FlexLogNet: A flexible deep learning-based well-log completion method of adaptively using what you have to predict what you are missing

Well logs are essential tools for understanding the characteristics of subsurface formations and exploring petroleum resources. However, well logs are often missing randomly due to cost constraints, instrument failures, or other factors. Many methods have been developed for completing missing well logs, but these methods are all based on fixed types of known well-log inputs to predict specific types of missing logs. This fixed input–output mode severely limits the application of these methods in actual data, where the known and missing well-log types are often varying. To address this problem, we propose a hybrid deep learning method with two heads of heterogeneous graph neural network (HGNN) and fully connected network (FCN) to achieve mutual prediction among multiple types of well logs. It can adaptively use all known well logs to predict any missing well logs, achieving a very flexible and practical well log completion function of using what you have to complete what you are missing. Specifically, the HGNN head infers the inter-relationships among multiple well logs to predict normalized logs that contain detailed information, which achieved by using multiple independent kernels to extracting and aggregating the features of the multiple logs. The FCN head estimates the global statistics of the predicted logs, including means and standard deviations, for de-normalizing the well logs estimated by the HGNN head. Both the HGNN and FCN heads are trained simultaneously by a hybrid loss function to ensure the consistency of their predictions. Furthermore, we present an adaptive training strategy that leverages all well logs, including those with missing segments. We demonstrate the capability of our model using four well logs: gamma ray (GR), bulk density (RHOB), neutron porosity (NPHI), and compressional waves sonic (DTC). Theoretically, the model trained on other logs can also predict each other. Our approach yields high Pearson correlation coefficients and small root mean square error on a dataset obtained from an offshore North Sea field near Norway, demonstrating the efficacy of our proposed technique.