Let it Flow – 2007 CSPG CSEG Convention 414 TTI Wave Equation Migration by Phase-Shift Plus Interpolation Richard A. Bale* CGGVeritas, Calgary, AB, Canada Richard.bale@cggveritas.com and Samuel H. Gray and M. Graziella Kirtland Grech CGGVeritas, Calgary, AB, Canada Summary We describe a phase-shift plus interpolation (PSPI) method for wave-equation migration in TTI media. To apply the PSPI methodology for anisotropy, we generate reference operators based upon phase error criteria with respect to the symmetry axis direction, and exploit correlations between parameters. The method is demonstrated on an elastic synthetic dataset generated over a thrust-belt setting, as found in the Canadian Foothills. Introduction Many hydrocarbon reservoirs, such as those in the Rocky Mountain Foothills of western Canada, lie below dipping clastic sequences characterized by tilted transverse isotropy (TTI) (Isaac and Lawton, 2004). Several authors (e.g. Vestrum et al., 1999) have shown the importance of accounting for the tilt of the symmetry axis when imaging such reservoirs using anisotropic depth migration, in order to correctly locate structures laterally. To realize this goal, typically Kirchhoff algorithms have been upgraded to handle TTI. As for isotropic migration, superior results for significantly greater effort are expected from the use of wave-equation migration methods on TTI data. In contrast to ray-tracing based methods, wave-equation migration is able to handle multi-pathing in a natural way, and is not based upon a high-frequency approximation to the wave equation. Shan and Biondi (2005) have demonstrated both 2-D and 3-D implementations of TTI wave-equation migration, using an implicit operator with explicit correction, applied in the space-frequency (x-y-f) domain. However, efficient x-y-f methods are usually based on circular symmetry. This luxury is not obviously available for TTI, which lacks such symmetry. An alternative approach to wave-equation migration is based upon applying phase-shift operators in the wavenumber-frequency (k-f) domain. This choice has advantages of operator stability and accurate steep dip behaviour. The main drawback, compared to x-f migration, is that lateral variations in the medium are not naturally accommodated by k-f domain operators. For isotropic migration, a number of methods have been proposed to address this issue, including: phase-shift plus interpolation (PSPI), split-step and Fourier finite difference. Generally, all of these are based