Seismic inversion with deep learning

This article investigates bypassing the inversion steps involved in a standard litho-type classification pipeline and performing the litho-type classification directly from imaged seismic data. We consider a set of deep learning methods that map the seismic data directly into litho-type classes, trained on two variants of synthetic seismic data: (i) one in which we image the seismic data using a local Radon transform to obtain angle gathers, (ii) and another in which we start from the subsurface-offset gathers, based on correlations over the seismic data. Our results indicate that this single-step approach provides a faster alternative to the established pipeline while being convincingly accurate. We observe that adding the background model as input to the deep network optimization is essential in correctly categorizing litho-types. Also, starting from the angle gathers obtained by imaging in the Radon domain is more informative than using the subsurface offset gathers as input.

Randomized maximum likelihood based posterior sampling

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples generated by minimization is not the desired target density, unless the observation operator is linear, but the distribution of samples is useful as a proposal density for importance sampling or for Markov chain Monte Carlo methods. In this paper, we focus on applications to sampling from multimodal posterior distributions in high dimensions. We first show that sampling from multimodal distributions is improved by computing all critical points instead of only minimizers of the objective function. For applications to high-dimensional geoscience inverse problems, we demonstrate an efficient approximate weighting that uses a low-rank Gauss-Newton approximation of the determinant of the Jacobian. The method is applied to two toy problems with known posterior distributions and a Darcy flow problem with multiple modes in the posterior.