The main contributions of this thesis are the following:
Migration using Riemannian wavefield extrapolation (rwe) addresses the intrinsic limitations of migration by downward continuation in presence of waves propagating away from the vertical axis of extrapolation. I demonstrate that one-way Riemannian wavefield extrapolation allows waves to propagate beyond the limit of relative to the vertical axis, while preserving the main characteristics of wavefield imaging methods: multipathing and robustness in presence of large velocity contrasts. Angle-domain common image gathers (adcig) enable velocity (MVA) and amplitude (AVA) analysis, as well as multiple attenuation for images created using wavefield extrapolation. I demonstrate that this method can be used to create angle gathers from depth migrated images, after migration by wavefield extrapolation. Many artifacts of angle transformation by slant-stacking are addressed by regularization in the Fourier domain. Prestack residual migration in the Fourier domain (storm) enables definition of image perturbations for wave-equation migration velocity analysis. I demonstrate that this residual migration method can be used to investigate how prestack images change relative to changes in velocity. Such changes concern both moveout and spatial focusing, and can be used for robust migration velocity analysis. Velocity analysis using wavefield extrapolation (wemva) overcomes many of the difficulties of ray-based methods in complex structures. I demonstrate that band-limited velocity analysis methods are robust in presence of large velocity contrasts and that such methods handle in a natural way frequency-dependent and multiple wavepaths. This method can be used for velocity analysis subsalt or for velocity analysis using diffracted energy (example).