Ascent of a granitoid diapir in a temperature varying medium

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Abstract
A relationship for the ascent velocity of a granitoid diapir is derived and used in conjunction with a crustal heat flow model which incorporates a depth‐dependent temperature to predict emplacement histories. Ascent rate is strongly dependent on the width of a deformation layer of variable viscosity that is formed by the transfer of heat to the country rock and on the buoyancy force which propels the diapir through it. Ascent velocity is described by the expressionU∞= 2Δρgd3Z/μ0R, where Δρ is the density contrast between diapir and country rock, g is gravitational acceleration,dis the deformation zone width,Zis a parameter which describes the increase in viscosity across the zone, μ0is the country rock viscosity at the contact, andRis the diapir radius. The width of the deformation zone, as dictated by the temperature distribution and rheological function, is the point at which the viscosity increases by a factorFfrom the contact value. Although ascent rates vary with choice of this parameter, ascent distances are not strongly dependent onF.Results of simulations which incorporate a spectrum of input parameters reveal that ascent distance is strongly dependent on both the rheology and ambient temperature of the encompassing rock, but only weakly dependent on the initial diapir temperature. Ascent velocity varies with the diapir size, with larger bodies moving more slowly and ascending for longer periods relative to smaller plutons. As a result of the proportionately larger amount of thermal energy available for ascent, larger bodies will rise greater distances than smaller diapirs. However, the additional ascent appears nominal relative to the contrast in available energy. Modeling diapirs using a no‐slip boundary condition decreases ascent velocity by a factor of about 3 relative to results incorporating a stress‐free boundary condition. The time scale of granitoid diapirism over crustal distances cannot be less than 104years, due to the rate limiting effect of thermal conduction above the body, and not greater than ∼105years, reflecting solidification times of kilometer‐sized plutons. A consequence of ascent by a deformation zone mechanism is the generation, following emplacement, of a mechanically weakened crust which extends from beneath the diapir to near the source, perhaps explaining the relatively common occurrence of synmagmatic to postmagmatic mafic dikes within granites believed to be derived from interaction of basalt with the lower crust.