  Deep Learning (DL) inversion is a promising method for real time
interpretation of logging while drilling (LWD) resistivity measurements for
well navigation applications. In this context, measurement noise may
significantly affect inversion results. Existing publications examining the
effects of measurement noise on DL inversion results are scarce. We develop a
method to generate training data sets and construct DL architectures that
enhance the robustness of DL inversion methods in the presence of noisy LWD
resistivity measurements. We use two synthetic resistivity models to test three
approaches that explicitly consider the presence of noise: (1) adding noise to
the measurements in the training set, (2) augmenting the training set by
replicating it and adding varying noise realizations, and (3) adding a noise
layer in the DL architecture. Numerical results confirm that the three
approaches produce a denoising effect, yielding better inversion results in
both predicted earth model and measurements compared not only to the basic DL
inversion but also to traditional gradient based inversion results. A
combination of the second and third approaches delivers the best results. The
proposed methods can be readily generalized to multi dimensional DL inversion.
