Stochastic analysis of shear-wave splitting length scales

The coherence of azimuthal seismic anisotropy, as inferred from shear-wave splitting measurements, decreases with the relative distance between stations. Stochastic models of a two-dimensional vector field defined by a von Karma'n [T. von Karma'n, Progress in the statistical theory of turbulence, J. Mar. Res., 7 (1948) 252–264.] autocorrelation function with horizontal correlation length L provide a useful means to evaluate this heterogeneity and coherence lengths. We use the compilation of SKS splitting measurements by Fouch [M. Fouch, Upper mantle anisotropy database, accessed in 06/2006, http://geophysics.asu.edu/anisotropy/upper/] and supplement it with additional studies, including automated measurements by Evans et al. [Evans, M.S., Kendall, J.-M., Willemann, R.J., 2006. Automated SKS splitting and upper-mantle anisotropy beneath Canadian seismic stations, Geophys. J. Int. 165, 931–942, Evans, M.S., Kendall, J.-M., Willemann, R.J. Automated splitting project database, Online at http://www.isc.ac.uk/SKS/, accessed 02/2006]. The correlation lengths of this dataset depend on the geologic setting in the continental regions: in young Phanerozoic orogens and magmatic zones L ∼ 600 km, smaller than the smooth L ∼ 1600 km patterns in tectonically more stable regions such as Phanerozoic platforms. Our interpretation is that the relatively large coherence underneath older crust reflects large-scale tectonic processes (e.g. continent–continent collisions) that are frozen into the tectosphere. In younger continental regions, smaller scale flow (e.g. slab anomaly induced) may predominantly affect anisotropy. In this view, remnant anisotropy is dominant in the old continents and deformation-induced anisotropy caused by recent asthenospheric flow is dominant in active continental regions and underneath oceanic plates. Auxiliary analysis of surface-wave anisotropy and combined mantle flow and anisotropic texture modeling is consistent with this suggestion. In continental regions, the further exploration of a stochastic description of seismic anisotropy may form a useful counterpart to deterministic forward modeling, particularly if we wish to understand the origin of discrepancies in heterogeneity estimates based on different seismological data sets.