The influence of microstructure on seismic wave speed anisotropy in the crust: computational analysis of quartz-muscovite rocks

P>We study the influence of microstructural variables on seismic wave speed anisotropy in crustal rocks. The bulk elastic properties and corresponding wave velocities are calculated for synthetic rock samples with varying amounts of muscovite and quartz, different muscovite and quartz grain orientations and varying spatial distributions of the muscovite grains to investigate the sensitivity of seismic wave speed anisotropy on these characteristics. The asymptotic expansion homogenization method combined with finite element modelling is used to calculate bulk stiffness tensors for representative rock volumes and the wave velocities are obtained from these tensors using the Christoffel equation. The aim of this paper is to (1) demonstrate how wave speeds computed from the rigorous asymptotic expansion homogenization method compare with those generated using stiffness tensors derived from commonly applied analytic estimates, and (2) explore how different microstructural variables influence seismic wave speeds. Our results show that the muscovite grain orientations have a significant influence on the wave speeds. Increasing the modal fraction and alignment of muscovite grains leads to greater seismic anisotropy of the rock. The P-wave speed at an incidence angle of 45 degrees between the foliation and seismic wave path is dependent on all tested microstructural variables, with the orientation distribution of muscovite grains having the largest effect. This so-called P45 effect is an important measure of wave speed anisotropy and here we provide the first analysis of its sensitivity to microstructural variables. Although we have explicitly considered only muscovite grains in this study, the methodology and observations are expected to apply in general to other phyllosilicates.