Plane-wave depth migration

We present fast and efficient plane-wave migration methods for densely sampled seismic data in both the source and receiver domains. The methods are based on slant stacking over both shot and receiver positions (or offsets) for all the recorded data. If the data-acquisition geometry permits, both inline and crossline source and receiver positions can be incorporated into a multidimensional phase-velocity space, which is regular even for randomly positioned input data. By noting the maximum time dips present in the shot and receiver gathers and constant-offset sections, the number of plane waves required can be estimated, and this generally results in a reduction of the data volume used for migration. The required traveltime computations for depth imaging are independent for each particular plane-wave component. It thus can be used for either the source or the receiver plane waves during extrapolation in phase space, reducing considerably the computational burden. Since only vertical delay times are required, many traveltime techniques can be employed, and the problems with multipathing and first arrivals are either reduced or eliminated. Further, the plane-wave integrals can be pruned to concentrate the image on selected targets. In this way, the computation time can be further reduced, and the technique lends itself naturally to a velocity-modeling scheme where, for example, horizontal and then steeply dipping events are gradually introduced into the velocity analysis. The migration method also lends itself to imaging in anisotropic media because phase space is the natural domain for such an analysis.