Abstract

This note describes the extension to unstacked seismic data of a computationally efficient form of the Kirchhoff integral published several years ago. In the previous paper (Berryhill, 1979), a wave-equation procedure was developed to change the datum of a collection of zero-offset seismic traces from one surface of arbitrary shape to another, even when the velocity for wave propagation is not constant. This procedure was designated "wave-equation datuming," and its applications to zero-offset data were shown to include velocity-replacement datum corrections and multilayer forward modeling. Extending this procedure to unstacked data requires no change in the mathematical algorithm. It is necessary only to recognize that operating on a common-source group of seismic traces has the effect of extrapolating the receivers from one datum to another, and that, because of reciprocity, operating on a common-receiver group changes the datum of the sources. Two passes through the data, common-source computations, then common-receiver computations, are required to change the datum of an entire seismic line before stack from one surface to another. Common-source and common-receiver trace groups must take the form of symmetric split spreads if both directions of dip are to be treated equally; reciprocity allows split spreads to be constructed artificially if the data were not actually recorded in the required form.

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