Bayesian seismic AVO inversion with a group optimization strategy

The seismic amplitude-versus-offset (AVO) inversion based on the Bayesian framework is effective for obtaining the elastic parameters of the stratum from observed seismic data. Usually, this algorithm is used to obtain sparse reflectivity levels of elastic parameters through a proper long-tailed prior probability distribution. Considering the high correlation between underground parameters, a group optimization strategy was used for Bayesian AVO inversion, where the model parameters were inverted in groups at reflection interfaces. A group Cauchy constraint consisting of Cauchy constraint and l(2)-norm was designed. In the constraint, the Cauchy constraint is executed between groups to promote the sparsity of model parameters, and l(2) regularization is executed within each group for constraining uniformity. The new Bayesian AVO inversion algorithm based on the group optimization strategy can help estimate the reflectivity levels of elastic parameters with desired sparsity. Additionally, even in the absence of the covariance matrix, the algorithm can still ensure the correlation of resulting solutions. It has been demonstrated that good results have been obtained from both numerical and field examples.