This thesis addressed the problem of finding background models yielding depth consistent migrated PP and PS images, i.e. geologically equivalent reflectors should be imaged at the same depth in the two images. The tomographic approach in search of a background medium, is performed as a combination of migration velocity analysis by differential semblance in angle and map migration. A practical strategy for obtaining estimates of all parameter values in a transversely isotropic medium with a known symmetry axis is presented. The approach combines the search of a background medium yielding optimum focusing ability by differential semblance and the matching of PP and PS key reflectors in depth by means of map migration. This can also be used to match the imaged reflectors with known depths e.g. from well markers. For the purpose of fast and computationally inexpensive imaging and tomography in angle, a complete review and analysis for the 2.5-D case is performed. The theory is also extended to anisotropic media under necessary and sufficient assumptions. An analysis is performed with regards to parameter issues in 2.5-D in anisotropic media. All inversion and migration results are derived in the natural coordinate system, namely scattering/reflection angle at the imaging point by means of the generalized Radon transform.