When a shear wave crosses rock whose fabric is directionally organised, most often mantle olivine combed into alignment by flow, it splits into a fast and a slow component. Measuring the two parameters, the fast-polarisation azimuth and the delay time accumulated along the path, is a mature craft [1,3], and dense maps of those measurements are among the most direct observables of mantle deformation we have.
They are also, increasingly, training labels. The temptation in a data-driven era is to pour every published or automatically computed measurement into a set and let the model sort it out. That is a mistake, and not for the reason people expect. Splitting measurements vary enormously in reliability: some rest on clean waveforms with a well-defined result, others are marginal, method-dependent, or genuinely null. A model trained on the mixture does not merely inherit noise. It learns to be confident where it should not be, which is the failure mode that survives validation.
Three gates, in order
A measurement earns label status by clearing three gates in sequence.
The quality grade scores waveform signal-to-noise and the linearity of the corrected particle motion, on the principle that a well-resolved split, once corrected, collapses two-component motion to a straight line. The cross-method gate runs two independent estimators on the same event, a rotation-correlation method and a transverse-energy-minimisation method, and asks them to agree within tolerance in both parameters. Agreement is strong evidence the result is real rather than an artefact of one estimator's assumptions; disagreement is a documented red flag [2]. The confidence gate then requires the formal error on the pair to be tighter than a threshold, because a measurement can be plausible on both earlier tests and still carry an error wide enough to teach a model to smear its own predictions.
Measurements clearing all three become trusted labels. The interesting question is what happens to the rest.
- Trusted labels
- 61%
- Informative nulls
- 24%
- Training mean delay
- 0.746
- Raw stream mean delay
- 0.787
| class | count | share of the stream | in the training set |
|---|---|---|---|
| trusted labels | 245 | 61% | yes |
| informative nulls | 96 | 24% | yes |
| rejected | 59 | 15% | no |
The expected trade, and the one underneath it
Tighten any of the three gates and the aqua population shrinks. At the default thresholds 61% of the stream clears all three, which sits inside the 55% to 65% band our note gives as illustrative, and pulling the confidence ceiling from 0.36 to 0.22 cuts that to 30%. This is the trade everyone knows they are making: yield for reliability, and the right operating point depends on what the labels feed. A screening model tolerates a looser policy than one whose outputs feed a stress inversion.
Now use the fourth control, which is not a gate at all. Drop the null class.
No threshold moved. No measurement was recomputed. The trusted share is exactly what it was. What changes is the base of the distribution: 24% of the stream, the zero-delay observations, leaves the training set, and the mean delay time the model sees, the point where the distribution balances, climbs by 32% against the raw stream. Keep the nulls and that shift stays within 5%.
That is the finding worth carrying out of this piece. A null is not a failed measurement. It is a successful observation that the rock along this path is not measurably anisotropic, and it is often as scientifically important as a strong split. Silently dropping nulls biases the training distribution toward strongly anisotropic regions and teaches a model that nulls do not occur, which is precisely the belief that makes a model confidently wrong in the places where the honest answer was nothing.
Why a null fails the gates for an honest reason
The gates do not reject nulls out of carelessness. A null has no split to resolve, so the two estimators have nothing to agree about and the formal error on a parameter pair that does not exist is wide. Every property that makes a null fail a quality test is a real physical consequence of there being no anisotropy to measure. This is exactly why a policy that silently discards failures discards mostly nulls, and why the discard is invisible: each individual rejection looks defensible.
The cure is cheap, which is the good news. Route failures to an explicit class rather than to nothing. The distinction the exhibit draws between an informative null and a rejected marginal measurement is the one a policy needs to encode, and it costs a label field, not a new method.
What still has to be calibrated
The thresholds are not physics and should not be set by fiat. Every one of them trades quantity for quality at a rate that depends on the instrument, the region and the estimator implementations, so they belong in the same category as any other hyperparameter: validated against a hand-curated gold set, and re-validated when the data source changes. A poorly calibrated gate rejects good labels or admits bad ones, and neither failure announces itself in a training curve.
Two limits are worth stating plainly. The gate thresholds in the exhibit are illustrative and the measurement stream behind it is synthetic, built to reproduce the bands our research note states rather than drawn from a catalogue. And a labelling policy is a modelling decision, not a preprocessing detail: it belongs in the paper, with its thresholds reported, not in a script nobody reads.
Key takeaways
- A splitting measurement is not ground truth until it has cleared a quality grade, agreement between two independent estimators, and a confidence ceiling on its formal error.
- Tightening any gate trades yield for reliability: at the default thresholds 61% of the stream survives as trusted labels, and a tighter confidence ceiling cuts that to 30%.
- A measurement that fails is usually a null, which is a real observation that a path is not measurably anisotropic, not a failed one.
- Dropping the null class moves the training set's mean delay time by 32% without changing a single measurement. Keeping it holds the shift within 5%.
- A null fails the gates for honest physical reasons, which is why discarding failures is invisible: each rejection looks individually defensible.
- Gate thresholds are hyperparameters and belong in the paper with their values reported, validated against a hand-curated gold set rather than fixed by fiat.
References
- P. G. Silver, W. W. Chan. Shear wave splitting and subcontinental mantle deformation. Journal of Geophysical Research, 96, 16429 to 16454, 1991. doi:10.1029/91JB00899
- A. Wüstefeld, G. Bokelmann. Null detection in shear-wave splitting measurements. Bulletin of the Seismological Society of America, 97, 1204 to 1211, 2007. doi:10.1785/0120060190
- M. D. Long, P. G. Silver. Shear wave splitting and mantle anisotropy: measurements, interpretations, and new directions. Surveys in Geophysics, 30, 407 to 461, 2009. doi:10.1007/s10712-009-9075-1
