Null-space and statistical significance of first-arrival traveltime inversion
Bibliographic record
Abstract
The strong uncertainty inherent in the traveltime inversion of first arrivals from surface sources is usually removed by using a priori constraints or regularization. This leads to the null-space (data-independent model variability) being inadequately sampled, and consequently, model uncertainties may be underestimated in traditional (such as checkerboard) resolution tests. To measure the full null-space model uncertainties, we use unconstrained Monte Carlo inversion and examine the statistics of the resulting model ensembles. In an application to 1-D first-arrival traveltime inversion, the τ–p method is used to build a set of models that are equivalent to the IASP91 model within small, ∼0.02 per cent, time deviations. The resulting velocity variances are much larger, ∼2–3 per cent within the regions above the mantle discontinuities, and are interpreted as being due to the null-space. Depth-variant depth averaging is required for constraining the velocities within meaningful bounds, and the averaging scalelength could also be used as a measure of depth resolution. Velocity variances show structure-dependent, negative correlation with the depth-averaging scalelength. Neither the smoothest (Herglotz–Wiechert) nor the mean velocity-depth functions reproduce the discontinuities in the IASP91 model; however, the discontinuities can be identified by the increased null-space velocity (co-)variances. Although derived for a 1-D case, the above conclusions also relate to higher dimensions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.056 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".