Azimuthally anisotropic 3D velocity continuation

Introduction

Velocity continuation (Fomel, 2003b,1994) provides a framework for describing how a seismic image changes given a change in the migration velocity model. Similar in concept to residual migration (Rothman et al., 1985) and cascaded migrations (Larner and Beasley, 1987), velocity continuation is a continuous formulation of the same process. Velocity continuation has found applications in migration velocity analysis (Fomel, 2003a; Schleicher et al., 2008a) and diffraction imaging (Fomel et al., 2007; Novais et al., 2006).

Fomel (1994) and Hubral et al. (1996) point out that velocity continuation is a wave propagation process. Instead of wavefronts propagating as a function of time, images propagate as a function of migration velocity. Recent work has extended the concept to heterogeneous and anisotropic velocity models (Duchkov and de Hoop, 2009; Alkhalifah and Fomel, 1997; Schleicher et al., 2008b; Schleicher and Alexio, 2007; Iversen, 2006; Adler, 2002). To account for anisotropy, the seismic velocity model must become multi-parameter. Consequentially, velocity continuation generalizes to a process of implementing image transformations caused by changes in multiple parameters rather than the single isotropic velocity alone.

Accounting for azimuthal variations in seismic velocity results in better event focusing and improved imaging in such media (Sicking and Nelan, 2008). Azimuthal variation in velocity has been shown to be an indicator of preferentially aligned vertical fractures (Crampin, 1984), lateral heterogeneity (Levin, 1985), regional stress (Sicking et al., 2007), or a combination of these factors. However, velocity analysis is commonly first performed on pre-stack common midpoint (CMP) gathers, where the geologic cause of any observed azimuthal velocity variation is ambiguous. Without the help of additional diagnostic gathers such as hybrid or cross-spread gathers (Dunkin and Levin, 1971), or an interpretive comparison between picked root-mean-square (RMS) and interval velocities (Jenner, 2008), the cause of azimuthal variations in velocity can be identified only after migration.

Azimuthal seismic imaging commonly requires iterations between velocity analysis and imaging. Residual azimuthal variations in traveltime after migration can be measured by using migration binning schemes which preserve both offset and azimuth information (Cary, 1999; Vermeer, 1999). After the first pass of (isotropic) migration, azimuthal variations in velocity are detected from residual moveout, which then provides the velocity model for anisotropic migration. Iterative processing flows that use these strategies are popular not only because they are fairly efficient and intuitive, but also because they can be implemented with minimal modification to existing software. However, iterative imaging flows cannot guarantee convergence to the correct or optimal velocity model (Deregowski, 1990). Velocity continuation has the underlying strategy of performing velocity analysis and imaging simultaneously, and can thus be used to directly find an optimal velocity model without iteration. Sicking et al. (2007) have demonstrated the success of a similar strategy of using imaging as a velocity analysis tool for 3D multiazimuth reflection seismic data. Azimuthal velocity continuation can provide a theoretical framework for this approach. With these benefits as motivation, we extend time-domain velocity continuation to 3D, accounting for the case of azimuthally variable migration velocity.

Azimuthally anisotropic 3D velocity continuation