Wave‐equation datuming before stack

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.