Inversion of well logs into facies accounting for spatial dependencies and convolution effects

• A convolutional hidden Markov model is applied to facies and wireline well log data.
• The reference facies layers and their layer thickness are reliably predicted.
• The proposed model outperforms a more common naïve Bayesian classifier.

We predict facies from wireline well log data for a fluvial deposit system offshore Norway. The wireline well logs used are sonic, gamma ray, neutron porosity, bulk density and resistivity. We solve this inverse problem in a predictive Bayesian setting, and perform the associated model parameter estimation. Spatial vertical structure of the facies is included in the model by a Markov chain assumption, making geological model interpretation possible. We also take convolution effect into account, assuming that the observed logs might be measured as a weighted sum of properties over a facies interval. We apply the methods on real well data, with thick facies layers inferred from core samples. The proposed facies classification model is compared to a naive Bayesian classifier, which does not take into account neither vertical spatial dependency, dependencies between the wireline well logs nor convolution effect. Results from a blind well indicate that facies predictions from our model are more reliable than predictions from the naive model in terms of correct facies classification and predicted layer thickness.