Investigating anisotropy and inhomogeneity using tomographic inversion of VSP traveltimes: validation of analytic expressions for linearly inhomogeneous elliptically anisotropic models

Tomographic inversions of zero-offset and walkaway VSP data were performed using an analytical traveltime expression for a linearly inhomogeneous elliptically anisotropic model. Both isotropic and anisotropic conditions were investigated by forward and inverse modelling. It was realized that to accommodate long offsets, i.e., beyond the turning-ray offset, the analytic equation for traveltime needed to be reformulated so that only single-valued functions were obtained with offset. -- A practical aspect of determining the elliptical anisotropy parameter, X, is in applying it in the expression for the curve that distinguishes between the downgoing and upgoing arrivals or 'turning points'. This has importance in the planning and designing of surveys, in that appropriate depths for receiver and source placements can be predetermined, with a reasonable estimation of inhomogeneity and anisotropy, to avoid acquiring data that would not be useful. -- Extensively applying the algorithm to a large volume of real and synthetic data is an indication of the robustness of the methodology.