On the interpretation of SKS splitting measurements in the presence of several layers of anisotropy

S U M M A R Y Concerns over the validity of expressions derived by Montagner et al. that link SKS splitting measurements to the variation with depth of anisotropic parameters in the upper mantle have been recently expressed, pointing out that the long period approximations applied by these authors may not be valid for the frequency range commonly used in SKS studies, and in particular, that the anisotropy splitting parameters should depend on the order in which different anisotropy layers are arranged with depth. We show here that indeed, measurements of splitting time and fast axis direction performed at individual azimuths do depend on the order of layering, however, the expressions of Montagner et al. concern station-averaged quantities that do not depend on the order of layers. It is therefore correct to use these expressions in joint inversions of surface waveforms and SKS station-averaged splitting measurements. On the other hand, the depth-dependent sensitivity of surface waveforms naturally provides constraints on the order of layering. Having clarified this confusion, we extend the expressions of Montagner et al. to the case of a tilted axis of symmetry and non-vertical incident waves, and show that station-averaged estimates of ‘effective’ splitting parameters: splitting time, fast axis direction and tilt of the fast axis, can be related to the integral with depth of quantities, which now depend not only on the local splitting time and fast axis direction, but also on the local tilt of the fast axis, thus providing constraints also on the variation of the tilt with depth. We show that the effective parameters used as constraints in the inversion can be obtained either from the measurement of splitting intensity, or through a parameter search and cross-convolution method. In particular, in the case when the effective tilt is significant, the splitting intensity no longer presents 180◦ periodicity with azimuth, providing a diagnostic tool for the presence of such tilts in the upper mantle. Thus, combining body-wave and surface wave observations also has the potential of constraining the variation with depth of the tilt of the fast axis of anisotropy, a geodynamically important parameter.