Generalised Central-Difference Time-Lapse Full-Waveform Inversion with Bayesian Analysis

This work introduces a generalised central-difference time-lapse Full-Waveform Inversion (FWI) aiming to mitigate time-lapse (4D) noise. Our proposal replaces the conventional arithmetic mean with the generalised Hölder mean, providing a more robust and flexible centrality measure. The Hölder generalised mean works with different levels of regularity in FWI models, reducing time-lapse noises that come from non-repetibility issues. Bayesian statistical methods enhance precision in determining Hölder mean weights and generalisation factors. This generalisation allows flexible averaging, emphasising individual values to different degrees. Applying this approach to seismic reservoir monitoring, we consider the Marmousi acoustic velocity model and a sparse ocean-bottom node (OBN) geometry. The resulting model from our proposal exhibits superior detail compared to traditional methods, emphasising the efficacy of the generalised central-difference approach. Besides, Bayesian analyses highlight a deviation from conventional norms, challenging the optimality of the arithmetic mean in time-lapse problems.