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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".