Weak Elastic Anisotropy in Global Seismology
Abstract:Most of the major features of the Earth’s interior were discovered using the concepts of isotropic seismology; however, subtle features require more realistic concepts. Although the importance of anisotropy has been known for over 50 years, only in the last decade has the increasing quality and quantity of data forced the wide recognition that anisotropyis crucial for accurate descriptions of upper mantle structure.
The persistence of the “plume hypothesis”, in spite of abundant evidence to the contrary, is partly based on the neglect of anisotropy, sparse and biased ray coverage, and the misuse of Occam’s razor. Whereas isotropic inversion of teleseismic near-vertical travel-time datasets suggests the presence of deep vertical zones of low velocity (interpreted as mantle plumes), anisotropic inversion of data having a range of polarizations and directions of approach suggests instead shallow zones of relatively high anisotropy. This raises the possibility that current understanding of manyof the subtle features of Earth structure could be erroneous, caused by over-simplified analysis.
The simplest plausible anisotropic model is that of polar anisotropy (“VTI” [sic!]), with a radial symmetry axis. The essential idea which makes anisotropic seismology feasible is the recognition that, in the Earth, the anisotropy is almost invariably weak, and the anisotropic equations (linearized in appropriately chosen small parameters) are quite simple (see below).
These equations show that, to first order, the anisotropic variation of velocity is not governed by the individual Cab , but rather by the combinations of parameters given above. Hence, inversions should seek these combinations, rather than the individual moduli.
The Rayleigh velocity VR is a simple function of VS0 and the P- and SV- anisotropies. The Love velocity VL is a complicated function of VS0 and the SH anisotropy γ.
The simplest plausible model of azimuthal anisotropy is orthorhombic (not (“HTI” [sic!]), which may be analyzed as a simple generalization of the foregoing. Along the two principle azimuths, the velocities are exactly those of two (different) polar anisotropic media, which may be simplified as above. At other azimuths, a 9th (δ-like) parameter is required. The VR-VL discrepancy is best described in these terms.