Using Convolutional Neural Networks and Monte-Carlo Dropout to Generate Synthetic Well Logs with Accurate Uncertainty Estimation

The common and most acquired well logs are the basic petrophysical and lithological logs which usually include density, porosity, resistivity, gamma-ray, and customarily, the caliper measurement of borehole diameter to provide an indication of borehole and log quality. Acoustic log acquisition may not be routine, especially in a cost-constrained environment and in older wells. Previous works have developed methods to generate synthetic acoustic logs using petrophysical-based models. However, their reliability and applicability heavily depend on the complexity, variability, and uncertainty of subsurface rocks and fluids. The challenge is compounded by rock heterogeneity such as the highly variable and laminated unconventional shales. Generation of synthetic acoustic log values is considerably more challenging when rock formation is highly heterogeneous. Predictive models that perform well on relatively homogenous rock formations often struggle to predict accurately for heterogeneous rock formations such as the highly laminated shales and mudrocks. In this paper, we use two datasets, one set of well logs is taken from a highly heterogeneous shale formation, and the other is from a much more homogenous rock formation. We introduce and evaluate robust deep learning models and quantify the uncertainty of prediction using Monte-Carlo dropout. These models are classes of time-series neural network models: the Multi-Layer Perceptron, Long- Short Term Memory model, and Convolutional Neural Networks. We test some common machine learning approaches as baseline models on our datasets and show that the deep learning architectures consistently outperform the baseline models. Furthermore, the Monte-Carlo dropout approach is adopted and integrated into the deep learning models, which provides an estimate of the prediction uncertainty. Generally, the Convolutional Neural Network coupled with Monte Carlo dropout provides the most robust results with adequate quantification of prediction uncertainty.

Keywords:acoustic well log, rock heterogeneity, LSTM, Monte-Carlo dropout, convolutional neural network