Analysis and Application of the Sparse Prior in Probabilistic Prediction of Elastic Parameters

Abstract

The probabilistic prediction approach can be used not only for obtaining the maximum posterior probability solution but also for uncertainty evaluation. Its prior distribution has a significant impact on the prediction result. An improper prior assumption may lead to prediction deviation. To improve the prediction accuracy of elastic parameters, a Laplace prior with total variation (TV) constraint is introduced in the probabilistic prediction. First, the effect of TV constraint on the probability distribution of elastic parameters is analyzed in detail. Then, two approaches are proposed to handle the cases where the elastic parameters have blocky boundaries and no blocky boundaries: probabilistic prediction scheme for elastic parameters with blocky boundaries and probabilistic prediction scheme with blocky lithology prior constraint. The former imposes a sparse constraint on the elastic parameters, while the latter imposes a sparse constraint on the TV processing lithology. Their posterior probabilities are re-derived. Considering that the discrete lithology is more likely to be blocky compared with the continuous elastic parameters, the sparse lithology constraint can handle more general cases. In addition, this approach allows for lithology prediction. The applications of numerical examples and field seismic data verify the feasibility of the proposed approaches.