Blind seismic deconvolution by exploiting the sparsity of mixing matrix and earth signal

Recently blind seismic deconvolution has received a great deal of attention. In seismic deconvolution, blind approaches can be considered in situations where the reflectivity sequence and the source wavelet, are unknown from given seismic traces. This paper provides a novel method to solve the blind seismic deconvolution problem using independent component analysis by exploiting the sparsity of both the reflectivity sequence and the mixing matrix. The reflectivity sequence can be modelled as Bernoulli Gaussian process where the nonzero elements of the sparse mixing matrix contain the convolution filter. Our technique incorporates the sparsity of the mixing matrix into the pre-processing step and a novel logistic function that matches the sparsity of reflectivity sequence distribution has been proposed and fitted into the information maximization algorithm. These results in a more accurate estimation of both the wavelet and the reflectivity sequence compared with conventional independent component analysis (ICA) algorithm. The mean square error (MSE) of estimated wavelet and estimated reflectivity sequence shows the improvement of proposed algorithm.