Separation of prestack seismic diffractions using an improved sparse apex-shifted hyperbolic Radon transform

Abstract

The apex-shifted hyperbolic Radon transform (ASHRT) which is defined as an extension of standard hyperbolic Radon transform (HRT) shifts the apexes of basis functions along the offset. In this paper, we develop an improved sparse ASHRT to separate the diffractions from reflections before stacking. To speed up the calculation, the forward and adjoint operators of ASHRT in the time domain are replaced with the Fourier-kernel Stolt-based modelling and imaging operators. To overcome the limitation of velocity variations, the time axis stretching is implemented. With lower computation cost compared to the time domain operators, we can collapse the apex-shifted events with one velocity. Meanwhile, we introduce a sparsity-promoting inversion by the fast iterative shrinkage thresholding algorithm (FISTA), which produces a sparse Radon panel to separate the diffracted energy easily. Two synthetic examples of variable velocity model show that our proposition is robust and efficient. Another marine data example further demonstrates the effectiveness of this method in separation of prestack seismic diffractions.