Direct Multi-Modal Inversion of Geophysical Logs Using Deep Learning

Geosteering of wells requires fast interpretation of geophysical logs which is a non-unique inverse problem. Current work presents a proof-of-concept approach to multi-modal probabilistic inversion of logs using a single evaluation of an artificial deep neural network (DNN). A mixture density DNN (MDN) is trained using the "multiple-trajectory-prediction" loss functions, which avoids mode collapse typical for traditional MDNs, and allows multi-modal prediction ahead of data. The proposed approach is verified on the real-time stratigraphic inversion of gamma-ray logs. The multi-modal predictor outputs several likely inverse solutions/predictions, providing more accurate and realistic solutions compared to a deterministic regression using a DNN. For these likely stratigraphic curves, the model simultaneously predicts their probabilities, which are implicitly learned from the training geological data. The stratigraphy predictions and their probabilities obtained in milliseconds from the MDN can enable better real-time decisions under geological uncertainties. Plain Language Summary Positioning the wells relative to geological targets and adjusting trajectory in real-time requires fast interpretation of streamed geophysical measurements. As such interpretations are not unique, high-quality decision-making requires the exploration of all likely interpretations and estimation of their probabilities. This study presents a mixture density deep neural network that correlates the log of the drilled well with the offset well and outputs a chosen number of interpretations of the geometry of geological layers and their probabilities. Moreover, by learning the likely configurations in the training geological data, one can extrapolate the interpretations ahead of the data. The presented model achieves good prediction accuracy while producing more realistic interpretations compared to the deterministic single-output model.