Linearized Inverse Scattering of Teleseismic Waves for Anisotropic Crust and Mantle Structure

In recent years, several studies exploiting teleseismic phases have identified small-scale anisotropy within the lower crust and upper mantle with implications for the dynamic evolution of continents. Detailed characterization of this anisotropy is afforded by scattered waves, most notably P-to-S conversions, which have a greater sensitivity to depth than SKS, the phase traditionally used to study mantle anisotropy. As the levels of anisotropy are generally small (<+/- 5 percent), one may obtain useful information from a linearized analysis of the inverse scattering problem about isotropic or anisotropic reference media. We derive linearized reflection/transmission coefficients for anisotropic media in terms of simple properties (group and phase slownesses, reference density and material property perturbations) which can be used to identify those elastic parameter combinations to which a given teleseismic data set is most sensitive. In contrast to purely isotropic 1-D inversions where only one (or, in ideal cases, two) independent parameter combinations can be retrieved using typical data sets, at least 5 parameter combinations can be resolved at comparable levels in generally anisotropic media. The linearized reflection and transmission coefficients can be combined with high-frequency asymptotic Green's functions for slowly varying background media to derive direct 1-D inversion formulae that allow one to recover the variation of these anisotropic parameter combinations as functions of depth. We demonstrate this approach with an examination of anisotropy across the crust-mantle boundary using data from the Canadian National Seismograph Network and discuss implications for continental dynamics.