Shear-wave velocity from a phase-velocity dispersion curve

Inverts a fundamental-mode Rayleigh phase-velocity curve (the SASW/MASW observable) for a 70-layer 1-D Vs profile in one forward pass — no initial model. Proposed physically-coded transformer encoder–decoder (2.44 M params: period tokens in, depth-query tokens out) trained on OpenSWI-shallow (22 M curve/profile pairs).
Scale factor k

Site scale: the physics is scale-invariant — measured periods are multiplied by k to enter the model's 0.2–10 s band, and output depths are divided by k. Velocities are never rescaled (support ≈ 0.3–4.5 km/s at any scale). Examples are native-scale; k applies to uploaded/pasted curves only. Picks are snapped to the nearest of the 100 grid periods; gaps and band-limited curves are handled natively.
Example (native scale, k = 1)
0.20000000298023224 10
0.20000000298023224 10
  • Model: physically-coded encoder–decoder (paper3): each dispersion pick is a token carrying its physical period; each output depth is a query token carrying its physical depth, reading the period tokens by masked cross-attention — band-limited and gappy curves are handled natively (no interpolation), and its learned attention reproduces the classical λ/3 sensitivity rule (paper3, Fig. 7).
  • Checkpoint: v4 finalist (valid masked MSE 0.0216 (km/s)²); test accuracy 0.151 km/s full-profile RMSE / 6.0 % MAPE / R² 0.949 on 50 k held-out samples; Long Beach field data 38 m/s MAE vs the tomographic reference (5,297 real curves).
  • Scope: trained on 0.2–10 s periods, 0–2.76 km depth, Vs ≈ 0.3–4.5 km/s (OpenSWI-shallow). Curves outside this envelope — e.g. soft-soil sites with Vs < 0.3 km/s — are out of distribution.
  • Site scale factor k: the elastodynamic problem is scale-invariant, so a high-frequency engineering curve is inverted by stretching its periods ×k into the training band and shrinking the output depths ÷k (e.g. k = 100 → 70 layers over 0.4–27.6 m at 0.4 m spacing). Velocities are never rescaled — the ≈ 0.3–4.5 km/s support applies at every scale; see paper3 §6.2.