Geophysical Inversion Using a Variational Autoencoder to Model an Assembled Spatial Prior Uncertainty

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.