Simultaneous reconstruction of seismic reflections and diffractions using a global hyperbolic Radon dictionary

Abstract

We have developed a new transform with basis functions that closely resemble seismic reflections and diffractions. The new transform is an extension of the classic hyperbolic Radon transform and accounts for the apex shifts of the seismic reflection hyperbolas and the asymptote shifts of the seismic diffraction hyperbolas. The adjoint and forward operators of the proposed transform are computed using Stolt operators in the frequency domain to increase the computational efficiency of the transform. This new transform is used, in conjunction with a sparse inversion algorithm, to reconstruct common-shot gathers. Our tests indicate that this new transform is an efficient tool for interpolating coarsely sampled seismic data in cases in which one cannot use small data windows to validate the linear event assumption that is often made by Fourier-based reconstruction methods.