Section: Scientific Foundations
The research program of Magique-3D for depth imaging is divided into two topics that both deal with the solution of the wave equation in a complex 3D medium but that differ in terms of the methods that are used. The first topic is entitled "One-way and two-way models" and is based on numerical micro-local analysis. From a practical point of view, such investigations are supposed to lead to the solution of approximate wave equations but they have the advantage of giving rise to fast solution methods which, if not accurate in general situation, can provide approximate solutions that can subsequently be used as data to initialize implicit schemes for solving full wave equations. The second topic is entitled "High-performance methods for solving wave equations". It is more classical and deals with the development of methods of resolution that are innovative and based on finite element methods. We essentially focus on the development of mixed hybrid methods which are based on the combination of Lagrange polynomials and plane waves. By using finite element discretization, we can take the topography into account which allows us to outperform existing Reverse Time Migration methods based on finite difference methods.