Introduction

Vertical structures such as salt flanks are usually not illuminated by primary reflections and so cannot be well imaged by conventional migration methods (Hale et al., 1992). If on the other hand strong diving waves are present, they can be reflected from the salt flank, recorded on the surface, and migrated by a two-way migration method, such as Kirchhoff migration (Ratcliff et al., 1991, 1992) or reverse time migration (RTM) (Baysal et al., 1983; McMechan, 1983; Whitmore, 1983). Even a one-way migration method can be modified (Hale et al., 1992) to incorporate diving waves for salt flank imaging.

If the diving wave is not extant due to the absence of a strong velocity gradient or a limited recording aperture, prism waves can be migrated to illuminate vertical reflectors. A prism wave is defined to be a doubly scattered wave from, typically, a vertical reflector, as illustrated by the ray diagram in Figure (a). Cavalca and Lailly (2005) studied the kinematics of prism waves and explored the possibility of incorporating the prism waves in traveltime inversion for salt flank locations. To incorporate amplitudes in the imaging, Marmalyevskyy et al. (2005) migrated the prism waves by a Kirchhoff-based method for salt flank delineation with subhorizontal reflection boundaries specified from the previous migration images. An iterative method was proposed by Malcolm et al. (2009) to progressively incorporate migration of prism waves and multiples with a modified one-way wave equation migration method, where each phase was isolated by a data fitting process. At each step, different partial images were computed to illuminate different structures, e.g., the prism waves for salt flanks. They later tested their method on North sea field data with the introduction of a regularization term for the inversion (Malcolm et al., 2011).

Figure 4.1: (a) A velocity model with a horizontal reflector and a vertical reflector. The yellow arrows indicate the ray path for a prism wave from the source at the star to the receiver at the triangle; (b) the wave path of the prism wave with a 20-Hz Ricker wavelet; and (c) the trace recorded at the triangle. The two arrivals in the red window are the reflections from the horizontal reflector and the prism wave in panel (b).

With reverse time migration, the migration of the prism waves can be accommodated in the process by embedding the subhorizontal reflection boundaries in the velocity model (Jones et al., 2007). However, incorporating the sharp boundaries into the velocity model is not trivial, and the complex migration velocity will excite complex wavefields that lead to artifacts in the RTM images (Liu et al., 2011). Another problem is that prism waves are doubly scattered waves, which are usually weaker than primaries, so that the contribution from the prism waves might be weak. In this chapter, I propose a new RTM method for migrating the prism waves separately from the other reflectors by utilizing the migration image from conventional RTM. The advantages of this approach over conventional RTM are as follows: (1) It does not require modifying the migration velocity as conventional RTM does; (2) It separately images different structures at different steps and reduces the artifacts from crosstalk of different phases. The disadvantage of the proposed method is that its computational cost is twice that of conventional RTM.

This chapter is organized into four sections. The first one is this introduction, which is followed by the theory section. In the numerical results section, the synthetic examples of a simple model and a salt model are presented. A summary will be provided in the end.