  Multi-azimuth walkaway vertical seismic profiling (VSP) is an established
technique for the estimation of in situ slowness surfaces and inferring
anisotropy parameters. Normally, this the technique requires the assumption of
lateral homogeneity, which makes the horizontal slowness components at depths
of downhole receivers equal to those measured at the surface. Any violations of
this assumption, such as lateral heterogeneity or a nonzero dip of intermediate
interfaces, lead to distortions in reconstructed slowness surfaces and,
consequently, to errors in estimated anisotropic parameters. Here, we relax the
assumption of lateral homogeneity and discuss how to correct VSP data for weak,
lateral heterogeneity (LH). We describe a procedure of downward continuation of
recorded travel times that accounts for the presence of both vertical
inhomogeneity and weak lateral heterogeneity, which produces correct slowness
surfaces at depths of downhole receivers. Once the slowness surfaces are found
and the desired type of anisotropic model to be inverted is selected, the
corresponding anisotropic parameters, providing the best fit to the estimated
slowness can be obtained. We invert the slowness surfaces of $P$-waves for
parameters of the simplest anisotropic model describing dipping fractures --
transversely isotropic medium with a tilted symmetry axis. Five parameters of
this model -- the $P$-wave velocity $V_0$ in the direction of the symmetry
axis, Thomsen's anisotropic coefficients $\epsilon$ and $\delta$, the tilt
$\nu$, and the azimuth $\beta$ of the symmetry axis can be estimated in a
stable manner when maximum source offset is greater than half of the receiver
depth.
