Julien Thurin: Using the Ensemble Kalman filter for Uncertainty Estimation in FWI
Julien Thurin, postdoctoral fellow at University of Alaska at Fairbanks, presents "Dynamic tool for a static problem: Using the ensemble Kalman filter for uncertainty estimation in Full Waveform Inversion" at the MIT Earth Resources Laboratory.
"Full Waveform Inversion (FWI) is an ill-posed non-linear inverse problem, aiming at recovering detailed pictures of subsurface physical properties, which are crucial to explore and understand Earth structures. Classically formulated as a least-squares optimization scheme, FWI yields a single subsurface model amongst an infinite possibility of solutions. With the general lack of systematic and scalable uncertainty estimation, this formulation makes the interpretation of FWI's outcomes complex.
I will present an unconventional, scalable way of tackling the lack of uncertainty estimation in FWI, thanks to data assimilation ensemble methods. Our method ought to combine classical FWI and the Ensemble Transform Kalman Filter (ETKF-FWI) and has been successfully applied on 2-D test cases. This scheme takes advantage of the theoretical common ground between least-squares optimization methods and Bayesian filtering. It allows recasting FWI in a local Bayesian inference framework, thanks to the ensemble representation. The ETKF-FWI provides high-resolution subsurface tomographic models and yields a low-rank approximation of the posterior covariance, holding the uncertainty and resolution information of the proposed solution. We show how the ETKF-FWI can be applied to evaluate uncertainty and resolution of the solution. Instead of providing a single solution, the filter yields an ensemble of models from which statistical information can be inferred."
Julien Thurin holds a Bachelor's degree from the University of Nice - Sophia Antipolis, and a Master's and Doctorate from the University of Grenoble-Alpes. He is now Postdoctoral Fellow at the Geophysical Institute of the University of Alaska Fairbanks within the Seismology & Geodesy group.