  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" (MTP) 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 than 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.
