Introduction

Downward continuation migration Claerbout (1985) increases in popularity with the continuing development of computer power. It is accurate, and can handle lateral velocity change and multi-pathing naturally. It is used to image complex geological structure, especially sub-salt reflectors. However, the dip angle of reflectors is limited in downward continuation, which makes it difficult to image steeply dipping reflectors and overturned waves. Downward continuation is based on the one-way wave equation and extrapolates the wavefields in the downward direction, although in reality, waves propagate in all directions. When the propagation direction of waves is too far from the extrapolation direction, the accuracy of extrapolation is limited.

Kirchhoff methods can handle steeply dipping reflectors and overturned waves, but they are based on a high-frequency approximation and are less reliable for imaging complex geological structure, where multi-path events are present. Reverse-time migration Baysal et al. (1983); Biondi and Shan (2002); Whitmore (1983), which is based on the two-way wave equation, can handle waves propagating in all directions, but it is still too expensive for today's computer power.

Many methods have been developed to handle waves that propagate at large angles to the extrapolation direction. They solve the problem either by developing a more accurate extrapolation operator to image high-angle waves, such as Fourier finite difference Biondi (2002); Ristow and Ruhl (1994) and generalized screen propagators Huang and Wu (1996); de Hoop (1996), or by making the extrapolation direction closer to the propagation direction, such as beam migration Albertin et al. (2001); Brandsberg-Dahl and Etgen (2003); Gray et al. (2002); Hill (2001), beamlet migration Chen et al. (2002) and coordinate-transformation based methods Etgen (2002); Sava and Fomel (2004); Zhang and McMechan (1997). Our method is of the latter type. We decompose both source and receiver wavefields into plane-waves and run plane-wave migration Duquet et al. (2001); Liu et al. (2002); Rietveld (1995); Zhang et al. (2003) on each of them within a tilted coordinate system Etgen (2002).

Offset-domain CIGs for shot-profile migration and reverse-time migration are generated by cross-correlating the source and receiver wavefields with a horizontal shift Rickett and Sava (2002), and can be transformed into ADCIGs by slant stack Sava and Fomel (2003). However, CIGs obtained from downward continuation are contaminated by smearing noise at steeply dipping reflectors Biondi and Shan (2002). Reverse-time migration can provide both horizontal and vertical CIGs. Both are then merged into dip-dependent CIGs, which are robust and immune to the smearing noise Biondi and Symes (2003). By performing plane-wave migration in tilted coordinates, we can obtain similar dip-dependent ADCIGs. These CIGs are robust and are useful for velocity analysis in the presence of steeply dipping reflectors in the subsurface.