A Discrete Synthetic Benchmark for PCA-Ridge and Reference-Ray 3-D Velocity Reconstruction from First-Arrival Travel Times

Abstract

Learned methods for seismic travel-time tomography are usually compared with physics-based inversion on benchmarks whose representation and evaluation choices are left implicit. We show that the apparent workflow ordering depends materially on the declared representation choices, not only on the estimator. The benchmark reconstructs 3-D P-wave velocity from first-arrival travel times: 250 synthetic geological targets in five families, 384 source–receiver observations each, split 175/37/38 by target, with travel times from a Fast-Sweeping calculation on a 1.25 km grid and errors measured against analytic velocity at 2.5 km cell centers. With the corpus and endpoint fixed, the declared identifier-ordered principal component analysis ridge (PCA-ridge) workflow gives root-mean-square error of 0.353 km/s, geometry-canonical re-ordering with penalty reselection gives 0.310 km/s, and a cell-native parameterization gives 0.261 km/s, against 0.272 km/s for an intentionally non-equivalent reference-ray baseline (the cell-native paired interval spans zero); a small neural network in place of the linear map gives 0.352 km/s. The main reported comparison, retrospectively designated and descriptive, is a paired difference of +0.0816 km/s (95% percentile-bootstrap interval [+0.0492, +0.120] km/s) favoring the baseline. Benchmarks should therefore declare encoding and parameterization explicitly. Conclusions are conditional on the declared operator and representation, and establish no field-scale accuracy or universal method ranking.