Conventional time migration of seismic data results in the incorrect positioning of reflectors where there are significant lateral variations in the velocity of the overburden. In such situations the basic migration procedure should use the provided velocity information and obey the wave equation with adequate accuracy to produce a cross-sectional representation of the reflectors in true depth.

A method involving finite-difference approximations to the wave equation has been implemented for obtaining migrated depth sections. The initial seismic data have the properties of an upcoming wavefield recorded at the earth's surface. This is projected downward in small increments of depth, making appropriate corrections for the transmission of the seismic waves through the assumed velocity variations within the layer. Thus, at an intermediate stage of processing, the data consist of an imaged depth section above the depth Z, followed by "conventional" unmigrated seismic data associated with shooting and recording at depth Z.

This depth-migration procedure applies to both two- and three-dimensional common depth point stacked data, where it is expected to be particularly important for oil field development projects. The method has also been developed for application to conventional unstacked two-dimensional data which have been recorded on a uniform grid with a shot at each receiving group. Although this latter mode becomes relatively expensive, it does offer the possibility of improved detailing of zones of exploration interest overlain by complex geology with rapid lateral velocity variations. The method also can be reversed to yield synthetic seismic data consistent with a given geologic model.

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