Microlocal analysis of imaging operators for effective common offset seismic reconstruction

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.