f Steep dip wave equation migration by the finite difference plus phase shift hybrid method

Two vital requirements of a practical migration scheme are that it should be able to accommodate velocity variations and that it should have no dip limitation. The finite differente method for seismic migration has been known for many years, and remains popular since it caters well for the first of these requirements. However, the low order approximations, usually known as the 15 degree and 45 degree equations, are dip limited and do not preserve steeply dieping events. The dip response can be improved by using higher order approximations to the wave equation; for example, Ma (1982) showed how a factorization of the continued fraction expansion could be combined with a splitting techniquè to obtain steep dip solutions. These higher order methods may be computationally inefficient, however, due to the number of iterative stages that make up a single step of wavefield extrapolation . Other techniques exist which aim for better dip handling capability. These include the explicit formulations developed by Harris (1979), Koehler (Sengbush, 1983), Beaumont et al. (1987) and Holberg (1988). They take the foren of convolutional operators and are usually table driven since the operator is velocity dependent. The accuracy of the result will depend on the length of the operator, but of course longer operators will be more expensive to use.