Physics-driven deep-learning inversion with application to transient electromagnetics

Machine learning, and specifically deep-learning (DL) techniques applied to geophysical inverse problems, is an attractive subject, which has promising potential and, at the same time, presents some challenges in practical implementation. Some obstacles relate to scarce knowledge of the searched geologic structures, a problem that can limit the interpretability and generalizability of the trained DL networks when applied to independent scenarios in real applications. Commonly used (physics-driven) least-squares optimization methods are very efficient local optimization techniques but require good starting models close to the correct solution to avoid local minima. We have developed a hybrid workflow that combines both approaches in a coupled physics-driven/DL inversion scheme. We exploit the benefits and characteristics of both inversion techniques to converge to solutions that typically outperform individual inversion results and bring the solution closer to the global minimum of a nonconvex inverse problem. The completely data-driven and self-feeding procedure relies on a coupling mechanism between the two inversion schemes taking the form of penalty functions applied to the model term. Predictions from the DL network are used to constrain the least-squares inversion, whereas the feedback loop from inversion to the DL scheme consists of the network retraining with partial results obtained from inversion. The self-feeding process tends to converge to a common agreeable solution, which is the result of two independent schemes with different mathematical formalisms and different objective functions on the data and model misfit. We determine that the hybrid procedure is converging to robust and high-resolution resistivity models when applied to the inversion of the synthetic and field transient electromagnetic data. Finally, we speculate that the procedure may be adopted to recast the way we solve inverse problems in several different disciplines.