Several techniques have been proposed over the years for automatic hypocenter localization. While those techniques have pros and cons that trade-off computational efficiency and the susceptibility of getting trapped in local minima, an alternate approach is needed that allows robust localization performance and holds the potential to make the elusive goal of real-time microseismic monitoring possible. Physics-informed neural networks (PINNs) have appeared on the scene as a flexible and versatile framework for solving partial differential equations (PDEs) along with the associated initial or boundary conditions. We develop HypoPINN -- a PINN-based inversion framework for hypocenter localization and introduce an approximate Bayesian framework for estimating its predictive uncertainties. This work focuses on predicting the hypocenter locations using HypoPINN and investigates the propagation of uncertainties from the random realizations of HypoPINN's weights and biases using the Laplace approximation. We train HypoPINN to obtain the optimized weights for predicting hypocenter location. Next, we approximate the covariance matrix at the optimized HypoPINN's weights for posterior sampling with the Laplace approximation. The posterior samples represent various realizations of HypoPINN's weights. Finally, we predict the locations of the hypocenter associated with those weights' realizations to investigate the uncertainty propagation that comes from those realisations. We demonstrate the features of this methodology through several numerical examples, including using the Otway velocity model based on the Otway project in Australia.
Full waveform inversion enables us to obtain high-resolution subsurface images. However, estimating the associated uncertainties is not trivial. Hessian-based method gives us an opportunity to assess the uncertainties around a given estimate based on the inverse of the Hessian, evaluated at that estimate. In this work we study various algorithms for extracting information from this inverse Hessian based on a low-rank approximation. In particular, we compare the Lanczos method to the randomized singular value decomposition. We demonstrate that the low-rank approximation may lead to a biased conclusion.
Reservoir characterization is a critical component in any oil and gas, geothermal, and CO 2 sequestration project. A fundamental step in the process of characterizing the subsurface is represented by the inversion of petrophysical parameters from seismic data. However, this problem suffers from various uncertainty sources originating from inaccuracies in the measurements, modeling errors, and complex geological processes. Moreover, the non-linearity of the rock-physics model and Zoeppritz equation that constitute the modelling operator, further complicates the inversion process. In this work, we propose a novel data-driven approach where well-log information is used to obtain optimal basis functions that link band-limited petrophysical reflectivities to pre-stack seismic data. Subsequently, the inversion of such band-limited reflectivities for petrophysical parameters is framed in a Bayesian framework where a generative adversarial network is used to produce a geologically realistic prior distribution. The trained prior distribution is updated using the Stein Variational Gradient Descent and a set of representative solutions is produced that is consistent with the uncertainties in the data and the nonlinear operators.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.