A Hidden Markov Model Approach to Quantify Uncertainty of High-Resolution 3D Lithofacies Models Using Seismic Data

High-resolution 3D lithofacies models are essential for subsurface resource forecasting, including groundwater, geothermal, mineral deposits, oil, and gas. However, conventional geostatistical approaches using variograms have difficulty modeling the repetition in lithofacies stratigraphy vertically and laterally. In addition, lithofacies models using seismic data are subject to a significant amount of uncertainty due to the low seismic resolution.

This study investigates the use of hidden Markov models (HMM) to address the above problems. Our HMM approach uses a Baum-Welch algorithm to model the vertical facies repetition. First, we use this algorithm to learn the lithofacies emission, transition, and prior probabilities from the borehole data. Then, these probabilities and the 3D seismic cube are used in the forward-backward algorithm to produce the 3D probability fields for every lithofacies. Next, we construct multiple lithofacies models sampling from the probability field distributions. Finally, we perform a falsification test using robust Mahalanobis distance for outliers' detection on validation boreholes to validate our models.

We apply the proposed approach to a pre-salt carbonate reservoir in Santos Basin, Brazil. Pre-salt carbonates have complex geological diagenesis, and building their lithofacies model is challenging. However, we implemented the proposed method efficiently and generated multiple lithofacies model realizations. This allowed us to quantify the geological uncertainty. The proposed approach can also be generalized to any high-resolution lithofacies model with a Markov chain property.