  Geophysical inversion attempts to estimate the distribution of physical
properties in the Earth's interior from observations collected at or above the
surface. Inverse problems are commonly posed as least-squares optimization
problems in high-dimensional parameter spaces. Existing approaches are largely
based on deterministic gradient-based methods, which are limited by
nonlinearity and nonuniqueness of the inverse problem. Probabilistic inversion
methods, despite their great potential in uncertainty quantification, still
remain a formidable computational task. In this paper, I explore the potential
of deep learning methods for electromagnetic inversion. This approach does not
require calculation of the gradient and provides results instantaneously. Deep
neural networks based on fully convolutional architecture are trained on large
synthetic datasets obtained by full 3-D simulations. The performance of the
method is demonstrated on models of strong practical relevance representing an
onshore controlled source electromagnetic CO2 monitoring scenario. The
pre-trained networks can reliably estimate the position and lateral dimensions
of the anomalies, as well as their resistivity properties. Several fully
convolutional network architectures are compared in terms of their accuracy,
generalization, and cost of training. Examples with different survey geometry
and noise levels confirm the feasibility of the deep learning inversion,
opening the possibility to estimate the subsurface resistivity distribution in
real time.
