Chevron (operator), Teikoku Oil, and Unocal hold the offshore Zaire concession, West Africa. Recently, Unocal performed an anisotropic 3-D prestack depth migration in an attempt to optimally image tilted fault blocks in the presalt section. Depth migration was required because large‐displacement faults juxtaposed a high‐velocity massive carbonate and a low‐velocity marl. Large compressional‐wave anisotropy caused by thin layering was inferred for most of the depth section. Evidence on the nature and magnitude of the anisotropy came from comparing stacking velocities with well velocities, analyzing a multioffset vertical seismic profile (VSP), thin‐layer modeling in the massive carbonate using well log data, and rock physics laboratory velocity measurements on core from the marl. The subsurface was characterized as being locally transversely isotropic and the Thomsen parameters were used to describe the anisotropy. This required that five parameters be specified at each subsurface location to represent the compressional‐wave 3-D velocity field. The observed anisotropy deviated far from the elliptical condition, and modeling indicated that isotropic migration would exhibit misfocusing and mispositioning of events, and its quality would be dip‐dependent. The anisotropic migration was performed using Kirchhoff summation for which the traveltimes were determined using a finite‐difference scheme. Interpreted horizons in the migrated depth section accurately tied well depths.