Reverse-time migration has the capability to image all dips including overturned structures. However, the conventional imaging condition produces high-amplitude noises in the image, which often seriously mask the shallow structures. In this paper, we propose a new imaging condition to eliminate these noises which works by decomposing the full wavefields to their one-way components, and applying the imaging condition to the appropriate combinations of the wavefield components. Numerical tests verify that this new imaging condition successfully removes the undesired noises.


One-way wave equation migration algorithms play a significant role in seismic data processing, especially in areas where strong lateral velocity variations are present. The migration equations come from the paraxial approximation to the hyperbolic wave equation, which results in an irrational mathematical equation, i.e., the square-root operator. Numerical solution in general media requires further approximations to rationalize this square-root operator, unless a simple laterally invariant media is encountered where a phase shift-like approach can be applied. All those approximations pose significant dip limitations to the resulting migration algorithms. As exploration for hydrocarbons becomes more and more challenging, many structures encountered have very high dips which are beyond the dip-limitations of one-way wave equation migration algorithms. Some of these structures can only be imaged with overturned rays. Several methods have been proposed to couple the traditional upgoing and downgoing wave fields to image the over-turned rays (Xu,, 2006, Zhang,, 2006). Reverse-time migration directly solves the hyperbolic wave equation (Whitmore 1983, Baysal et. al. 1983). It has many advantages over the one-way wave equation methods. It has no dip limitation, and can properly image over-turned rays. However, due to the extensive computation, prestack reverse-time depth migration has only become affordable in production in recent years. Prestack reverse-time migration forward extrapolates the source wavefield and backward extrapolates the receiver field in time and constructs the image by applying an imaging condition. Traditionally, the image is constructed by the zerolag cross-correlation of the extrapolated source and receiver fields, which often produces a significant amount of high amplitude noises at a sharp boundary in the model. Those noises result from the unwanted cross-correlation of head waves, diving waves and back-scattered waves. The behavior of the noises strongly depends on the complexity of the hard boundary, as they are controlled by the reflection illumination. In post-stack reverse-time migration, these noises can be effectively suppressed by matching the impedance of the media, i.e., utilizing the nonreflecting wave equation (Baysal, 1984) or by smoothing the velocity model to reduce the reflections (Loewenthal, et. al, 1987). However, both approaches become less effective in the prestack case, because reflections can still be generated at large incident angles. Those noises should be eliminated by a different imaging condition. Yoon (2006) proposed using the Poynting vector to improve the cross-correlation imaging condition. Fletcher, (2005) suggest removing the imaging noise by applying a directional damping factor. Guiton, (2006) propose removing the artifact using a least square filter.

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