Accurate estimation of the interval velocity and its lateral variations is one of the most problematic steps in seismic data processing. In conventional seismic processing, the interval velocity model is derived from the stacking velocities, which are determined by measuring the coherency of the reflections along hyperbolic trajectories. Hubral et al. 1980 have shown that this method is an approximation which is only valid for horizontally stratified media and slight variations in lateral velocity.

A common approach to obtaining a velocity model varying horizontally and
vertically, *V*(*x*,*z*), is reflection tomography, based on traveltime
inversion. Many variations on reflection tomography have been tested in
recent years. They usually differ in the choice and parametrization of
the data and the model space. Toldi 1985 presented a
method for inverting stacking velocities. Landa et al.
1988 proposed to produce a velocity depth model
that maximizes some measure of the coherency computed along traveltime
curves. Harlan 1989
compared estimated traveltime with that of picked horizons but he does not
allow for strong velocity gradients. Van Trier 1990
and Etgen 1990 used residual migration to determine
interval velocities. Biondi used beam stacking in
conjunction with prestack migration in iterative inversion schemes to estimate
the velocity model. Reflection tomography is an expensive process that is not
currently used on 3-D data.

One of the most difficult problems facing the seismic processing industry is how to incorporate additional sources of information such as well logs and geologic models into seismic imaging Toldi (1995); Versteeg and Symes (1994). Several studies have shown that a strict layering approach does not describe the velocity structure adequately, but does provide a starting point Hanson and Whitney (1995).

11/12/1997