Calculation of dike trajectories from volcanic centers

[1] Patterns of dike swarms around volcanic centers or above mantle plumes are interpreted by a mechanical analysis of regional and dike-induced stresses, in which dike emplacement is controlled and guided by the stress state. Comparisons of dike patterns with patterns of principal-stress trajectories caused by a source and a regional stress system are commonly used to infer paleostresses. However, dike trajectories are determined by a complex interaction between dike-induced stresses and the source/regional stress system. We present numerical calculations based on a novel boundary-integral formulation, which examines the simultaneous effects of regional stresses, magma pressure, and dike injection on the local stress state around a continuously curving dike. Dike paths are calculated from the condition that dikes propagate by mode I failure. Our results suggest that the magnitude of the regional stresses would be 2–5 times higher than previous estimates based on principal-stress trajectory analysis.

[1]  E. M. Anderson.  XVII.—The Dynamics of Sheet Intrusion , 1939 .

[2]  D. A. Spence,et al.  Magma‐driven propagation of cracks , 1985 .

[3]  S. L. Crouch,et al.  Boundary element methods in solid mechanics , 1983 .

[4]  B. Lawn.  Fracture of Brittle Solids by Brian Lawn , 1993 .

[5]  Jon E. Olson,et al.  Inferring paleostresses from natural fracture patterns; a new method , 1989 .

[6]  Jon E. Olson,et al.  Joint pattern development: Effects of subcritical crack growth and mechanical crack interaction , 1993 .

[7]  Ken C. Macdonald,et al.  Overlapping spreading centers: Implications from crack growth simulation by the displacement discontinuity method , 1986 .

[8]  Guozhu Zhao,et al.  Analysis of minor fractures associated with joints and faulted joints , 1991 .

[9]  J. Sládek,et al.  Regularization Techniques Applied to Boundary Element Methods , 1994 .

[10]  D. Pollard,et al.  Mapping and modeling of radial fracture patterns on Venus , 1998 .

[11]  B. Lawn.  Fracture of brittle solids: Indentation fracture , 1993 .

[12]  Peter M. Shearer,et al.  An analysis of large‐scale variations in small‐scale mantle heterogeneity using Global Seismographic Network recordings of precursors to PKP , 2000 .

[13]  D. Pollard,et al.  Formation and interpretation of dilatant echelon cracks , 1982 .

[14]  D. Pollard,et al.  Origins of blade-like dikes in volcanic rift zones. , 1987 .

[15]  John R. Lister,et al.  Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks , 1990, Journal of Fluid Mechanics.

[16]  J. Lister,et al.  The effect of solidification on fluid–driven fracture, with application to bladed dykes , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[17]  J. Rice,et al.  Slightly curved or kinked cracks , 1980 .

[18]  R. C. Kerr,et al.  Fluid‐mechanical models of crack propagation and their application to magma transport in dykes , 1991 .

[19]  James W. Head,et al.  The global distribution of giant radiating dike swarms on Venus: Implications for the global stress state , 1994 .

[20]  E. M. Anderson,et al.  The dynamics of faulting : and dyke formation with applications to Britain , 1953, Geological Magazine.

[21]  S. Mogilevskaya.  Numerical modeling of 2-D smooth crack growth , 1997 .

[22]  Lionel Wilson,et al.  Giant radiating dyke swarms on Earth and Venus , 1993 .

[23]  Helmer Odé,et al.  MECHANICAL ANALYSIS OF THE DIKE PATTERN OF THE SPANISH PEAKS AREA, COLORADO , 1957 .

[24]  David D. Pollard,et al.  The stress state near Spanish Peaks, colorado determined from a dike pattern , 1977 .

[25]  E. M. Anderson.  IX.—The Dynamics of the Formation of Cone-sheets, Ring-dykes, and Caldron-subsidences , 1937 .

[26]  David D. Pollard,et al.  The geometry of echelon fractures in rock: implications from laboratory and numerical experiments , 1993 .

[27]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[28]  James M. McKenzie,et al.  Dike emplacement on Venus and on Earth , 1992 .

[29]  G. Baer,et al.  Mechanics of emplacement and tectonic implications of the Ramon Dike Systems, Israel , 1991 .

[30]  A. Rubin.  Dikes vs. diapirs in viscoelastic rock , 1993 .

[31]  A. Rubin.  Tensile fracture of rock at high confining pressure: implications for dike propagation , 1993 .

[32]  Y. Chen.  Numerical solution of a curved crack problem by using hypersingular integral equation approach , 1993 .

[33]  C. Pozrikidis.  Boundary Integral and Singularity Methods for Linearized Viscous Flow: Index , 1992 .