Testing observables for teleseismic shear-wave splitting inversions: ambiguities of intensities, parameters, and waveforms

We assess the capabilities of different observables for the inversion of core-refracted shear waves (XKS phases) to uniquely resolve the anisotropic structure of the upper mantle. For this purpose, we perform full-waveform calculations for relatively simple, canonical models of upper-mantle anisotropy. The models are characterized by two and four domains of different anisotropic properties. Specifically, we assume hexagonal symmetry with arbitrarily chosen strength of the anisotropy and orientation of the horizontal fast axis. XKS waveforms, generated from plane-wave initial conditions, traverse through anisotropic models and are recorded at the surface by a single station (in case of vertical variations) and by a dense station profile across the laterally and vertically varying structure. In addition to waveforms, we consider the effects of anisotropic variations on apparent splitting parameters and splitting intensity. The results show that, generally, it is not possible to fully resolve the anisotropic parameters of a given model, even if complete waveforms (under noisefree conditions and for the complete azimuthal range) are considered. This is because waveforms for significantly different anisotropic models can be indistinguishable. However, inversions of both waveforms and apparent splitting parameters lead to similar models that exhibit systematic variations of anisotropic parameters. These characteristics may be exploited to better constrain the inversions. The results also show that splitting intensity holds some significant drawbacks: First, even from measurements over a wide range of back-azimuth, there is no characteristic signature that would indicate depth variations of anisotropy. Secondly, identical azimuthal variations of splitting intensity for different anisotropic structures do not imply that the corresponding split waveforms are also similar. Thus, fitting of observed and calculated splitting intensities could lead to anisotropic models that are incompatible with the observed waveforms. We conclude that (bandlimited) XKS-splitting inversions and related tomographic schemes, even if based on complete waveforms, are not sufficient to fully resolve the heterogeneous anisotropic structures of the upper mantle and that combinations with alternative methods, based on e.g., receiver-function splitting, P-wave travel-time deviations, or surface waves, are required.