Uncertainty Quantification of Seismic Imaging Using Neural Posterior Principal Components

Seismic hazard assessment and engineering planning rely on accurate velocity images of Earth’s interior derived from travel-time data. Yet nonlinear wave physics, uneven station coverage, and the ill-posed inverse problem mean existing methods often return point estimates with little spatially resolved uncertainty. We propose a two-stage learning framework that combines a restoration network for predicting posterior-mean velocity images with a Neural Posterior Principal Components (NPPC) wrapper that learns low-dimensional modes of posterior variability. This adaptation of NPPC to seismic tomography produces uncertainty maps that explicitly link uncertainty structure to data coverage and acquisition geometry. On synthetic transmission and random-geometry datasets, our approach yields velocity images consistent with held-out data and uncertainty maps that expose stable versus underconstrained regions, offering the first spatially interpretable, data-driven uncertainty quantification framework for seismic travel-time tomography.