Time migration algorithms have the disadvantage of erroneously handling
lateral velocity variations, even if the correct velocity is provided (Hatton *et al.*, 1981).
Additionally, algorithms based on the one-way wave equation cannot
handle steep dips correctly. Depth migration seems to be
the answer to time migration weaknesses. This explains why it is
necessary to develop depth migration algorithms. Li (1986),
presents a theoretical model that he calls Linearly Transformed
Wave Equation (LITWEQ) to do migration in lateraly varying media.
However, it was only implemented
for vertical velocity variations.

I propose a numerical method which allows us to incorporate lateral velocity variations. The method discretizes completely the LITWEQ operator. This discretization is performed with a nine point star pattern finite difference scheme. The circular shape of the impulse response shows the capability of this algorithm to migrate events with arbitrary angle of inclination. Further tests are necessary to show the stability of the scheme in the presence of strong lateral velocity variations.

11/17/1997