P-SH Conversions in Layered Media with Hexagonally Symmetric Anisotropy: A CookBook

Abstract

—Reflectivity synthetic seismograms demonstrate that the type, layering and orientation of 1-D anisotropy influences strongly the coda of teleseismic P waves at periods T > 1 sec, particularly P-SH converted waves. We assume the simplest form of anisotropy described by an elastic tensor with a symmetry axis ŵ of arbitrary orientation. The resulting phase velocities vary as cos 2ξ with respect to that axis. Using three families of simple crustal models, we compare the effects of an anisotropic surface layer with reverberations caused by both "thick" and "thin" layers of anisotropy at depth. If anisotropy in the surface layer is significant, the polarization of direct P can be distorted to generate a transverse component, followed by Ps and a prominent shear reverberation converted from direct P at the free surface. If the anisotropic layer is buried, the first, and often the most prominent, arrival on the transverse component is the P-to-SH conversion at its upper surface. If the anisotropic layer is sufficiently thin, P-to-SH conversions from its boundaries interfere to form a derivative pulse shape on the transverse component, which could be mistaken as the signature of shear-wave splitting. If ŵ is horizontal, compressional (P) and shear (S) anisotropy both produce similar waveform perturbations with four-lobed azimuthal patterns, suggesting that a weighted stack of P coda from different back-azimuths would improve signal-to-noise. For ŵ tilted between the horizontal and vertical, however, the effects of P- and S-anisotropy differ greatly. The influence of P-anisotropy on P-to-S conversion is greatest for a symmetry axis tilted at 45° to the vertical, where its azimuthal pattern has two lobes, rather than four. Combinations of P- and S-anisotropy typically lead to a composite azimuthal dependence in the P-coda reverberations.