Application of conditional generative model for sonic log estimation considering measurement uncertainty

Well-log data is a cost-effective means to characterize the petrophysical properties of a geological formation. Among the data, compressional- and shear-slowness (DTC and DTS, respectively) are the most reliable and have been widely applied in the interpretations. However, the availability of DTS data tends to be limited because of its high acquisition cost. This study proposes a method to reproduce or reconstruct the DTS data using other well-log data, such as gamma ray, neutron porosity, bulk density, and DTC. The developed method is based on the conditional variational autoencoder (CVAE) and effectively considers uncertainty associated with the variability of the measured data. The performance of this developed method is validated by applying the well-log data acquired from Satyr-5 and Callihoe-1 wells in the Northern Carnarvon Basin, Western Australia, and the prediction accuracy of the developed method is compared to recently developed data-driven methods (i.e., long short-term memory (LSTM) and bidirectional LSTM (bi-LSTM)). The results reveal that the developed method produces a better DTS estimation than LSTM and bi-LSTM. Furthermore, the effectiveness of the proposed method remains unaltered regardless of whether the data contain a specific trend over the depth or amount of training data are insufficient. As a further application of the developed method, an uncertainty relative to DTS estimation is quantitatively obtained from Monte-Carlo estimation, which uses a trained probability model of the developed method. Sensitivity analysis reveals the high effectiveness of DTC in improving the performance of the CVAE method. From our results, we can conclude that the proposed CVAE-based method is an effective tool for improving the efficiency and accuracy of DTS estimation.