Initial Publication Date: June 15, 2022

Deducing Deformation from Quartz Crystallographic Preferred Orientation Data

Joshua Davis, Carleton College
Matty Mookerjee, Sonoma State University
Wasin Meesena, Carleton College


We describe a novel method for deducing deformation from quartz crystallographic preferred orientation (CPO) textures in deformed rocks. Unlike methods commonly in use, our method makes few assumptions about the macroscopic kinematics of the deformation. In our approach, a CPO texture is binned in orientation space to produce a vector of real numbers. We assume that the orientations were uniformly random before deformation, and that the texture developed according to the Taylor-Bishop-Hill theory. Under any hypothesized deformation, the CPO vector approximately follows a multivariate normal distribution, which implies a certain likelihood function. By maximizing the likelihood, we obtain a best-fit deformation for the CPO texture.

We describe a series of numerical experiments on synthetic CPO data sets from transpressional shear zones. The accuracy of the maximum likelihood estimates improves as the sample size and deformation intensity increase. Shear zone geometry and calculational details have only a small effect on accuracy. The experiments also explore how accuracy improves with greater knowledge of the critical resolved shear stresses on the quartz slip systems.


Session 2: Rheology of the Lithosphere