  The advent of fast sensing technologies allows for real-time model updates in
many applications where the model parameters are uncertain. Bayesian
algorithms, such as ensemble smoothers, offer a real-time probabilistic
inversion accounting for uncertainties. However, they rely on the repeated
evaluation of the computational models, and deep neural network (DNN) based
proxies can be useful to address this computational bottleneck. This paper
studies the effects of the approximate nature of the deep learned models and
associated model errors during the inversion of extra-deep borehole
electromagnetic (EM) measurements, which are critical for geosteering. Using a
deep neural network (DNN) as a forward model allows us to perform thousands of
model evaluations within seconds, which is very useful for quantifying
uncertainties and non-uniqueness in real-time. While significant efforts are
usually made to ensure the accuracy of the DNN models, it is known that they
contain unknown model errors in the regions not covered by the training data.
When DNNs are utilized during inversion of EM measurements, the effects of the
model errors could manifest themselves as a bias in the estimated input
parameters and, consequently, might result in a low-quality geosteering
decision. We present numerical results highlighting the challenges associated
with the inversion of EM measurements while neglecting model error. We further
demonstrate the utility of a recently proposed flexible iterative ensemble
smoother in reducing the effect of model bias by capturing the unknown model
errors, thus improving the quality of the estimated subsurface properties for
geosteering operation. Moreover, we describe a procedure for identifying
inversion multimodality and propose possible solutions to alleviate it in
real-time.
