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\begin{document}

\title{Geophysical Inversion Using a Variational Autoencoder to Model an
Assembled Spatial Prior Uncertainty}



\author[1]{Jorge Lopez-Alvis}%
\author[2]{Frederic Nguyen}%
\author[3]{Thomas Hermans}%
\author[4]{Majken C. Looms}%
\affil[1]{University of Liege}%
\affil[2]{University of Liège}%
\affil[3]{Ghent University}%
\affil[4]{University of Copenhagen}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
Prior information regarding subsurface 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, e.g.
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. 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. Estimation of
absolute values of wave velocity is also possible by assuming a linear
mixing model and including two additional parameters in the inversion.%
\end{abstract}%



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