Calculating splitting parameters for plume-type anisotropic structures of the upper mantle

We apply a forward-propagator method to calculate shear wave splitting para meters for general (3-D) weakly anisotropic upper mantle structures. The ap proach is valid under the assumption that the ray paths of the two quasi-sh ear (qS) waves can be approximated by a common reference ray within an isot ropic background medium. Along the reference ray the incremental splitting is expressed in terms of qS polarizations and slownesses in the direction o f propagation. Using a ray theory ansatz, we show that the resulting shear wave seismogram is equivalent to the coupling ray theory of Coates & Chapma n (1990) under the assumption of smoothly varying anisotropy. Here, we use the forward-propagator method to calculate apparent shear wave splitting pa rameters that can be compared directly with observations of teleseismic she ar wave splitting. A comparison with finite difference calculations is used to assess the validity of the method. As an application we consider shear wave splitting due to a plume-type anisotropic upper mantle structure. The anisotropy is assumed to result from the preferred alignment of orthorhombi c olivine. We show examples of waveforms and splitting parameters as functi ons of backazimuth and angle of incidence. Anisotropic effects for SKS are weak at stations near the central upwelling due to the combined effects of initial polarization and olivine a-axis orientation. Here, the splitting pa rameters are irregular and fast-axis directions may vary by up to 70 degree s depending on the vertical incidence angle. At larger distances splitting parameters slowly converge towards Values expected for homogeneous media. T he results suggest that direct evidence for mantle plumes from shear wave s plitting is more likely to come from (OBS) stations at some distance away f rom the central upwelling. At shallower incidence, the apparent splitting p arameters for S exhibit a 90 degrees periodicity as functions of the initia l polarization of the incident shear wave, provided that the ray path is ke pt fixed. Our results show that this is a general characteristic of shear w ave splitting in inhomogeneous anisotropic media. The effect can be used to identify complex anisotropic regions within the Earth's mantle.