Bull Volcanol (2003) 65:606–619 DOI 10.1007/s00445-003-0289-7 ORIGINAL ARTICLE Agust Gudmundsson Surface stresses associated with arrested dykes in rift zones Received: 14 January 2002 / Accepted: 19 March 2003 / Published online: 16 July 2003  Springer-Verlag 2003 Abstract Many theoretical models predict that arrested dykes may generate major grabens at rift-zone surfaces. Arrested dyke tips in eroded rift zones, however, are normally not associated with major grabens or normal faults that could be generated by dyke-induced stresses ahead of the tips, and normal faults and grabens tend to be less common in those parts of eroded rift zones where dykes are comparatively abundant. Similarly, there are feeder dykes, as well as dykes arrested a few metres below the surface, that do not generate faults or grabens at the surface. Here I propose that this discrepancy between theoretical models and field observations may be ex- plained by the mechanical layering of the crust. Numer- ical models presented here show that abrupt changes in Young’s moduli, layers with high dyke-normal compres- sive stresses (stress barriers), and weak, horizontal contacts have large effects on the dyke-induced stress fields. For the models considered, the surface tensile stresses induced by arrested dykes are normally too small to lead to significant fault or graben formation at the rift- zone surface. The only significant dyke-induced surface tensile stresses (2 MPa) in these models are for a dyke tip arrested at 1 km depth below the surface of a rift zone with a weak contact at 400 m depth and subject to extension. That tensile stress, however, peaks above the ends of the weak horizontal contact, which, in the model considered, occur at distances of 4 km to either side of the dyke, and shows no simple relation to the depth to the dyke tip. Thus, for a layered crust with weak contacts, straightforward inversion of surface geodetic data to infer dyke geometries may result in unreliable results. Keywords Rift zones · Surface deformation · Grabens · Dykes · Stresses · Layered crust Introduction Magma in nearly all volcanic eruptions is transported to the surface through inclined sheets or subvertical dykes. In the past two decades there has been considerable interest in fluid flow in propagating dykes, as well as the surface deformation associated with arrested dykes. Works that explicitly deal with the dynamics of magma transport in dykes include those of Wilson and Head (1981), Spence et al. (1987), Lister and Keer (1991), Rubin (1995), Meriaux and Jaupart (1998), Fialko and Rubin (1999), Bolchover and Lister (1999), and Dahm (2000). When considering surface deformation associated with arrested dykes and sheets, magma transport is, however, no longer very relevant. It follows that magma flow in dykes is mostly outside the scope of the present paper. Surface deformation studies are becoming increasingly important for assessing volcanic hazards and are routinely used to infer the geometry and shape of magma-filled fractures. Recent studies on surface stresses and defor- mation associated with dykes include those of Pollard et al. (1983), Davis (1983), Rubin and Pollard (1988), Rubin (1992), and Cayol and Cornet (1998). These authors rely mostly on numerical methods for finding the solutions, which are also used in the related problem of propagation pathways of fluid-filled fractures (Dahm 2000). Analyt- ical, or semi-analytical, techniques, however, have long been used for studying surface deformation above ellip- tical cracks (Isida 1955) and ellipsoidal cavities (Tsuchida and Nakahara 1970) in semi-infinite, elastic plates and half-spaces. These techniques have also been applied to the surface stresses and displacements associated with vertical fluid-filled fractures and dykes (Okada 1985; Bonafede and Olivieri 1995; Bonafede and Danesi 1997). Most works cited above deal with vertical, fluid-filled fractures in an elastic half space that is both homogeneous and isotropic. Surface deformation in a layered elastic medium, however, has been considered by Roth (1993) and by Bonafede and Rivalta (1999a, b). Editorial responsibility: A. Woods A. Gudmundsson ( ) ) Department of Structural Geology and Geodynamics, Geoscience Centre, University of Göttingen, Goldschmidtstrasse 3, 37077 Göttingen, Germany e-mail: Agust.Gudmundsson@gwdg.de