Wave propagation in complex media, scattering theory, and application to seismic imaging

Migration is a seismic imaging method that consists of creating a representation of the Earth’s subsurface structure from the recording of seismic waves. Migration is essentially equivalent to solving an inverse scattering problem in structurally complex media. Conventional migration algorithms rely on linearized inversion schemes and assume single-scattering dominance. The primary focus of this thesis is an alternative nonlinear scattering-based approach to seismic migration. The goal is to take advantage of multiple scattering in seismic imaging in order to produce better images in complex geological subsurface environments. The foundation of the method I proposed is the integral formulation of the inverse scattering problem based on the representation theorems and similar to the formulation used for retrieving Green’s functions in seismic interferometry. The first part of this thesis presents representation theorems for general perturbed systems. Based on this study of the retrieval of scattered fields, I develop a new imaging condition for seismic migration. By taking into account the fundamental nonlinear relation between the seismic data and the model of the subsurface, this imaging condition takes advantage of multiply scattered waves, including multiple reflections, in the imaging process. Then, I design an imaging algorithm referred to as nonlinear reverse-time migration. This migration exploits multiply scattered waves, including internal multiples, and is of particular interest for advanced interpretation in complex subsurface environment. In the exploration industry, the development of new imaging methods coincides with innovations in data processing and acquisition. The last part of this thesis focuses on a reverse-time migration that makes optimal use of the novel multi-component marine seismic data which have recently been available for offshore exploration.