M.Sc Student | Heimer Alon |
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Subject | Multichannel Deconvolution of Sparse Reflectivity Images Using Layered Medium Models |

Department | Department of Electrical Engineering |

Supervisor | Professor Israel Cohen |

Full Thesis text |

In this work, we develop two algorithms for deconvolution of sparse reflectivity images in the context of seismic exploration and investigate their performance. The algorithms are based on two models of the reflectivity pattern and attempt to maximize a global probabilistic criterion rather than a local one as was done in previous works. Both models are based on the fact that the reflectors in the reflectivity pattern tend to be arranged along continuous paths representing boundaries between areas of the explored medium with different acoustic impedance. The incorporation of this tendency in the model and in the algorithms allows us to achieve better recovery of the underlying reflectivity pattern from the data. In the first part of the work, the reflectivity is modeled as having reflectors that form continuous paths that start at the left side of the reflectivity image and end at the right side, hence do not account for discontinuities. The developed algorithm for this model uses Dynamic Programming combined with maximum a posteriori probability (MAP) estimation to iteratively find continuous paths of reflectors across the estimated reflectivity image that mostly increase the a posteriori probability. In the second part we model the reflectivity as a Bernoulli Markov random field which accounts for discontinuities of the reflecting boundaries. The algorithm developed for this model constructs a set of states each column of the reflectivity estimate can have, and defines the probability of transitions between these states. We then use the Viterbi algorithm, which is a specific type of Dynamic Programming, to iteratively find the sequence of states with maximal a posteriori probability, and update the reflectivity estimate according to the reflectors described by this sequence. Both algorithms produce an estimate of the two dimensional reflectivity pattern which exhibits better continuity of the recovered reflecting boundaries and therefore allow for better interpretation of the underground structure. The performance of the proposed algorithms with a comparison to a competitive algorithm, is investigated for simulated and real seismic data in a blind and non blind deconvolution scenarios.