A Missing Well-Logs Imputation Method Based on Conditional Denoising Diffusion Probabilistic Models

Well logs comprise sequential data detailing the geological properties of formations at varying depths encountered during drilling. They are fundamental for various applications in the petroleum industry. However, acquired well logs often contain noise and missing data, which impedes their utility. To address this, numerous methods have been developed to impute missing components in well logs, ranging from traditional deterministic methods to modern data-driven models. Despite their effectiveness, these methods face several challenges. First, many are deterministic, lacking the ability to capture and represent the inherent uncertainties in the data. In addition, they often require complete logging data as input, which presents challenges in data sets with substantial missing data. Moreover, most are predictive models designed with specific targets that require retraining for different variables, which limits their versatility in handling data sets with diverse missing components. This work proposes the use of a generative model based on the conditional denoising diffusion probabilistic model (CDDPM) to impute missing components within well logs. The CDDPM offers several advantages. Its inherent probabilistic nature allows it to capture uncertainties in the data, providing predictions in the form of probability distributions rather than single-point estimates. This helps engineers make more robust and informed decisions in practice, thus mitigating potential risks. More importantly, due to its generative nature, the model is trained to learn the underlying data distribution, not the specific input-output map, which enables it to impute all missing data simultaneously. Through experiments on a real-world data set, we demonstrate that our proposed method surpasses conventional data-driven techniques in performance. Both qualitative and quantitative evaluations confirm the effectiveness of the model in imputing missing components. This research highlights the potential of modern deep generative models in petroleum engineering applications.