The magnitudes, orientations and spatial distributions of elastic anisotropy in Earth?s crust and mantle carry valuable information about gradients in thermal, mechanical and kinematic parameters arising from mantle convection, mantle-crust coupling and tectonic plate interactions. Relating seismic signals to deformation regimes requires knowledge of the elastic signatures (bulk stiffnesses) of different microstructures that characterize specific deformation environments, but the influence of microstructural heterogeneity on bulk stiffness has not been comprehensively evaluated. The objectives of this project are to: (1) scale up a preliminary method to determine the bulk stiffness of rocks using integrated analytical (electron backscatter diffraction) and computational (asymptotic expansion homogenization) approaches that fully account for the grain-scale elastic interactions among the different minerals in the sample; (2) apply this integrated framework to investigate the effect on elastic anisotropy of several common crustal microstructures; (3) integrate time-dependent microstructure modeling with bulk stiffness calculations to investigate the effects of strain- and process-dependent microstructure evolution on elastic anisotropy in mantle rocks; and (4) disseminate open-source software for the calculation of bulk stiffnesses from electron backscatter diffraction data and creation of synthetic (computer generated) microstructures that can be used in sensitivity analyses among other applications. Because commonly used methods, such as the Voigt, Reuss and Voigt-Reuss-Hill averages, for calculating bulk rock stiffnesses do not account for elastic interactions among the constituent minerals, they exhibit marked, non-systematic differences from stiffnesses obtained using asymptotic expansion homogenization.
These objectives are important because the results would substantially improve understanding of the nature of seismic anisotropy in the Earth's crust, which is composed of rocks dominated by low symmetry minerals with complex structures. Traditional methods for performing these calculations do not easily incorporate these effects. This project will develop an elegant, easily-implemented alternative method for anisotropic materials. The scientific results and computational tools that result from this project will have global application across a number of solid Earth and engineering disciplines. Open-source codes developed in this project will made available through existing open-source ELLE platform. Classroom exercises developed for Earth Science and Mechanical Engineering courses that employ this software will be make available to the community, probably through the Science Education Resource Center website at Carleton College.