Introduction

Datuming is the process of deriving wavefields at one datum from those at another datum. There is great utility in this process for land static correction (Berryhill, 1979, 1984; Shtivelman and Canning, 1988; Bevc, 1992) and for layer replacement in migration (Berryhill, 1979, 1984; Yilmaz, 1987). There are two ways to do it. One is by simple time shifting along individual traces, as in first-stage land data static correction. The other is by wavefield extrapolation based on the wave equation. Datuming is closely linked to migration; both need to extrapolate the wavefields from one datum to another. Several methods of wavefield extrapolation have been developed for migration, among them, finite-difference methods (Claerbout, 1976, 1985), Kirchhoff-integral methods (French, 1975; Schneider, 1978), f-k methods (Gazdag, 1978; Stolt, 1978), and reverse-time migration methods (Baysal et. al., 1983; McMechan, 1983). For datuming, Berryhill (1979, 1984) applied the Kirchhoff-integral method to wavefield extrapolation. But his method is only easy to implement and accurate in a constant velocity medium. When the velocity of the medium varies, his method encounters various problems associated with the approximate solution to the wave equation and further difficulty in doing the ray tracing. Shtivelman and Canning (1988) presented an extrapolation scheme based on the asymptotics of the Kirchhoff-integral solution to the 2-D scalar wave equation. Their method is similar to that of Berryhill (1979), though more accurate. Bevc (1992b) implemented the datuming scheme given by Berryhill (1979) with the addition of being an anti-aliasing approximation to the Kirchhoff-integral. The inclusion of anti-aliasing of the Kirchhoff-integral has a low-cut filtering effect on the resulting wavefields. Ji et al. (1992) applied phase-shift method to perform datuming (Gazdag, 1978; Reshef, 1991); this method has the difficulty of implementing lateral velocity variations. Popovici (1992) applied phase-shift plus interpolation (PSPI) to perform datuming; but implementation of PSPI is clumsy in an irregular geometry.

This paper proposes a method of datuming that uses the exact two-way acoustic wave equation to do wavefield extrapolation along with depth migration. This method is implemented in the space-time domain by the finite-difference method. The paper first demonstrates upward and downward datuming for poststack data. It then demonstrates upward and downward datuming for prestack common-shot gather and common-receiver gather data and suggests application procedures for seismic data static correction for irregular land topography. Tests with synthetic data show good results. This method of datuming shows great promise for applications in land data static correction and migration in complex velocity areas.