Dimensionality reduction for geophysical inversion in highly structured subsurface environments

For highly structured subsurface, the use of strong prior information in geophysical inversion produces realistic models. Machine learning methods allow to encode or parameterize such models with a low dimensional representation. These methods require a large number of examples to learn such latent or intrinsic parameterization. By using deep generative models, inversion is performed in a latent space and resulting models display the desired patterns. However, the degree of nonlinearity for the generative mapping (which goes from latent to original representation) dictates how useful the parameterization is for tasks other than mere compression. After recognizing that changes in curvature and topology are the main cause of such nonlinearity, an adequate training for a variational autoencoder (VAE) is shown to allow the application of gradient-based inversion. Data obtained in highly structured subsurface may also be represented by low-dimensional parameterizations. Compressed versions of the data are useful for prior falsification because they allow modeling marginal probability distributions of structural parameters in a latent space. An objective way based on cross-validation is proposed to choose which compression technique retains information relevant to high-level structural parameters. Inversion and prior falsification using dimensionality reduction provide a computationally efficient framework to produce realistic models of the subsurface. This framework is successfully applied to a field dataset using a prior distribution assembled from distinct patterns resemble a realistic geological environment including deformation and intrafacies variability.