Review of the methodology for the inversion of surface-wave phase velocities in a slightly anisotropic medium

In this paper, a new inversion scheme for surface-wave velocities in a slightly anisotropic medium will be presented, revisiting the inversion method performed by Corchete and Badal (2004). Tecnociencia 6(2), 23–41). An extension of the Smith–Dahlen formulation will be examined and revised. The surface-wave propagation in a slightly anisotropic medium will be considered, and the inversion of the azimuthal dependence of the surface-wave dispersion will be performed. The new inversion scheme proposed in this paper will be verified by numerical matrix inversion in two examples: hexagonal symmetry and 13 nonzero canonical harmonic components. Also, two additional experiments with observed data will be performed. The new method will be shown as more efficient than the method previously used by Corchete and Badal. This new method should be a useful tool for studying the slightly anisotropic structure of wide areas of the Earth, if sufficient high-quality dispersion data are collected and the isotropic properties of the medium are well known.