EFFICIENT DESIGN OF DIGITAL-FILTERS FOR 2-D AND 3-D DEPTH MIGRATION

Two- and three-dimensional (2-D and 3-D) depth migration can be perfor med using 1-D and 2-D extrapolation digital filters, respectively. The depth extrapolation is done, one frequency at a time, by convolving t he seismic wavefield with a complex-valued, frequency- and velocity-de pendent, digital filter. This process requires the design of a complet e set of extrapolation filters: one filter for each possible frequency -velocity pair. Instead of independently designing the frequency- and velocity-dependent filters, an efficient procedure is introduced for d esigning a complete set of 1-D and 2-D extrapolation filters using tra nsformations. The problem of designing a desired set of migration filt ers is thus reduced to the design of a single 1-D filter, which is the n mapped to produce all the desired 1-D or 2-D migration filters. The new design procedure has the additional advantage that both the 1-D an d 2-D migration filters can be realized efficiently and need not have their coefficients precomputed or tabulated.