An ensemble-transform Kalman filter: Full-waveform inversion scheme for uncertainty estimation
Résumé
Uncertainty Quantification is a major topic for most geophysical tomography techniques, in particular for large-scale problems. In this work, we present an original application of ensemble-based methods to Full Waveform Inversion. This approach relies on a deterministic Ensemble-Transform Kalman Filter borrowed from the Data Assimilation community, and a frequency-domain Full Waveform Inversion. This methodology gives access to a low-rank version of the posterior covariance matrix of our inverse problem, thanks to the ensemble repartition. We can thus extract information from this covariance matrix to assess uncertainty in the Bayesian sense. This proof-of-concept is applied to a 2D Marmousi case, before discussing many questions associated with the design of the scheme.