A comparison of rank-reduction strategies for uncertainty estimation in full-waveform inversion

SUMMARY Full-waveform inversion has been broadly adopted for acoustic and elastic media, but it lacks widely accepted methods for robust uncertainty quantification. This lack is in part due to an absence of assessment of proposed uncertainty quantification strategies. Here, we investigate four relatively inexpensive uncertainty estimation approaches based on truncated singular value decomposition of the inverse problem Hessian and its inverse. We numerically test these approaches across a range of parameter scales and application problems. We find that uncertainty estimates based on truncated singular value decomposition of the Hessian outperform those based on singular values of the inverse Hessian, due to both favourable singular value spectra of the former, and the greater ease of sampling the Hessian.