Towards generative seismic kriging with normalizing flows

Our goal is to build realistic parameterized (acoustic, velocity, permeability etc) earth models where the training and testing phase of our method uses only data that is available in the field. We first demonstrate the expressive power of normalizing flows to generate detailed realistic earth models by training on supervised pairs of full earth models and borehole wells. Our results are compared with traditional variogram kriging to show that our generated models can be used in parameterizations of various downstream tasks such as simulations of realistic acoustic waves and fluid flow for reservoir simulations. Then we introduce a novel unsupervised training objective that can train normalizing flows to generate full earth models without needing training pairs of the full earth models. By using a known proxy earth model as a testbed, we make preliminary prescriptions on how many wells our method needs to generate permissible earth models in a target area.