Uncertainty quantification of FWI solutions using sequential local ensemble transform Kalman filter for full waveform data

SUMMARY Full waveform inversion (FWI) has enjoyed increased attention in the past decade, becoming the state of the art for estimating parameters influencing wave propagation in a medium. However, only a few recent emerging efforts have attempted to tackle the challenge of uncertainty quantification in FWI. In this study, we suggest joining FWI with the Bayesian approach, where we provide a post-processing step with an advantageous starting point defined by the global minimum stemming from a deterministic FWI algorithm. Then, using the local ensemble transform Kalman filter (LETKF), we obtain the uncertainty as a follow-up step to the FWI procedure. Within a probabilistic Bayesian inversion framework, the LETKF uses local seismic data to update sets of variables in the subsurface domain. Seismic data for each shot and receiver in the time-domain is in this way matched with subsurface layers, and assimilated in a sequential manner. The methodology is showcased on a realistic model of the Gullfaks field in the North Sea, where we study effects of various seismic acquisition design set-ups, algorithm and model parameter settings. We investigate how these acquisition designs and parameters influence the uncertainty reduction and bias of the inversion results. We highlight the importance of studying statistical performance metrics to ensure a balance between bias and underestimation of uncertainty.