Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy
TLDR
In this article, a model of a horizontal circular crack in a semi-infinite elastic solid was proposed and exact expressions for vertical and horizontal displacements of the free surface of a half-space were derived for a special case of a uniformly pressurized crack.Abstract:
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.read more
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Journal ArticleDOI
Segmented lateral dyke growth in a rifting event at Bárðarbunga volcanic system, Iceland
Freysteinn Sigmundsson,Andrew Hooper,Sigrún Hreinsdóttir,Kristín Vogfjörd,Benedikt G. Ófeigsson,Elías Rafn Heimisson,Stéphanie Dumont,Michelle Parks,Karsten Spaans,Gunnar B. Gudmundsson,Vincent Drouin,Thóra Árnadóttir,Kristín Jónsdóttir,Magnús T. Gudmundsson,Thórdís Högnadóttir,Hildur M. Fridriksdottir,Hildur M. Fridriksdottir,Martin Hensch,Páll Einarsson,Eyjólfur Magnússon,Sergey Samsonov,Bryndís Brandsdóttir,Robert S. White,Thorbjörg Ágústsdóttir,Tim Greenfield,Robert G. Green,Ásta Rut Hjartardóttir,Rikke Pedersen,Richard A. Bennett,Halldór Geirsson,Peter C. La Femina,Helgi Björnsson,Finnur Pálsson,Erik Sturkell,Christopher J. Bean,Martin Möllhoff,Aoife Braiden,Eva P. S. Eibl +37 more
TL;DR: Lateral dyke growth with segment barrier breaking by pressure build-up in the dyke distal end explains how focused upwelling of magma under central volcanoes is effectively redistributed over long distances to create new upper crust at divergent plate boundaries.
Journal ArticleDOI
A model for the origin of large silicic magma chambers: precursors of caldera-forming eruptions
TL;DR: In this paper, the authors address the question of why buoyant and otherwise eruptible high-silica magma should accumulate for long times in shallow chambers rather than erupt more continuously as magma is supplied from greater depths.
Journal ArticleDOI
Intrusion triggering of the 2010 Eyjafjallajokull explosive eruption
Freysteinn Sigmundsson,Sigrún Hreinsdóttir,Andrew Hooper,Thóra Árnadóttir,Rikke Pedersen,Matthew J. Roberts,Niels Oskarsson,A. Auriac,J. Decriem,Páll Einarsson,Halldór Geirsson,Martin Hensch,Benedikt G. Ófeigsson,Erik Sturkell,H. Sveinbjornsson,Kurt L. Feigl +15 more
TL;DR: It is shown that deformation associated with the 2010 Eyjafjallajökull eruptions was unusual because it did not relate to pressure changes within a single magma chamber, and clear signs of volcanic unrest signals over years to weeks may indicate reawakening of such volcanoes, whereas immediate short-term eruption precursors may be subtle and difficult to detect.
Journal ArticleDOI
Probing the mechanical properties of seismically active crust with space geodesy: Study of the coseismic deformation due to the 1992 Mw7.3 Landers (southern California) earthquake
TL;DR: In this article, the authors investigated the coseismic deformation due to the 1992 M(w)7.3 Landers earthquake using synthetic aperture radar (SAR) and Global Positioning System (GPS) measurements.
Journal ArticleDOI
An InSAR‐based survey of volcanic deformation in the central Andes
Matthew E. Pritchard,Mark Simons +1 more
TL;DR: In this paper, the authors extend an earlier interferometric synthetic aperture radar (InSAR) survey covering about 900 remote volcanos of the central Andes (14°-27°S) between the years 1992 and 2002.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Book
Theory of elasticity
TL;DR: The equilibrium of rods and plates Elastic waves Dislocations Thermal conduction and viscosity in solids Mechanics of liquid crystals Index as discussed by the authors The equilibrium of rod and plate elastic waves Elastic waves