Reservoir characterization involves integration of different types of data to understand the subsurface rock properties. To incorporate multiple well log types into reservoir studies, estimating missing logs is an essential step. We have developed a method to estimate missing well logs by using a bidirectional convolutional long short-term memory (bidirectional ConvLSTM) cascaded with fully connected neural networks. We train the model on 177 wells from mature areas of the UK continental shelf (UKCS). We test the trained model on one blind well from UKCS, three wells from the Volve field in the Norwegian continental shelf, one well from the Penobscot field in the Scotian shelf offshore Canada, and one well from the Teapot Dome data set in Wyoming. The method takes into account the depth trend and the local shape of logs by using ConvLSTM architecture. The method is examined on sonic log prediction and can produce an accurate prediction of sonic logs from gamma-ray, density, and neutron porosity logs. The advantages of our method are that it is not applied on an interval by interval basis like rock-physics-based methods and it also outputs the uncertainties facilitated by dropout layers and Monte Carlo sampling at inference time.