  Efficient and high-fidelity prior sampling and inversion for complex
geological media is still a largely unsolved challenge. Here, we use a deep
neural network of the variational autoencoder type to construct a parametric
low-dimensional base model parameterization of complex binary geological media.
For inversion purposes, it has the attractive feature that random draws from an
uncorrelated standard normal distribution yield model realizations with spatial
characteristics that are in agreement with the training set. In comparison with
the most commonly used parametric representations in probabilistic inversion,
we find that our dimensionality reduction (DR) approach outperforms principle
component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform
(DCT) DR techniques for unconditional geostatistical simulation of a
channelized prior model. For the considered examples, important compression
ratios (200 - 500) are achieved. Given that the construction of our
parameterization requires a training set of several tens of thousands of prior
model realizations, our DR approach is more suited for probabilistic (or
deterministic) inversion than for unconditional (or point-conditioned)
geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D
transient hydraulic tomography data are used to demonstrate the DR-based
inversion. For the 2D case study, the performance is superior compared to
current state-of-the-art multiple-point statistics inversion by sequential
geostatistical resampling (SGR). Inversion results for the 3D application are
also encouraging.
