  Borehole resistivity measurements recorded with logging-while-drilling (LWD)
instruments are widely used for characterizing the earth's subsurface
properties. They facilitate the extraction of natural resources such as oil and
gas. LWD instruments require real-time inversions of electromagnetic
measurements to estimate the electrical properties of the earth's subsurface
near the well and possibly correct the well trajectory. Deep Neural Network
(DNN)-based methods are suitable for the rapid inversion of borehole
resistivity measurements as they approximate the forward and inverse problem
offline during the training phase and they only require a fraction of a second
for the evaluation (aka prediction). However, the inverse problem generally
admits multiple solutions. DNNs with traditional loss functions based on data
misfit are ill-equipped for solving an inverse problem. This can be partially
overcome by adding regularization terms to a loss function specifically
designed for encoder-decoder architectures. But adding regularization seriously
limits the number of possible solutions to a set of a priori desirable physical
solutions. To avoid this, we use a two-step loss function without any
regularization. In addition, to guarantee an inverse solution, we need a
carefully selected measurement acquisition system with a sufficient number of
measurements. In this work, we propose a DNN-based iterative algorithm for
designing such a measurement acquisition system. We illustrate our DNN-based
iterative algorithm via several synthetic examples. Numerical results show that
the obtained measurement acquisition system is sufficient to identify and
characterize both resistive and conductive layers above and below the logging
instrument. Numerical results are promising, although further improvements are
required to make our method amenable for industrial purposes.
