  Deep learning techniques have been shown to be extremely effective for
various classification and regression problems, but quantifying the uncertainty
of their predictions and separating them into the epistemic and aleatoric
fractions is still considered challenging. In oil and gas exploration projects,
tools consisting of seismic, sonic, magnetic resonance, resistivity, dielectric
and/or nuclear sensors are sent downhole through boreholes to probe the earth's
rock and fluid properties. The measurements from these tools are used to build
reservoir models that are subsequently used for estimation and optimization of
hydrocarbon production. Machine learning algorithms are often used to estimate
the rock and fluid properties from the measured downhole data. Quantifying
uncertainties of these properties is crucial for rock and fluid evaluation and
subsequent reservoir optimization and production decisions. These machine
learning algorithms are often trained on a "ground-truth" or core database.
During the inference phase which involves application of these algorithms to
field data, it is critical that the machine learning algorithm flag data as out
of distribution from new geologies that the model was not trained upon. It is
also highly important to be sensitive to heteroscedastic aleatoric noise in the
feature space arising from the combination of tool and geological conditions.
Understanding the source of the uncertainty and reducing them is key to
designing intelligent tools and applications such as automated log
interpretation answer products for exploration and field development. In this
paper we describe a methodology consisting of a system of dual networks
comprising of the combination of a Bayesian Neural Network (BNN) and an
Artificial Neural Network (ANN) addressing this challenge for geophysical
applications.
