The S discrepancy revisited: traveltime shifts in randomly heterogeneous media

It has been known for many years that observed S wave traveltimes are advanced relative to those traveltimes predicted in an elastic Earth model derived from normal mode data. This phenomenon, the so-called S discrepancy, has long been attributed to the anelastic dispersion of the mantle in the frequency range between normal modes and body waves. While this effect is undoubtedly present in the Earth, there is another mechanism by which higher frequency waves are able to travel more rapidly though the Earth. In a 3-D heterogeneous medium, rays preferentially sample higher velocities thus advancing the traveltimes of waves. However, for lower frequency waves, healing effects will act to destroy the corrugations developing in the wavefront. For this reason, a purely elastic but highly heterogeneous medium exhibits dispersion. To determine how much, if any, this dispersion contributes to the magnitude of the S discrepancy, we conduct numerical studies of wave propagation in various randomly heterogeneous media, and use the recorded seismograms to measure velocity shifts at various propagation distances.