EAR-PF: Advanced statistical analysis to relate microstructural fabrics and finite strain in ductilely deformed rocks

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Dr. Alexander Lusk has been granted an NSF EAR Postdoctoral Fellowship to carry out research and education plans at the University of Wisconsin Madison. Geologists characterize how rocks deform by measuring a quantity called finite strain. Finite strain is conceptualized in three dimensions as an ellipsoid. When rocks are not deformed, the 3-D object is a sphere; with increasing deformation, it becomes more elliptical. However, most deformed rocks do not have any large-scale indicators that record finite strain. As a result, geologists make microscope slides of rocks to study microscopic features called microstructures. The goals of Dr. Lusk’s project are two-fold: (1) to provide methods of characterizing finite strain uncertainty (i.e. error bars) in three dimensions to better understand rock deformation, and (2) to provide geologists with methods to relate rock microstructures developed in quartz (a common crustal rock constituent) to the finite strain experienced during deformation. To characterize finite strain, Dr. Lusk will apply statistical methods to rocks that contain quartz pebbles, which preserve a direct record of finite strain. During his postdoctoral fellowship, Dr. Lusk will carry out an education plan involving the following: (1) development of an undergraduate level, exploration based virtual education module that will aim to make students comfortable with measuring and interpreting finite strain in the field; (2) development of software for the statistical analysis of finite strain, integrated in the StraboSpot field app; (3) mentoring of two UW-Madison students in undergraduate research projects. This project aims to evaluate the response of rock microstructure developed in ductile quartz-rich rocks to the finite strain magnitude, geometry, and strain path in which deformation occurred. The proposed approach differs from previous work in that it applies multivariate statistical methods to quantitatively characterize ellipsoidal finite strain data – with a measure of uncertainty – for the first time. The key to statistical analysis of ellipsoids is that orientations and magnitudes, while independent measurements, must be combined and transformed into an ellipsoid tensor; in tensor form, multivariate statistical analysis can be applied. The project will be carried out by analyzing finite strain and rock microstructure in the ductile Bygdin (Norway) and Funzie (Scotland) quartz-rich metaconglomerates. Finite strain will be determined at the outcrop scale by measuring clast orientation and all three ellipsoid axes to constrain clast shape. At the grain scale, two measures of finite strain will be determined: (1) the grain shape and shape preferred orientation of relict metamorphic grains, and (2) the spatial relationship of relict metamorphic grain center points. Electron backscatter diffraction will be used for microstructural characterization, including measurement of grain shape, crystallographic vorticity axis orientation, and crystallographic preferred orientation. By relating statistical measures of finite strain directly to rock microstructural fabrics, Dr. Lusk aims to improve our current understanding of how finite strain and strain history is preserved in the microstructural record and to provide structural geologists with methods to infer strain history without a direct measurement of finite strain.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.