Azimuthal anisotropy in the upper mantle from observations ofP-to-Sconverted phases: application to southeast Australia

Wave propagation in heterogeneous media depends on the relative scales of the wavelength and the spatial correlation length of the heterogeneities. Heterogeneities can give rise to velocity dispersion due to the fast path effect. Short wavelengths tend to diffract around the slower inhomogeneities, causing the arrival times to be biased towards lower values than the arrival times for the average slowness of the medium. The difference between the high-frequency, short-wavelength velocity obtained from the mean arrival time and the mean velocity of the heterogeneous medium is known as the velocity shift. The velocity shift depends on the spatial autocorrelation function of the heterogeneous random medium. Previous investigations of velocity shift in heterogeneous media have mostly been limited to media with isotropic spatial correlation functions. We extend the analysis to media with anisotropic distributions of spatial inhomogeneities. A smallperturbation, asymptotic geometrical optics formulation is used to derive expressions for the first and second moments of the phase of a wavefield propagating in a random heterogeneous medium. This allows us to express the velocity shift as a function of angle between direction of propagation and direction of maximum spatial correlation. We show how anisotropic spatial heterogeneity can cause a splitting of the isotropic velocity-shift behaviour. The velocities become much faster along the direction of high spatial correlation, but are slower along the perpendicular direction.