We propose an approach to perform migration and imaging using secondary scattered waves. Secondary scattered waves are extracted through a back propagation plus cross-correlation approach. The surface shot gathers are thus transformed to subsurface shot gathers with sources located at some subsurface scatterers (gathers of scattering sources). Numerical examples confirm the validity of this secondary scattered wave retrieval approach. Migration and imaging from these secondary scattered wave gathers improves the final image. We apply this secondary scattered wave retrieval approach to SEG-EAGE salt model and improve the image of subsalt faults.
Traditional one-way wave equation based migration and imaging methods are formulated to use primary scattered waves from subsurface reflectors. Multiples (including surface-related and internal multiples) and secondary scattered waves are often abandoned or treated as noises. From the point of view of wave propagation and time reversal back propagation, all these kinds of waves contribute to the final image if they are properly handled during migration and imaging. Reverse-time migration is supposed to handle all these waves but requires formidable computation. One-way/one-return wave equation based migration methods (Thomson, 2005; Wu et al., 2008) have been proved to be quite efficient to obtain sharp images of subsurface structure. However, the acquisition system in practice limits the illumination of primary reflections, leaving some ‘shadow zones’, e.g., some part of the subsalt region (Xie et al., 2006). Nevertheless, secondary scattered waves and multiples have potential to improve the illumination due to their complex but different-from-primary wave path (Cao and Wu, 2008; Malcolm et al., 2009). Diffracted waves, mainly first scattered waves, can also be separated from data to obtain clear images of subsurface structure whose scale is smaller or comparable to the wavelength such as pinchouts (Khaidukov et al., 2004; Bansal and Imhof, 2005; Fomel et al., 2007; Zhu and Wu, 2008).
Secondary scattered waves help to image some poorly-illuminated areas such as subsalt regions. This requires strong scatterers in the medium, e.g., sharp edge points on salt boundaries. On the one hand, these scatterers serve as new subsurface sources, emitting waves to illuminate ‘shadow zones’ where primary transmitted waves can not reach. On the other hand, these scatterers serve as ‘transporters’, changing the direction of primary reflected waves to allow surface receivers to record signals from subsurface structures. As an example of secondary scattering sources (Figure 1a), primary waves travel along the black trajectories and secondary scattered waves travel along the red trajectories. If a smooth velocity model is used during migration, back propagation of secondary scattered waves will travel along the red solid arrow (Figure 1b), which results in no contribution to the real image. Another advantage of these secondary scattered waves is that they can be recorded even for small aperture as long as the time record is long enough. Take the SEGEAGE model for an example: the reflection signals from the sub-salt structure are scattered by the sharp edges of the salt. These secondary scattered waves from sharp edges could possibly be recorded though the direct reflected waves can not reach the receivers due to limited aperture.