A perturbation solution for dyke propagation in an elastic medium with graded density

Abstract

We present a perturbation method to investigate the steady-state propagation of a dyke from an over pressured source (e.g. a magma chamber) into a semi-infinite elastic solid with graded mass density. The non-linear dyke propagation/magma transport problem is reduced to a series of linear problems using a perturbation technique with the small non-dimensional parameter ε = 12ηV/(H2 Δρ0g), where η is the magma viscosity, V the propagation velocity, Δρ0 the difference between the densities of the host rock and magma at the dyke tail, g the gravitational acceleration and H a parameter on the order of maximum dyke thickness. In general, the perturbation method is applicable to mafic dyke propagation at a relatively low propagation velocity wherein ε remains small (e.g. less than 0.1). We describe an integral equation approach to obtain the stress intensity factor at the dyke tip and the separation displacement of the two dyke surfaces. Numerical examples are presented to examine the effects of various physical parameters, for example, buoyancy, density gradation, propagation velocity and overpressure on the dyke propagation behaviour. It is found that dyke propagation could reach a steady-state in some specific ranges of growth for a given density gradient of the host rock. The propagation tends to decelerate when the dyke tip approaches the level of neutral buoyancy. © 2007 The Authors Journal compilation © 2007 RAS.