An FIO Calculus for Marine Seismic Imaging: Folds and Cross Caps

Abstract

We consider a linearized inverse problem arising in offshore seismic imaging. Following Nolan and Symes (1997b), one wishes to determine a singular perturbation of a smooth background soundspeed in the Earth from measurements made at the surface resulting from various seismic experiments; the overdetermined data set considered here corresponds to marine seismic exploration. In the presence of only fold caustics for the background, we identify the geometry of the canonical relation underlying the linearized forward scattering operator F, which is a Fourier integral operator. We then establish a composition calculus for general FIOs associated with similar canonical relations, which we call folded cross caps, sufficient for identifying the normal operator F*F. In contrast to the case of a single source experiment, treated by Nolan (2000) and Felea (2005), the resulting artifact is order smoother than the main pseudodifferential part of F*F.