Introduction

Seismic data acquired in areas with irregular topography introduce a numerical problem for migration algorithms that are based on depth extrapolation. Since numerically efficient migration schemes start on a flat interface, wave equation datuming is required prior to the migration. An accurate solution to the problem of varying elevation is to propagate the wavefield from the recording surface to a specified flat datum using wave equation datuming (Berryhill, 1979). Wave-equation datuming (Berryhill, 1979, 1984) has several applications in seismic data processing -horizon flattening, layer replacement, and forward modeling- which can be performed on either unstacked or stacked data. The computationally expensive datuming procedure is often replaced by a simple time shift for the elevation to datum correction. This simple time shift, or elevation static correction, cannot properly reposition wide angle or steeply dipping reflections.

A simple technique to correct for the error caused by the static time shift was introduced by the ``zero velocity layer'' concept (Beasley and Lynn, 1989). This technique, however, cannot even be applied to the computationally attractive phase-shift algorithms, because it includes the nonphysical characteristic of zero velocity.

This paper presents phase-shift datuming and migration techniques for data acquired on any irregular surface.