  Numerical issues for the 3D travel time tomography problem with
non-overdetemined data are considered. Truncated Fourier series with respect to
a special orthonormal basis of functions depending on the source position is
used. In addition, truncated trigonometric Fourier series with respect to two
out of three spatial variables is used. First, the Lipschitz stability estimate
is obtained. Next, a globally convergent numerical method is constructed using
a Carleman estimate for an integral operator.
