Three-dimensional sparse seismic deconvolution based on earth Q model

We propose a multichannel efficient method for recovery of three-dimensional (3D) reflectivity signal from 3D seismic data. The algorithm consists of solving convex constrained optimization problems that promote the sparsity of the solution. It is formulated so that it fits the earth Q model that describes the attenuation and dispersion propagation effects of reflected waves. At the same time, the method also takes into account the relations between spatially-neighboring traces. These three features together with low computational cost make the proposed method a reliable solution for the emerging need to accurately estimate reflectivity from large volumes of 3D seismic data. We also derive a theoretical bound on the recovery error in the case of horizontal layered sub-terrain. We show that the recovery error is inversely proportional to the number of traces taken into account in the estimation process. Synthetic and real data examples demonstrate the robustness of the proposed technique compared to single-channel recovery.