ABSTRACT
A mathematical model for granitoid diapirism has been developed that accounts for the time dependent thermal and rheological conditions encountered by the intruding body. This model is derived by the simultaneous solution of the partial differential equations of energy, continuity, and momentum utilizing scaling analysis. The underlying assumption is that deformation of the surrounding country rock is confined to a relatively thin layer with a temperature dependent Newtonian viscosity. When the country rock is modeled as a power-law fluid, the effective viscosity is dependent upon temperature and shear strain rate.
This model allows for realistic temperature gradients within the crust and variable shear strain rates. This is made possible through use of a numerical approximation referred to as the "snapshot" approach. This method allows the pluton to ascend in finite time increments while the boundary conditions remain fixed. Following each snapshot, the ascent velocity is calculated and new boundary and initial conditions are set for the next increment of time.
Several model runs have been performed using a FORTRAN program. The results exhibit time dependent variations in the ascent velocity due to corresponding changes in the overall rheology, and thickness, of the deformation layer. One of the conclusions from this study is that larger plutons ascend at slower rates, but emplace higher in the crust due to the additional energy available relative to smaller plutons.

Mahon, K.I., 1985. A numerical approach for determining the variable ascent velocity of a granitoid diapir.  Unpublished MSc. thesis, State University of New York at Albany. 158 pp., +ix
University at Albany Science Library call number:  SCIENCE Oversize (*) QE 40 Z899 1985 M35

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