Seismic Migration by downward continuation using the one-way wave equation approximations has two shortcomings: imaging steep dip reflectors and handling evanescent waves. Complex Padé approximations allow a better treatment of evanescent modes, stabilizing finite-difference migration without requiring special treatment for the migration domain boundaries. Imaging steep dip reflectors can be improved using several terms in the Padé expansion. We discuss the implementation and evaluation of wide-angle complex Padé approximations for finite-difference and Fourier finite-difference migration methods. The dispersion relation and the impulsive response of the migration operator provide criteria to select the number of terms and coefficients in the Padé expansion. This assures stability for a prescribed maximum propagation direction. The implementations are validated on the Marmousi model dataset and SEG/EAGE salt model data.

With a string of recent discoveries in the pre-salt areas in deep-water offshore Brazil, this hydrocarbon province has proven to be of global importance. The pre-salt reservoirs, however, present many challenges for exploration. In this paper, we describe the acquisition and processing of a fullazimuth towed-streamer seismic survey designed for presalt exploration offshore Brazil. We show that this solution overcomes many of the pre-salt exploration challenges to provide high-quality reservoir information in an efficient manner. Figure 6: Areal map of traveltime residuals (ms) plotted at the 3D VSP source locations, using an intermediate velocity model. Figure 7: Existing 2D depth migration (top) and full-azimuth TTI anisotropic Kirchhoff depth migration of the coil data (bottom). Pre-salt reflections (highlighted) are well imaged 2D data courtesy of TGS and WG

Standard real-valued finite-difference (FD) and Fourier finite-difference (FFD) migrations cannot handle evanescent waves correctly, which can lead to numerical instabilities in the presence of strong velocity variations. A possible solution to these problems is the complex Padé approximation, which avoids problems with evanescent waves by rotating the branch cut of the complex square root. We have applied this approximation to the acoustic wave equation for vertical transversely isotropic media to derive more stable FD and hybrid FD/FFD migrations for such media. Our analysis of the dispersion relation of the new method indicates that it should provide more stable migration results with fewer artifacts and higher accuracy at steep dips. Our studies lead to the conclusion that the rotation angle of the branch cut that should yield the most stable image is 60° for FD migration, as confirmed by numerical impulse responses and work with synthetic data.

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