{"ID":2879192,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.17122","arxiv_id":"2508.17122","title":"HV Metric For Time-Domain Full Waveform Inversion","abstract":"Full-waveform inversion (FWI) is a powerful technique for reconstructing high-resolution material parameters from seismic or ultrasound data. The conventional least-squares (\\(L^{2}\\)) misfit suffers from pronounced non-convexity that leads to \\emph{cycle skipping}. Optimal-transport misfits, such as the Wasserstein distance, alleviate this issue; however, their use requires artificially converting the wavefields into probability measures, a preprocessing step that can modify critical amplitude and phase information of time-dependent wave data. We propose the \\emph{HV metric}, a transport-based distance that acts naturally on signed signals, as an alternative metric for the \\(L^{2}\\) and Wasserstein objectives in time-domain FWI. After reviewing the metric's definition and its relationship to optimal transport, we derive closed-form expressions for the Fréchet derivative and Hessian of the map \\(f \\mapsto d_{\\text{HV}}^2(f,g)\\), enabling efficient adjoint-state implementations. A spectral analysis of the Hessian shows that, by tuning the hyperparameters \\((κ,λ,ε)\\), the HV misfit seamlessly interpolates between \\(L^{2}\\), \\(H^{-1}\\), and \\(H^{-2}\\) norms, offering a tunable trade-off between the local point-wise matching and the global transport-based matching. Synthetic experiments on the Marmousi and BP benchmark models demonstrate that the HV metric-based objective function yields faster convergence and superior tolerance to poor initial models compared to both \\(L^{2}\\) and Wasserstein misfits. These results demonstrate the HV metric as a robust, geometry-preserving alternative for large-scale waveform inversion.","short_abstract":"Full-waveform inversion (FWI) is a powerful technique for reconstructing high-resolution material parameters from seismic or ultrasound data. The conventional least-squares (\\(L^{2}\\)) misfit suffers from pronounced non-convexity that leads to \\emph{cycle skipping}. Optimal-transport misfits, such as the Wasserstein di...","url_abs":"https://arxiv.org/abs/2508.17122","url_pdf":"https://arxiv.org/pdf/2508.17122v1","authors":"[\"Matej Neumann\",\"Yunan Yang\"]","published":"2025-08-23T19:28:47Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}