Anisotropy and P-wave tomography: A new approach for inverting teleseismic data from a dense array of stations

A new formulation is given for inverting teleseismic P-wave residuals in terms of both 3-D variations of seismic velocity and anisotropy of the subcrustal lithosphere. Two restrictive assumptions are made on the anisotropic elastic tensor to reduce the number of model parameters. First, the upper-mantle anisotropy is modelled by a preferred orientation of olivine crystals with b- and c-axes randomly distributed around the a-axis, and second, the elastic properties of polycrystalline aggregates are computed according to the Voigt averaging rule. The latter assumption allows us to link linearly the observed P-wave residuals to the proportion of oriented crystals in a realistic polycrystalline assemblage. In the inversion process, the orientation of the symmetry axis is fixed, either by a trial procedure or by using a priori hypotheses from independent data. A linear inversion scheme is then applied to the data to retrieve the 3-D variations of two scalar parameters giving the isotropic velocity perturbation and the amount of anisotropy. The inversion algorithm is tested for different source-receiver configurations. Using several idealistic ray geometries, it is concluded that the teleseismic P-wave residuals could potentially carry enough information for retrieving both the 3-D isotropic velocity variations and the amount of anisotropy. However, from a more practical point of view, by looking at the distributions of rays for two recent tomographic experiments in the southern Rhine Graben area and in the Pyrenees, it is concluded that the distributions of rays in these experiments do not fulfil the necessary requirements for retrieving reliable information about the lithospheric anisotropy. Additional data are thus needed to constrain the anisotropic model. If the symmetry axis is set as horizontal, the inversion of the P-wave residual of the Pyrenees leads to an east-west fast P-wave velocity orientation. The resulting anisotropy is compatible with SKS observations made in the Pyrenees. Whatever the anisotropy is, the numerical tests performed with the actual ray configurations show the robustness of the isotropic components in the inverted model. A long-wavelength anisotropy in the lithosphere, if present, should not drastically alter the isotropic 3-D velocity distributions that are obtained from classical methods of teleseismic tomography.