermediate lava flows. All the models are fastened in the corners (with the conditions of no displacement) to avoid rigid-body rotation and translation.
 Consider a magma chamber of a circular cross s ection with 10 horizontal layers above the host layer where an internal excess magmatic pressure (pressure in excess of the lithostatic pressure at the margin of the chamber) of pe = 10 MPa is the only loading. The in situ pe is likely to be similar to the in situ tensile strength of the host rock of the chamber, and thus normally less than 6 MPa [cf. Gudmundsson, 2002]. However, laboratory tensile-strength values are higher than in situ values, and since we use the laboratory values of the stiffnesses we use the average laboratory tensile-strength value of 10 MPa for pe [Afrouz, 1992; Bell, 2000].
 The model (Figure 2) shows that the tensile stresses concentrate, first, around the upper part of the magma chamber and, second, in the stiff layers above the chamber. There are no significant tensile-stress concentrations in the soft layers. Also, the tensile-stress concentrations within the stiff layers occur primarily in the upper part of each layer whereas the lower parts are subject to compressive stresses. Thus, the stress effects due to inflation of a magma chamber in a composite volcano are similar to those that result from convex bending of a layered plate in that tensile stresses concentrate above, and compressive stresses below, the neutral surface of each layer. Thus, even the stiff layers, in addition to the soft layers, would tend to arrest upward-propagating dikes.
 This conclusion is further supported by the abrupt rotation of the σ1-trajectories, from subvertical to subhorizontal, in the layers above the magma chamber (Figure 3). When the tips of dikes injected from the chamber meet with layers with subhorizontal σ1-trajectories, there are three possible scenarios. First, the dike tip may propagate horizontally so that the dike becomes a sill. Second, the dike tip may propagate horizontally for a while and then, at a suitable location, follow inclined or subvertical σ1-trajectories to shallower levels in the crust. Third, the dike tip may become arrested. All these cases are well known from field studies of dikes [Gudmundsson, 2002, 2003].
 These results indicate that during a period of unrest in a composite volcano or a rift zone with magma-chamber inflation and surface doming, the local stresses in the soft mechanical layers encourage dike arrest. The lower parts of many of the stiff layers also encourage dike arrest. During unrest periods with dike injection, there are thus normally local stresses that tend to prevent dike propagation to the surface, and thus to prevent volcanic eruptions.
 The model results also indicate that, during an unrest period with doming, some layers, particularly stiff ones, may develop local tensile stresses that favor normal faulting and associated seismicity. By contrast, other layers, particularly soft ones, or parts of layers (for example the lower parts of many stiff layers), may develop local relative compressive stresses that act as stress barriers to normal-fault propagation. Thus, the soft layers may arrest updip and downdip fault propagation. In this way, the seismicity during an unrest period may be confined to certain mechanical layers within the composite volcano while other layers remain seismically quiet.
 The present results indicate that dike injections lead to eruptions only if special stress conditions are satisfied: namely, that the local stresses along the potential pathway are favorable for the propagation of magma-driven fractures up to the surface of the composite volcano or rift zone. More specifically, for a dike-fed eruption to occur, the local stresses along the entire pathway of the magma-driven fracture must favor the formation of a subvertical extension fracture. If there is any local stress field along the pathway of the magma-driven fracture that is entirely unfavorable to the propagation of that fracture, then it will almost certainly become arrested. Thus, for an eruption to occur the local stresses along the potential pathway of the magma-driven fracture must be basically the same and, therefore, homogenized.
 Stress-field homogenization in a composite volcano or a rift zone consisting of layers with contrasting mechanical properties occurs through smoothing out the differences between the local stresses in these layers. Perhaps the main processes that encourage stress-field homogenization in volcanoes are host-rock alteration and host-rock deformation since both tend to bring about a uniform stress field and, in particular, reduce the differences between the stiffnesses of individual layers. Host-rock alteration involves healing and sealing of contacts and faults, and filling of fractures and cavities in the rock with secondary minerals. As a result of alteration, the thicknesses of layers with essentially the same (homogeneous) mechanical properties gradually increase.
 Brittle host-rock deformation in a composite volcano or a rift zone is primarily related to injection of dikes, fracturing and faulting. In the shallow parts of active composite volcanoes and rift zones, normal faulting may be the primary mechanism of deformation, but in deeper parts dike injection [Gudmundsson, 2000; Acocella and Neri, 2003]. These deformation mechanisms tend to lessen stress differences between individual mechanical layers and thus to make the stresses essentially homogeneous in large parts of the volcanoes.
 As an example of a development toward stress-field homogenization, compare the model in Figure 3 with that in Figure 4. In both models the only loading is the internal magma excess pressure of 10 MPa and there are 10 layers above the layer hosting the chamber. However, in the model in Figure 4 the surface layer has a stiffness of 10 GPa, and then the stiffness increases gradually by 2 GPa for each layer, the layer hosting the chamber having a stiffness of 30 GPa.
 Clearly, the σ1-trajectories in Figure 4 are more similar (than those in Figure 3) to the trajectories of a homogeneous model (Figure 1). This suggests that, provided there are no abrupt changes in stiffnesses between layers but rather a gradual increase with depth (as may be common in older and deeper layers) parts of a composite volcano or a rift zone can function as a broadly homogeneous, isotropic half space. In other words, the stress field becomes homogenized through the lessening of the stiffness difference between the layers that constitute the composite volcano. New eruptive layers, however, commonly generate strong mechanical contrasts in the uppermost part of a volcano and may develop local stresses that favor dike arrest. The gradual stress-field homogenization is thus interrupted with periods of local stress-field heterogenization which may be one reason for the comparatively long repose times of many volcanoes.
 We thank Joan Marti and an anonymous referee for helpful comments, Nadine Friese and Steffi Burchardt for help with the figures, and the European Commission for financial support (EVG1-CT-2002-00073 PREPARED).