Migration and velocity analysis by wavefield extrapolation

The goal of this thesis is to design methods for imaging complex geologic structures of the Earth's Lithosphere. Seeing complex structures is important for both exploration and nonexploration studies of the Earth and it involves dealing with complex wave propagation in media with large velocity contrasts.; The approach I use to achieve this goal is depth imaging using acoustic waves. This approach consists of two components: migration and migration velocity analysis. No accurate imaging is possible without accurate, robust and efficient solutions to both components. I address both migration and migration velocity analysis in the general framework of one-way wavefield extrapolation. In this context, both imaging components are consistent and use the entire acoustic wavefields with accurate, robust and computationally feasible techniques.; The migration state-of-the-art involves downward continuation of wavefields recorded at the Earth's surface. I introduce Riemannian wavefield extrapolation as a general framework for wavefield extrapolation. This technique allows us to overcome the steep-dip limitation of downward continuation, while retaining the main characteristics of wave-equation techniques.; Riemannian wavefield extrapolation propagates waves in semi-orthogonal coordinate systems that conform with the general direction of wave propagation. Therefore, extrapolation is done forward relative to the direction in which waves propagate, so we can achieve high-angle accuracy with small-angle operators.; The velocity estimation state-of-the-art involves traveltime tomography from sparse reflectors picked on migrated images. I introduce wave-equation migration velocity analysis as a more accurate and robust alternative. With this technique, I overcome the instability of traveltime tomography caused by ray tracing in areas with high velocity contrasts.; I formulate wave-equation MVA with an operator based on linearization of wavefield extrapolation using the first-order Born approximation. I define the optimization objective function in the space of migrated images. Since the entire images are sensitive to migration velocities, I use image perturbations for optimization, in contrast with traveltime tomography which employs traveltime perturbations picked at selected locations. I construct image perturbations with linearized residual migration operators by measuring angle-gather flatness or spatial focusing.