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Published July 2001 | Published
Journal Article Open

Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy


We consider deformation due to sill-like magma intrusions using a model of a horizontal circular crack in a semi-infinite elastic solid. We present exact expressions for vertical and horizontal displacements of the free surface of a half-space, and calculate surface displacements for a special case of a uniformly pressurized crack. We derive expressions for other observable geophysical parameters, such as the volume of a surface uplift/subsidence, and the corresponding volume change due to fluid injection/withdrawal at depth. We demonstrate that for essentially oblate (i.e. sill-like) source geometries the volume change at the source always equals the volume of the displaced material at the surface of a half-space. Our solutions compare favourably to a number of previously published approximate models. Surface deformation due to a 'point' crack (that is, a crack with a large depth-to-radius ratio) differs appreciably from that due to an isotropic point source ('Mogi model'). Geodetic inversions that employ only one component of deformation (either vertical or horizontal) are unlikely to resolve the overall geometry of subsurface deformation sources even in a simplest case of axisymmetric deformation. Measurements of a complete vector displacement field at the Earth's surface may help to constrain the depth and morphology of active magma reservoirs. However, our results indicate that differences in surface displacements due to various axisymmetric sources may be subtle. In particular, the sill-like and pluton-like magma chambers may give rise to differences in the ratio of maximum horizontal displacements to maximum vertical displacements (a parameter that is most indicative of the source geometry) that are less than 30 per cent. Given measurement errors in geodetic data, such differences may be hard to distinguish.

Additional Information

© 2001 RAS. Accepted 2001 February 11. Received 2001 February 8; in original form 2000 March 23. Article first published online: 20 Dec. 2001. We thank Alan Beck, Paul Davis and an anonymous reviewer for thoughtful comments that helped to improve this manuscript. Lupei Zhu kindly provided us with a numerical code for modelling deformation due to point sources in a layered halfspace. This work was supported by NSF grant EAR-9980664. A Matlab program that calculates displacements of a half-space surface due to a horizontal penny-shaped crack is available from the authors. Contribution number 8707 of the Division of Geological and Planetary Sciences, Seismological Laboratory, California Institute of Technology.

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