Conventional seismic exploration surveys acquire P-wave reflection data with surface-based acquisition geometry. Increasingly, though, non-conventional surveys provide additional and complementary constraints on the seismic imaging process. One non-conventional survey example is massive 3-D vertical seismic profiling (VSP), which generates increased subsurface ray coverage and affords enhanced resolution of complex geologic structure Bicquart (1998); Payne et al. (1994); Sullivan et al. (2003). A second example is the use of long-offset refracted waves in conventional reflection surveys to improve migration velocity analysis (MVA) through wavefield inversion Pratt (1999); Sirgue and Pratt (2004). Non-conventional surveys often incorporate alternative acquisition geometry and/or novel sources such as in passive seismic imaging; many are designed to measure forward-scattered energy with sufficient spatial sampling to permit wavefield-based processing. Hence, a careful examination the utility of forward-scattered wavefields in the seismic imaging process is warranted.
The forward-scattering scenario arises when a source wavefield interacts with discontinuous structure generating a secondary scattered wavefield of diffracted and converted energy that propagates sub-parallel to the source wavefield. Importantly, because these two wavefields travel in similar directions, and thereby sample the subsurface in a similar way, they contain important velocity profile information in both absolute (i.e., direct waves) and relative (i.e., differential) travel-times. The utility of this information for velocity analysis and/or imaging is well-known, and is used frequently in many branches of seismology Bostock et al. (2001); Langston (1977); Sheley and Schuster (2003); VanDecar (1991).
Most forward-scattering MVA and imaging methods do not process entire wavefield records, and instead rely on the analysis of picked relative or global traveltimes. Analogous to conventional reflection seismic processing, though, significant MVA and imaging improvements should be achievable by moving from forward-scattered traveltime-based processing to forward-scattered wavefield inversion methods. However, before we can test this assertion, a number of forward-scattering MVA and imaging tools must be developed - in particular, the forward-scattering equivalent of the angle domain common image gather (ADCIG) Biondi (2005); Prucha et al. (1999); Rosales and Biondi (2005); Sava and Fomel (2003a)
In this paper, we modify existing 2-D ADCIG theory to account for the differences arising in the forward-scattering scenario. We use the shot-profile configuration of wave-equation migration to provide a ADCIG framework for both forward-scattered diffracted (P-P) and converted (P-S) wavefields. We begin by reviewing the wavefield extrapolation and imaging condition steps of shot-profile migration. We then specify planar source and receiver wavefields, and generate parametric surfaces in the intermediate offset-domain common-image gather (ODCIG) space. Subsequently, we show how to transform ODCIGs to their angle domain representation, and detail how to compute angle-dependent source- and receiver-side reflectivity and the geologic dip angle directly from the ODCIG volume. We then apply the approach to a synthetic teleseismic plane-wave data set Shragge (2003). This data set is comprised of elastic wavefields, which allows us to test our ADCIG theory for both P-P and P-S forward-scattered scenarios.