Microlocal analysis of imaging operators for effective common offset seismic reconstruction. (10th September 2018)

• Record Type: Journal Article
• Authors: Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas
• Is Part Of: Inverse problems. Volume 34:Number 11(2018:Nov.)
• Publication Date: 2018-09-10
• Subjects: generalized Radon transforms -- Fourier integral operators -- microlocal analysis -- seismic imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aadc2a
• Languages: English
• ISSNs: 0266-5611

Abstract

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.