  A two-point ray-tracing technique for 3D smoothly heterogeneous, weakly
transversely-isotropic media is based on Fermat's principle and takes advantage
of global Chebyshev approximation of both the model and curved rays. This
approximation gives explicit derivatives of traveltimes with respect to ray
parameters and allows one to use the rapidly converging conjugate gradient
method to compute traveltimes. The method is fast because, for smoothly
heterogeneous media, approximation of rays by only a few polynomials and a few
conjugate gradient iterations provide excellent precision of traveltime
calculation.
