Blind seismic deconvolution using variational Bayesian method

• A variational Bayesian method for blind seismic deconvolution is proposed.
• Kullback–Leibler divergence is used in variational Bayesian blind deconvolution.
• We give how hyperparameter distributions can be inferred in actual situations.
• The proposed method shows superior resolution activity and error performance.

Blind seismic deconvolution, which comprises seismic wavelet and reflectivity sequence, is a strongly ill-posed problem. The reflectivity sequence is modeled as a Bernoulli–Gaussian (BG) process, depending on four parameters (noise variance, high and low reflector variances, and reflector density). These parameters need to be estimated from the seismic record, which is the convolution of the reflectivity sequence and the seismic wavelet. In this paper, we propose a variational Bayesian method for blind seismic deconvolution which can determine the reflectivity sequence and the seismic wavelet. The connection between variational Bayesian blind deconvolution and the minimization of the Kullback–Leibler divergence of two probability distributions is also established. The gamma, beta distributions are used for the unknown parameters (hyperparameters) as prior distribution and also we give how these distributions can be inferred in actual situations. The proposed algorithms are tested by simulation and compared to existing blind deconvolution methods. The results show that variational Bayesian method has better agreement with the actual value.