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

Abstract

Machine learning, and specifically deep learning 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 of the obstacles relate to scarce knowledge of the searched geological structures, a problem that can limit both the interpretability and the generalizability of the trained deep learning 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 develop a hybrid workflow, which combines both approaches in a coupled physics-driven/deep learning inversion scheme. We exploit the benefits and characteristics of both inversion techniques to converge to solutions that typically outperform individual inversions results and bring the solution closer to the global minimum of a non-convex 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 deep learning network are used to constrain the least-square inversion while the feedback loop from inversion to the deep learning scheme consists of the network re-training 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 data and model misfit. We demonstrate that the hybrid procedure is converging to robust and high-resolution resistivity models when applied to the inversion of both synthetic and field transient electromagnetic (TEM) data. We finally speculate that the developed procedure may be adopted to recast the way we solve inverse problems for several different disciplines.

DL-RMD: a geophysically constrained electromagnetic resistivity model database (RMD) for deep learning (DL) applications

“…2, in the generation of the DL-RMD. We also train an additional network using the random resistivity models, similarly to several DL studies (Colombo et al, 2021b;Moghadas, 2020;Moghadas et al, 2020;Noh et al, 2020;Puzyrev and Swidinsky, 2021;Qin et al, 2019;Wu et al, 2021b) as mentioned in Table 1. To have the same level of complexity, the number of layers, depth discretization, and the number of random resistivity models are kept the same as used to train the other two networks for a fair comparison, and the resistivity of each layer is chosen randomly from a log-uniform distribution to take into account the nonlinearity of the forward responses with the resistivity values.…”

Physics-Driven Deep Learning Inversion with Application to Magnetotelluric

“…Fuks and Tchelepi [21] embedded the initial and boundary conditions in a composite loss function and performed training on smaller datasets. Colombo et al [22] incorporated DL techniques into standard deterministic inversion schemes to obtain better, more stable and unique transient electromagnetic (TEM) inversion results. Inspired by the conventional inversion considering the governing wave equation, some other works incorporated the physical laws of the inverse problem into the DL inversion architecture.…”

2.5-D Deep Learning Inversion of LWD and Deep-Sensing EM Measurements Across Formations With Dipping Faults

“…Meanwhile, modern machine learning methods such as deep learning (DL) are now widely employed for solving various scientific and engineering problems [10]- [12]. In particular, DL methods have recently been applied to solve geophysical inverse problems [13], [14]. DL inversion offers the practical possibility of real-time imaging of spatially complex subsurface structures.…”