Geophysical Inversion Using a Variational Autoencoder to Model an Assembled Spatial Prior Uncertainty. Issue 3 (27th February 2022)

• Record Type: Journal Article
• Authors: Lopez‐Alvis, J.; Nguyen, F.; Looms, M. C.; Hermans, T.
• Is Part Of: Journal of geophysical research. Volume 127:Issue 3(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-02-27
• Subjects: prior information -- geophysical inversion -- variational autoencoder -- deep learning -- ground‐penetrating radar -- traveltime tomography; Geomagnetism -- Periodicals; Geochemistry -- Periodicals; Geophysics -- Periodicals; Earth sciences -- Periodicals; 551.1
• DOI: 10.1029/2021JB022581
• Languages: English
• ISSNs: 2169-9313

Abstract

Abstract: Prior information regarding subsurface spatial patterns may be used in geophysical inversion to obtain realistic subsurface models. Field experiments require prior information with sufficiently diverse patterns to accurately estimate the spatial distribution of geophysical properties in the sensed subsurface domain. A variational autoencoder (VAE) provides a way to assemble all patterns deemed possible in a single prior distribution. Such patterns may include those defined by different base training images and also their perturbed versions, for example, those resulting from geologically consistent operations such as erosion/dilation, local deformation, and intrafacies variability. Once the VAE is trained, inversion may be done in the latent space which ensures that inverted models have the patterns defined by the assembled prior. Gradient‐based inversion with both a synthetic and a field case of cross‐borehole GPR traveltime data shows that using the VAE assembled prior performs as good as using the VAE trained on the pattern with the best fit, but it has the advantage of lower computation cost and more realistic prior uncertainty. Moreover, the synthetic case shows an adequate estimation of most small‐scale structures. The absolute values of wave velocity are computed by assuming a linear mixing model which involves two additional parameters that effectively shift and scale velocity values and are included in the inversion. Plain Language Summary: Obtaining realistic images of the subsurface is important for characterizing processes that are sensitive to small‐scale structures such as solute transport. Geophysical methods usually require additional information concerning the spatial patterns of the subsurface materials to obtain such realistic images. If more than one kind of pattern is deemed likely, enforcing a set of patterns in the geophysical image is not straightforward and traditional methods often result in over‐simplified representations of the subsurface. In this work, we propose a new method that is capable of enforcing a diverse set of spatial patterns. The method is based on a pair of convolutional neural networks that form a model called variational autoencoder (VAE). The VAE is trained with a large number of samples of all the possible patterns and then it is capable of generating new patterns that are consistent with those of the training samples. The geophysical images are then constrained only to those generated by the VAE. We show that our method effectively assembles the set of possible patterns and provides a more realistic and less biased image when compared to other methods or even a VAE trained with a single kind of pattern. Key Points: A variational autoencoder (VAE) may be used to effectively assemble a diverse set of patterns in a single prior for geophysical inversion Geologically consistent transformations can be used to improve pattern diversity when training the VAE A VAE assembled prior produces less biased geophysical images than those produced by smooth inversion or a VAE trained on a single pattern