The reported result
GeoFormer, a geometry-aware Transformer, recorded the lowest reported root-mean-square error (RMSE), an error measure used for first-arrival picks, on each of the four field datasets in the evaluation. Against a Vision Transformer, the reported RMSE was 1.73 versus 14.62 on Brunswick, 1.84 versus 14.23 on Halfmile, and 1.61 versus 14.39 on Dongbei, with errors expressed in time samples.
The tests used Brunswick, Halfmile, Lalor and Dongbei, with 1,541, 690, 905 and 10 shots, respectively. The share of traces with labels was 83.1%, 90.7%, 55.2% and 97.9%, respectively. Scores were calculated only from traces with valid labels, so the reported labeled-trace share was not the same at each site.
Putting geometry into the signal
Each seismic trace becomes a token that combines its waveform with four source-receiver coordinates. Offset and relative elevation are included as trace-level geometric attributes, producing the paper's five-dimensional representation.
The model injects that geometry at three points in the Transformer. GeomMLP works at the token level, GeomAdaLN at normalization, and GeomAttnBias at the attention stage. The paper compared GeoFormer with a Vision Transformer and two task-specific baselines, and also ran ablations that removed individual geometry mechanisms or all of them together.
First-arrival picking was treated as per-sample binary segmentation, trained with masked binary cross-entropy. A Nearest-Point Picking step then converted the predicted pattern into a first-arrival sample index. To limit information leakage, the split was made by shot, keeping every trace from a shot in one partition. Training, validation and test sets were approximately 80%, 10% and 10%, and all deep-learning models used identical splits.
Performance was summarized with hit rates at tolerances of 1, 3, 5, 7 and 9 time samples, alongside three error summaries: RMSE, MAE and MBE. Those calculations used only traces with valid labels.
A large gap, with a small-sample caveat
On Dongbei, the smallest dataset, GeoFormer had a hit rate of 80.9% within one time sample of the labeled arrival, and RMSE of 1.61. The Vision Transformer’s RMSE was 14.39. That comparison comes from 10 shots, compared with 1,541 at Brunswick, 690 at Halfmile and 905 at Lalor.
Lalor is a less tidy part of the picture. Its GeoFormer row reports RMSE of 5.32 time samples, while the reported GeoFormer values were 1.73 on Brunswick, 1.84 on Halfmile and 1.61 on Dongbei. The results nevertheless report GeoFormer as the lowest-RMSE method on every dataset.
The paper also includes qualitative examples with strong noise and missing traces. In those examples, GeoFormer was described as producing more continuous picking curves with fewer visible deviations than the baselines. The supplied result is qualitative rather than a quantitative noise-stratified estimate.
What the ablations show
On Halfmile, the full GeoFormer had RMSE of 1.84. After all geometry modules were removed, the reported figure was 10.30, a difference the paper described as a factor of 5.6. In the single-module tests, removing GeomMLP produced RMSE of 5.55 and was accompanied by a 4.7-percentage-point decrease in HR@1, while removing GeomAttnBias or GeomAdaLN produced RMSE of 2.87 and 2.90, respectively.
The reported numbers are point estimates from the comparison. No confidence intervals, significance tests or other uncertainty estimates were reported, and the metrics were calculated only on traces with valid labels.
Preprint status
GeoFormer is presented as a preprint, arXiv:2608.25668v1, dated 26 August 2026. The paper states that its code is available through a GitHub repository.
Paper data and sources
Original title: GeoFormer: Geometry-Aware Transformer and its application to 5D First-Arrival Picking
Authors: Tianxiang Gao, Jianwei Ma
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text