Blind marine seismic deconvolution by a SEM/MPM method: application to the ESSR4 campaign

As the source wavelet cannot be considered as a stationary signal, a blind deconvolution of seismic traces is necessary to improve seismic image resolution. The reflectivity sequence is modeled as a Bernouilli-Gaussian process, depending on four parameters (noise variance, high and low reflector variances, reflector density) and the wavelet by its impulse response. These parameters are unknown, and must be estimated from the recorded trace, which is the convolution of the reflectivity sequence and the wavelet. The maximum likelihood estimation is obtained by a stochastic EM method (SEM), because it is a typical case of incomplete data problem. Having estimated the parameters, one can proceed to the deconvolution. A MPM (Maximum Posterior Mode) algorithm is chosen, which consists in the maximization of the marginal distribution of the reflectors. It is made by a MCMC method, using the Gibbs sampler. This procedure is applied to the seismic data of the IFREMER ESSR4 campaign. The source is composed of 11 synchronized airguns, giving a very long wavelet of 150 ms, and the streamer consists in 360 hydrophone clusters spread over a 4.5 km length. The wavelet duration blurs the reflectivity, and a deconvolution, in this case, is needed to improve the seismic trace analysis.