Bayesian estimation of non-minimum phase wavelets applied to marine reflection seismic data

The problem of wavelet estimation for marine seismology is investigated with a Bayesian approach applied to a Bernoulli-Gaussian model. We specify proper prior distributions for all unknown quantities including the seismic wavelet, the parameters of the reflectivity sequence and noise. To solve this estimation problem, an algorithm close to a stochastic version of the EM algorithm is used. The random variables are generated iteratively by a simple Monte-Carlo method namely the Gibbs sampler. But the direct application of this procedure often leads to a local minimum of the likelihood function resulting in a shifted and distorted wavelet. We propose a general method to obtain the true solution which systematically uses different shifted wavelets to reinitialize the algorithm. Then we rerun the procedure on each initialization and retain the wavelet which minimizes the noise variance