A synthesis of seismic P and S anisotropy

Upper-mantle seismic anisotropy has been observed using a variety of methods, including S and SKS splitting, P and P-n traveltimes, P polarization anomalies and P to S conversions, and surface waves. Care must be taken when comparing the results from different methods because of bias introduced by depth sensitivity, frequency dependence, and simplifying assumptions concerning the form of anisotropy. We examine the differences and show that some apparent contradictions cited in previous studies can be reconciled using simple models. We perform forward modelling on a suite of anisotropic media, progressing from simple elastic symmetries to tensors obtained from laboratory measurements and numerical strain models. The results provide a systematic overview of the effect of a given anisotropy class and geometry on seismic observables. We simulate the full complement of body wave measurements-SKS and S splitting, P-n traveltimes, teleseismic P traveltimes and teleseismic P particle motion (P-pol )-to show any apparent differences between the phases. We also investigate depth and frequency sensitivity using reflectivity modelling in layered anisotropic media. Our principal findings are as follows. (1) No models, including low-order symmetries and multiple layers, exhibit a mean fast shear wave splitting direction nearly orthogonal to a consistent fast direction determined from P observables. For P delays, the azimuthal cos(2theta) variation is representative of the fast direction of anisotropy (rather than cos(1theta), which has led to a certain amount of confusion in the literature). (2) P times average linearly over the raypath; SKS weights toward the upper part of the model; and P-pol and P-n are even more sensitive to shallow anisotropy. Conclusive evidence in the literature for a disagreement between fast directions from SKS , on one hand, and P-n and P (pol), on the other hand, can be explained by layering. (3) The azimuthal dependence of SKS splitting results does not necessarily indicate layered or laterally heterogeneous anisotropy. The azimuthal dependence of SKS splitting is not observed for hexagonal symmetry with horizontal fast or slow axes, but has to be taken into consideration for dipping hexagonal and any orthorhombic and lower symmetry media. Teleseismic S shows a much stronger azimuthal dependence than SKS and SKKS . This makes procedures that stack splitting results over a wide range of incidence angles or azimuths questionable.