USING DEFORMABLE CLASTS TO CONSTRAIN ROCK DEFORMATION: AN EXAMPLE FROM THE GEM LAKE SHEAR ZONE

The dynamic theory of deformable ellipsoidal inclusions in viscous flows was worked out by Eshelby (1957, 1959) and further developed and applied by various authors. We describe a new method for computing Eshelby's dynamics, which relies on differential-geometric techniques on a Lie group. The advantages of our method over previous techniques include preservation of geometric properties of the ellipsoids (e.g. volume), computational speed, and high precision.

We apply our new method to naturally deformed rocks from the Gem Lake shear zone, a 1 km wide mylonite zone exposed in the Ritter Range pendant of the Sierra Nevada arc. Deformed rocks within the shear zone include both a volcaniclastic conglomerate and a lithic-lapilli tuff. Horsman et al. (2008) collected three-dimensional finite strain data for felsic, intermediate, and quartz-rich clasts, both inside and outside the shear zone.

Our kinematic model quantifies deformation in the shear zone by solving for the best-fit deformation that takes the undeformed clasts to the deformed clasts. We test commonly-used shear zone geometries such as monoclinic and triclinic transpression, solving for the magnitude of shortening perpendicular to the zone (generally ~25%), the angle of convergence across the zone (5˚-10˚), and the viscosity ratios among the rock types (3-10). The felsic and quartz-rich clasts are more competent than the intermediate-composition clasts, and the clast-rich tuff is more competent than the volcanoclastic conglomerate. Our results largely agree with a previous deformation model from Horsman et al. (2008), whose method relied on a different set of field data at a more regional scale of observation. They are also consistent with field observations of clast deformation and the effective viscosities from numerous other studies. In summary, our method for computing deformable ellipsoids facilitates the exploration of a wide range of kinematic models.