Missing well-log reconstruction using a sequence self-attention deep-learning framework

Well logging is a critical tool for reservoir evaluation and fluid identification. However, due to borehole conditions, instrument failure, economic constraints, etc., some types of well logs are occasionally missing or unreliable. Existing logging curve reconstruction methods based on empirical formulas and fully connected deep neural networks (FCDNN) can only consider point-to-point mapping relationships. Recurrently structured neural networks can consider a multipoint correlation, but it is difficult to compute in parallel. To take into account the correlation between log sequences and achieve computational parallelism, we develop a novel deep-learning framework for missing well-log reconstruction based on state-of-the-art transformer architecture. The missing well-log transformer (MWLT) uses a self-attention mechanism instead of a circular recursive structure to model the global dependencies of the inputs and outputs. To use different usage requirements, we design the MWLT in three scales: small, base, and large, by adjusting the parameters in the network. A total of 8609 samples from 209 wells in the Sichuan Basin, China, are used for training and validation, and two additional blind wells are used for testing. The data augmentation strategy with random starting points is implemented to increase the robustness of the model. The results show that our proposed MWLT achieves a significant improvement in accuracy over the conventional Gardner's equation and data-driven approaches such as FCDNN and bidirectional long short-term memory, on the validation data set and blind test wells. The MWLT-large and MWLT-base have lower prediction errors than MWLT-small but require more training time. Two wells in the Songliao Basin, China, are used to evaluate the cross-regional generalized performance of our method. The generalizability test results demonstrate that density logs reconstructed by MWLT remain the best match to the observed data compared with other methods. The parallelizable MWLT automatically learns the global dependence of the parameters of the subsurface reservoir, enabling an efficient missing well-log reconstruction performance.