Conventional one-way wave equation migration has dip limitations. Two-way reverse time migration (RTM) is one approach to overcome the dip limitations of one-way. It is, however, considerably more expensive in 3D pre-stack depth migration with respect to computation and memory. In this expanded abstract, we propose a two-way wave equation migration using a cumulative forescattering single backscattering (CFSB) approximation, called CFSB twowaywave equation migration, as an alternative to the reverse time migration, to image the dips which are nearly 90° or greater. The proposed algorithm is first applied to an impulse response test in V(z) medium to check the theoretical validity. Next we apply the algorithm to the BP 2004 2D benchmark model in order to image the steeply dipping salt boundaries, the overhanging salt body and the nearly vertical salt wall. Finally we apply it to the SMAARTJV Sigsbee2A model to image the overhanging salt flanks. While the computational cost of the CFSB twoway wave equation migration is more than that of conventional one-way wave equation migration, it is less than that of RTM, while retaining most of the advantages of RTM.
In seismic data processing, 3D one-way wave equation prestack depth migration has been widely applied to image complex structures due to its capabilities of properly handling multi-pathing and strong lateral velocity variations. However, the conventional one-way wave equation migration technique inherently has dip limits. Specifically, one-way wave migration can only accurately image steep dips up to 85° in 2D, and about 70° for all azimuths in 3D. It fails when faced with waves that propagate close to horizontal, or with duplex waves, or with turning waves. These waves directly contribute to the images of (nearly) vertical reflectors or overhanging salt flanks. Over the years, some approaches have been made to image turning waves and duplex waves by wave equation migration. Two-way reverse time migration (Baysal et al. 1983) is typical of these approaches, however, it is considerably time-consuming in 3D and has a huge storage requirement. As an alternative, other efforts have pursued modified one-way approaches. As can be seen in, e.g., Claerbout (1985) who proposed a two-pass one-way wave equation 2D post-stack time migration in v(z) medium using evanescent waves, Zhang et al. (2006) who used a pseudo-differential operator G , an amplitude term, to generate the reflected waves, and Jin et al. (2006) using a one-return approximation to migrate duplex-waves. In this paper, we use a cumulative forescattering single backscattering (CFSB) approximation (De Wolf 1971, 1985) to the full-wave two-way wave equation, to image the dips nearly 90° or greater. We present here the detailed formulae of forward scattering and backscattering wavefields (Wu 1994, Wild and Hudson 1998, Xie and Wu 2001) and have specially modified the backscattering wavefield formulae in terms of interfaces instead of thinslabs. We first apply this CFSB two-way wave equation migration method to an impulse response test in the V(z) medium to check its theoretical validity.