Microlocal analysis of imaging operators for effective common offset seismic reconstruction. (10th September 2018) - Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas
Abstract: The elliptic Radon transform (eRT) integrates functions over ellipses in 2D and ellipsoids of revolution in 3D. It thus serves as a model for linearized seismic imaging under the common offset scanning geometry where sources and receivers are offset by a constant vector. As an inversion formula of eRT is unknown we propose certain imaging operators (generalized backprojection operators) which allow to reconstruct some singularities of the searched-for reflectivity function from seismic measurements. We calculate and analyze the principal symbols of these imaging operators as pseudo-differential operators to understand how they map, emphasize or de-emphasize singularities. We use this information to develop local reconstruction operators that reconstruct relatively independently of depth and offset. Numerical examples illustrate the theoretical findings.