Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network

Abstract

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-theart multiple-point statistics inversion by sequential geostatistical resampling (SGR).

Towards a robust parameterization for conditioning facies models using deep variational autoencoders and ensemble smoother

“…Our tests indicate that if we train the network with realizations conditioned to hard data, most of the reconstructed facies honor these data, but there is no guarantee. In fact, Laloy et al (2017) reported that in one of their tests only 68% of the realizations honor all nine hard data points imposed in the training set. For this reason, here we investigate the ability of the proposed ES-MDA-CVAE to condition the prior realizations to facies data.…”

“…One possible approach is to consider each layer of the reservoir model separately. This is the approach used in (Laloy et al, 2017). However, this procedure do not account for the geometry of the facies in the vertical direction as the convolutional operations are performed in 2D.…”

Training‐Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network

“…We propose a 3‐D extension of the original 2‐D SGAN by Jetchev et al (). To enable efficient Markov chain Monte Carlo (MCMC) inversion, we take advantage of the fact that, similarly to the deep variational autoencoder (VAE) used by Laloy et al (), the standard GAN architecture defines a low‐dimensional “latent” representation of the original high‐dimensional data (i.e., spatial subsurface property fields in our case). In such an architecture, the high‐dimensional data realizations are obtained by propagating a low‐dimensional random noise vector through the network.…”

HESS Opinions: Deep learning as a promising avenue toward knowledge discovery in water sciences

“…While DL has stimulated exciting advances in many disciplines and has become the method of choice in some areas, water sciences so far have only had a very limited set of DL applications. Despite scattered early reports of promising DL results Laloy et al, 2017Laloy et al, , 2018Tao et al, 2016;Vandal et al, 2017;Zhang et al, 2018), water scientists seemed to have reservations about these new tools, perhaps with good reasoning. This opinion paper, endorsed by the cohort of authors, argues that there are many opportunities in water sciences where DL can help provide both stronger predictive capabilities and 5 a complementary avenue toward scientific discovery.…”

“…(7) DL also provides new opportunities for multiple-point (geo)statistics (MPS). A few researchers have started to use deep 20 generative models for multiple-point geostatistical simulation (Mosser et al, 2017) along with inversion (Laloy et al, 2017(Laloy et al, , 2018 but progress in deep generative modeling are constantly made and the potential of this type of DL models for MPS applications (unconditional and conditional simulation, inversion, 2D to 3D pore space reconstruction, etc) is yet largely unexplored.…”