MCMC Inversion of Offshore West Africa AVA Data

We define the Bayesian posterior probability distribution in terms of the data likelihood, the prior distributions of unknown parameters, the prior distribution of lithology indexes and the prior distribution of data signal to noise. The prior distribution of lithology indexes is represented as a 3D Markov random field where the cell to cell coupling is parameterized using 3D Kriging parameters of angles and ranges. We show that the resulting PDFs of the geophysical parameters (Acoustic Impedance, Vp/Vs, and density) can be non-Gaussian (multi-modal).

We compare the MCMC inversion predictions of oil in place (OIP) and net-to-gross (NTG) to an industry standard work flow of simultaneous (SI) elastic joint inversion followed by Bayesian inference for porosity prediction. For the data set considered, which is representative of most West Africa data sets, the sampling based MCMC algorithm provides superior prediction of lithology and porosity, the two parameters that drive drilling decisions. Comparisons at two blind wells show that the MCMC NTG and OIP predictions are ∼ 5x better, in terms of % error, than the SI workflow. In this example an industry standard SI algorithm and workflow would significantly underestimate the OIP, which could have significant impact on a prospect’s viability.