Deblending using robust inversion of Stolt-based Radon operators

Amr Ibrahim, Daniel O. Trad

In this report, we compare the denoising and inversion-based methods for deblending using Stolt-based Radon operators. These operators are used to construct a robust inversion problem with a sparsity constraint. Sparsity promoting transforms, such as Radon transform, can focus seismic data and produce a sparse model which can be used to separate signals, remove noise, or interpolate missing traces. For this reason, Radon transforms are a suitable tool for deblending. We can incorporate Radon transform into the deblending problem in two ways, either using denoising-based or an inversion-based approach. The denoising-based method treats blending interferences as random noise by sorting the data into new gathers, such as common receiver gathers. In these gathers, blending interferences exhibit random structures due to the randomization of the source firing times. On the other hand, the inversion-based method treats blending interferences as a signal, and the transformation can model this signal in the Radon domain by incorporating the blending operator to formulate an inversion problem. We compare both methods using sparse inversion in the hyperbolic Radon domain. Synthetic and field data examples show that the inversionbased approach can produce more accurate separation and better convergence. However, the inversion-based method increases the computational cost of deblending.