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Drilling boreholes for gas and oil extraction is an expensive process and profitability strongly depends on characteristics of the subsurface. As profitability is a key success factor, companies in the industry utilise well logs to explore the subsurface beforehand. These well logs contain various characteristics of the rock around the borehole, which allow petrophysicists to determine the expected amount of contained hydrocarbon. However, these logs are often incomplete and, as a consequence, the subsequent analyses cannot exploit the full potential of the well logs. In this paper we demonstrate that Machine Learning can be applied to \emph{fill in the gaps} and estimate missing values. We investigate how the amount of training data influences the accuracy of prediction and how to best design regression models (Gradient Boosting and neural network) to obtain optimal results. We then explore the models' predictions both quantitatively, tracking the prediction error, and qualitatively, capturing the evolution of the measured and predicted values for a given property with depth. Combining the findings has enabled us to develop a predictive model that completes the well logs, increasing their quality and potential commercial value.