Abstract: High dimensionality, complex physics, and lack of access to the ground truth make seismic imaging one of the most challenging inversion problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks conducted on these images. By making use of a Markov-chain Monte Carlo (McMC) sampling technique, we demonstrate how uncertainty in the data can be propagated to the task of seismic horizon tracking. While this example shows that uncertainty can in principle be handled in a systematic manner by using neural nets as deep priors, it unfortunately also reveals that the McMC method fundamentally lacks ability to scale to relevant problem sizes. To overcome this shortcoming, we introduce a variational formulation based on normalizing flows. In this approach, invertible neural networks are trained to generate samples from the posterior. There are strong indications that this approach has the capability to scale better to problems where the forward operator is expensive to evaluate.
This is joint work with Ali Siahkoohi, Mathias Louboutin, and Gabrio Rizzuti.
Felix J. Herrmann graduated from Delft University of Technology in 1992 and received his Ph.D. in engineering physics from that same institution in 1997. After research positions at Stanford University and the Massachusetts Institute of Technology, he became back in 2002 faculty at the University of British Columbia. In 2017, he joined the Georgia Institute of technology where he is now a Georgia Research Alliance Scholar Chair in Energy, cross-appointed between the Schools of Earth & Atmospheric Sciences, Computational Science & Engineering, and Electrical & Computer Engineering. His cross-disciplinary research program spans several areas of computational imaging including seismic, and more recently, medical imaging. Dr. Herrmann is widely known for tackling challenging problems in the imaging sciences by adapting techniques from randomized linear algebra, PDE-constrained and convex optimization, high-performance computing, machine learning, and uncertainty quantification. Over his career, he has been responsible for several cost-saving innovations in industrial time-lapse seismic data acquisition and wave-equation based imaging. In 2019, he toured the world presenting the SEG Distinguished Lecture “Sometimes it pays to be cheap – Compressive time-lapse seismic data acquisition”. In 2020, he was the recipient of the SEG Reginald Fessenden Award for his contributions to seismic data acquisition with compressive sensing. At Georgia Tech, he leads the Seismic Laboratory for Imaging and modeling and he is co-founder/director of the Center for Machine Learning for Seismic (ML4Seismic), designed to foster industrial research partnerships to drive innovations in artificial-intelligence assisted seismic imaging, interpretation, analysis, and time-lapse monitoring.