Full Waveform Inversion (FWI) is an ill-posed nonlinear inverse problem, which aims at recovering high-resolution geophysical subsurface models. This work focuses on the joint application of the Ensemble Transform Kalman Filter and Quasi-Newton Full Waveform Inversion (ETKF-FWI) on seismic-exploration field-data to estimate uncertainty. We reintroduce the ETKF-FWI formalism under a compact form and apply our scheme on a 2D line from the 3D OBC data from the North Sea Valhall field. This scheme allows us to express our solution as an ensemble of subsurface parameter models in a Bayesian formalism. The mean of the output ensemble yields a parameter estimation similar in quality to that of standard adjoint-based FWI, and the posterior covariance of the ensemble holds the uncertainty of the parameter estimation as well as resolution information. We show that both the uncertainty estimation and the resolution information are consistent with our understanding of the FWI problem. This application demonstrates the suitability of ETKF-FWI for uncertainty estimation in full waveform tomography beyond synthetic benchmarks.


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