Bayesian lithology/fluid inversion—comparison of two algorithms

Algorithms for inversion of seismic prestack AVO data into lithology-fluid classes in a vertical profile are evaluated. The inversion is defined in a Bayesian setting where the prior model for the lithology-fluid classes is a Markov chain, and the likelihood model relates seismic data and elastic material properties to these classes. The likelihood model is approximated such that the posterior model can be calculated recursively using the extremely efficient forward–backward algorithm. The impact of the approximation in the likelihood model is evaluated empirically by comparing results from the approximate approach with results generated from the exact posterior model. The exact posterior is assessed by sampling using a sophisticated Markov chain Monte Carlo simulation algorithm. The simulation algorithm is iterative, and it requires considerable computer resources. Seven realistic evaluation models are defined, from which synthetic seismic data are generated. Using identical seismic data, the approximate marginal posterior is calculated and the exact marginal posterior is assessed. It is concluded that the approximate likelihood model preserves 50% to 90% of the information content in the exact likelihood model.