Empirical comparison of two Bayesian lithology–fluid prediction algorithms

We consider a Bayesian model for doing lithology–fluid prediction from prestack (amplitude versus offset) seismic data. Related to the Bayesian model, we look at two inversion algorithms. The first algorithm simulates from the posterior distribution with no approximations, but the algorithm is quite computer demanding. The second inversion algorithm introduces an approximation in the likelihood model and is in this way able to evaluate the resulting approximate posterior distribution very rapidly. The consequences of the approximation for the inversion result are not clear. The objective of this paper is to evaluate the consequences of the approximation in a synthetic but realistic empirical case study. The consequences are evaluated by comparing the inversion results from the two inversion algorithms. In the case study we observe that, dependent on the parameters in the model, typically the approximate likelihood model preserves between 55% and 80% of the information in the original likelihood model. The consequences of the approximation increase when the amount of noise in the model increases. The approximation works better when most of the variability is in the rock physics model and it is little seismic noise, compared to the opposite.