Uncertainty Quantification for Travel-Time Tomography Using Deep Operator Networks With Randomized Priors

Seismic travel-time tomography is an effective approach for exploring subsurface structures. In recent years, machine learning (ML) has been successfully applied in seismic travel-time tomography; however, the uncertainty quantification of predictive outputs has been less frequently addressed. To tackle these challenges, we adopt the deep ensemble of deep operator networks with randomized priors (DERP-DON) for travel-time tomography, based on measured travel-time data from surface and cross-well measurements. Deep ensembles provide informative uncertainty estimates, and the incorporation of randomized priors allows the network model to offer more conservative uncertainty quantification. Through numerical experiments, we demonstrate that DERP-DON can provide reasonable and conservative uncertainty estimates while accurately inferring the velocity field. Notably, DERP-DON is particularly effective in offering meaningful uncertainty estimates for out-of-distribution data.