Variational Bayesian Learning for Decentralized Blind Deconvolution of Seismic Signals Over Sensor Networks

This work discusses a variational Bayesian learning approach towards decentralized blind deconvolution of seismic signals within a sensor network. Blind seismic deconvolution is cast into a probabilistic framework based on Sparse Bayesian learning developed for blind image deconvolution. The posterior distribution of the signals of interest is then approximated using a variational Bayesian method. Depending on a particular form of selected variational factors, the scheme is shown to generalize the state-of-the-art distributed seismic blind deconvolution algorithm. The algorithm operates by repeatedly alternating between two stages: (i) estimation of seismic source wavelet and (ii) reflectivity estimation. The wavelet is computed in a distributed fashion using Alternating Direction Method of Multipliers. Based on this estimate each sensor then locally obtains a sparse reflectivity estimate. Numerical evaluation with synthetic seismic data shows that the proposed method outperforms existing deconvolution algorithms in the high signal-to-noise ratio (SNR) regime. In the low SNR regime a higher sensitivity of sparse Bayesian learning regarding model mismatches in the estimated source wavelet is observed. Also, processing of seismic data generated with an acoustic wave equation shows that the proposed method is able to recover the original reflectivities more accurately, with more distinct support of the reflectivities, as compared to existing methods despite present model mismatches. The algorithm is also applied to the estimation of real seismic data, and shows improved performance as compared to a state-of-the-art estimation method.