  We consider an anisotropic inhomogeneous model to simulate measured
vertical-seismic-profile traveltimes. In this model, we assume that velocity
increases linearly with depth and anisotropy is the result of elliptical
velocity dependence. Using a series of sources in a line to a single receiver,
we minimize the least-squares residual between measured and modelled
traveltimes to estimate the anisotropy and inhomogeneity parameters of the
subsurface. To verify the approach, we construct synthetic traveltime data for
a one- and two-layer model and perform the traveltime inversion. We justify the
convergence-ensuring specifications and model-parameter restrictions that are
intrinsic to the parameter estimation. To determine the approach's
practicality, we assess the reliability of results under the influence of
noise. From this assessment, we discern the noise threshold for both models and
determine that the noise restriction is severely restrictive for increasing
model complexity. We estimate parameters, using the same methodology, for a
real-data case and conclude with a discussion of results.
