Efficient design of digital filters for 2-D and 3-D depth migration

Two-and three-dimensional depth migration can be performed using one-and two-dimensional extrapolation digital lters, respectively. The depth extrapolation is done, one frequency at a time, by convolving the seismic waveeeld with a complex-valued, frequency-and velocity-dependent, digital lter. This process requires the design of a complete set of extrapolation lters, one lter for each possible frequency-velocity pair. Instead of independently designing the frequency-and velocity-dependent lters, an eecient procedure is introduced for designing a complete set of one-and two-dimensional extrapolation lters using transformations. The problem of designing a desired set of migration lters is thus reduced to the design of a single one-dimensional lter which is then mapped to produce all the desired one-or two-dimensional migration lters. The new design procedure has the additional advantage that both the one-and two-dimensional migration lters can be realized eeciently and need not have their coeecients precomputed or tabulated.