Deep generative networks for multivariate fullstack seismic data inversion using inverse autoregressive flows

The simultaneous prediction of the subsurface distribution of facies and acoustic impedance ($I_P$) from fullstack seismic data requires solving an inverse problem and is fundamental in natural resources exploration, carbon capture and storage, and environmental risk management. In recent years, deep generative models (DGM), such as variational autoencoders (VAE) and generative adversarial networks (GAN), were proposed to reproduce complex facies patterns honoring prior geological information. Variational Bayesian inference using inverse autoregressive flows (IAF) can be performed to infer the solution to a geophysical inverse problem from the encoded latent space of such pre-trained DGM. Successful applications of such approach on crosshole ground-penetrating radar synthetic data inversion demonstrated that the technique's accuracy is comparable to that of Markov chain Monte Carlo (MCMC) inference methods, while significantly reducing the computational cost. Nonetheless, these application examples did not account for the spatial uncertainty affecting the facies-dependent continuous physical property, from which the geophysical data are calculated. This uncertainty can significantly affect the inversion accuracy and its applicability to real data. In this work, specific VAE and GAN architectures are proposed to simultaneously predict facies and co-located $I_P$, while accounting for their spatial uncertainties. The two types of generative networks are used in Bayesian inversion with IAF for the inversion of seismic data. The results are found to reproduce the statistics of the training images and solve the seismic inversion problem accurately, comparably to MCMC inversion. Furthermore, advantages and limitations of the two DGMs are evaluated by comparing the results obtained.