Static correction by prestack datuming

Land seismic data are usually recorded over an irregular surface, and static correction has long been a problem. There are two kinds of statics, long-wavelength (large time shift) and short-wavelength (small time shift) statics. They are solved in two separate stages. The first stage is datum correction, used to correct long-wavelength statics, by which simple vertical time shifts are applied to common-shot gathers and common-receiver gathers to datum from an irregular earth surface to a planar surface. This planar surface is either above, below, or through all the shot and receiver elevations, depending on the requirements of a survey area. The details of this datuming procedure can be found in seismic data processing manuals. Next, the sorted common midpoint (CMP) gathers are normal moveout (NMO) corrected and stacked to generate the zero-offset section. Then statistical residual static corrections are applied to the zero-offset stack section to flatten a user-predefined main reflection event, thus correcting the short-wavelength statics. Throughout the years, even though many methods have been developed to deal with this problem, static correction still remains a difficult unsolved problem. These methods are mostly designed for the stage of residual static corrections. Because in the first stage, the vertical time shift processing does not correspond to the wave equation, one might not expect that the second stage, statistical residual static corrections, which is designed for small time shifts, could do much better.

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.