Introducing Nonuniform Sparse Proximal Averaging Network for Seismic Reflectivity Inversion

We consider the problem of seismic reflectivity inversion, which pertains to the high-resolution recovery of interface locations and reflection coefficients from seismic measurements, which are vital for estimating the subsurface structure. We develop two model-based neural networks within the framework of deep-unfolding. First, we propose a nonuniform minimax concave penalty regularized formulation for reflectivity inversion and unfold the resulting iterative algorithm into a network. Second, we propose a nonuniform sparse model that relies on a combination of regularizers (composite regularization) and develop the nonuniform sparse proximal averaging network (NuSPAN). We demonstrate the efficacy of the proposed approaches over the benchmark techniques through numerical experiments on synthetic 1-D seismic traces and 2-D wedge models. We also report validations on the 2-D Marmousi2 simulated model and 3-D real field measurements from the Penobscot 3D survey off the coast of Nova Scotia, Canada. The accuracy of the proposed approaches is higher than the state-of-the-art techniques in terms of amplitude and support recovery. Further, for Marmousi2, the proposed deep-unfolding networks result in 600× faster inference than the fast iterative shrinkage-thresholding algorithm (FISTA). In terms of combined training and inference times, the learned iterative shrinkage-thresholding algorithm (LISTA) is the fastest. The inference speed-up is significant given that the volume of data is typically large in seismic signal processing.