A new, statistically reliable method for shear wave splitting

Shear wave splitting, which measures the effects of elastic anisotropy, has proven to be an excellent technique for constraining the strain history of the lithosphere. However, the two most commonly used methods for measuring shear wave splitting both suffer from limitations. The widely-used Silver and Chan [1991] method is not easily adaptable to complex anisotropic scenarios without significant assumptions, and has been shown to underestimate uncertainties [e.g. Walsh et al., 2013]. The cross-convolution method by Menke and Levin [2003] can analyze more complex anisotropy, but there is no clear way to assess uncertainties. Without true uncertainties, one cannot conduct formal hypothesis testing. Moreover, in an Earth with complex lithospheric and asthenospheric strain histories, having a method to correctly combine multiple observations to improve resolution of layered structure is essential. We propose a statistical augmentation to the cross-convolution approach. In our method, correlation structures of the noise are accounted for to create a log-likelihood surface of the splitting parameters that provides the statistical context for formal hypothesis testing of anisotropy. The method has been benchmarked using synthetics along with data from the Pasadena, California seismic station (PAS) and the results have been sensible and consistent with previous studies [e.g. Liu et al., 1995]. The current method has been developed for a single-layer approach, but the path is clear for analyses of anisotropy for multiple and dipping layer models. References:Liu, H., P. M. Davis, and S. Gao (1995), SKS splitting beneath southern California, Geophys. Res. Lett., 22(7), 767, doi:10.1029/95GL00487. Menke, W., and V. Levin (2003), The cross-convolution method for interpreting SKS splitting observations, with application to one and two-layer anisotropic earth models, Geophys. J. Int., 154(2), 379-392, doi:10.1046/j.1365-246X.2003.01937.x. Silver, P. G., and W. W. Chan (1991), Shear Wave Splitting and Sub continental Mantle Deformation, J. Geophys. Res., 96, 429-454, doi:10.1029/91JB00899. Walsh, E., R. Arnold, and M. K. Savage (2013), Silver and Chan revisited, J. Geophys. Res. Solid Earth, 118(September), 5500-5515, doi:10.1002/jgrb.50386.