Static correction by wave equation datuming has been reported by several researchers, who all reported solving the wave equation by the Kirchhoff method. Berryhill (1979, 1984) demonstrated by the Kirchhoff method, and Shtivelman and Canning (1988) demonstrated by the asymptotic Kirchhoff method that wave equation upward and downward datuming can help solve the static correction problem. [Bevc (1991) described using refraction inversion to solve the problem of land static correction.] Bevc (1992) proposed upward continuing the data to some planar datum above the topography with some fictitious (appropriate) extrapolation velocity by the Kirchhoff method and anticipated that this operation could help solve the static correction problem. 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 resulted wavefields. The problems with the different implementations of Kirchhoff-integral method, as mentioned in the introduction, are its approximate solution to the wave equation, the difficulty of doing ray tracing when the medium velocity varies, and the high cost of prestack implementation (Berryhill,1984).
In the research this paper describes, I replaced conventional datuming static time shift correction with wave equation datuming in order to correct from an irregular earth surface to a upper or lower planar surface (Dobrin, 1976). The upper planar surface must be above all the shot and receiver elevations and the lower planar surface below them in order to implement the wave equation datuming. The running of the wave equation is thus either forward or backward in time. At this stage, the long wavelength static has been removed, and the new datum wavefields are correct to the wave equation. From this point, one carries on the conventional seismic data processing sequence, which consists of NMO, brute stack, statistical residual static correction, and final stack. This paper shows only the results of upward extrapolation datuming, since the downward extrapolation is a similar procedure.