The integration of multiple geophysical well logs together with seismic data can greatly reduce the ambi-guity of geological interpretation and help to construct a better hydrocarbon reservoir model. However, not all types of logs are available at every single well in an area of interest because of cost limitations or borehole problems.
Several statistical and empirical models have been used to estimate missing logs. Gardner’s equation provides a reasonable relationship between sonic and density for brine-saturated rock types (Gardner et al., 1974). Castagna et al. (1985); Greenberg and Castagna (1992) propose empirial relationships to calculate S-wave velocities (Vs) from P-wave velocities (Vp). These models can produce a useful pre-dicted log; however, they are interval-based, depend on rock types, and often their calibration requires time and expertise. An alternative data-driven method is to use deep learning for missing well-log pre-diction. The method predicts missing logs at a specific well based on nearby training wells incorporating all available well log types. Rolon et al. (2009); Salehi et al. (2017) use fully connected neural networks (FCNNs) for predicting non-recorded logs from existing logs. However, FCNNs only produce a point-to-point mapping from input logs to output logs. Rock properties often demonstrate a trend with depths at a specific well, which are important for geological studies. Recurrent neural networks (RNNs) consider both internal input from previous step (e.g. trend) and external inputs. Zhang et al. (2018) use RNNs to generate synthetic well logs; however, the uncertainty of the predicting model is not quantified.
We propose a method to estimate missing logs (in this case Vs logs from other 8 types of logs) by us-ing bidirectional LSTM cascaded with FCNN. We further add a dropout layer to quantify the uncertainty of the model. Output from our method is a Monte-Carlo distribution of log curves whose variance is the uncertainty of the model. We apply our method to 35 Central North Sea wells and show performance on three blind wells.