Inferring the Crystal Orientation Fabrics of Olivine from Oblique Seismic Data using a Spectral Fabric Representation

Olivine, the most abundant mineral in the Earth's upper mantle, affects seismic wave propagation through its crystallographic preferred orientation (CPO) developed during deformation. As a result, the seismic anisotropy of the crystals serves as a crucial tool for constraining large-scale geodynamic models, linking seismic observations to mantle flow processes via the orientation of olivine crystals.

Building on this link, we propose an optimization problem for inferring the crystal orientation fabrics of upper mantle olivine using oblique seismic data by adapting a method from ultrasound tomography, previously used to infer orientation fabrics of polycrystalline ice. The method relies on (i) a harmonic expansion of the grain orientation distribution function (unknown to be inferred), (ii) a fourth-order closure approximation of the distribution function (reducing the dimensionality of the problem), and (iii) a simple strain homogenization scheme (Voigt homogenization) over elastically orthotropic grains. We construct a one- and two-layer homogeneous slab model of olivine to demonstrate the feasibility of our method in idealized settings and discuss potential applications to regions where sufficient seismic data might exist for real-world application. We also discuss the limitations of our method and the caveats of the assumptions made, in particular the assumed orientation fabric symmetries assumed (hence the assumed mantle flow regime) and the well-posedness of our cost function approach.