Test 03 — Is there a day/night difference in the b-value?
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
README.md
# Test 03 — Is there a day/night difference in the b-value? **Hypothesis tested.** The notebook reports a higher Gutenberg–Richter b-value at night (b = 1.272) than by day (b = 1.167) in a Japan box, **+0.105, z = 4.36**, and states that the mechanism is not explained. The suggested explanation — better night-time detection lowering the magnitude of completeness — was rejected inside the notebook because Mc moved the *wrong way* (higher at night). **Verdict: the difference reproduces exactly, and it is an artefact of the method.** b is estimated above a completeness threshold, so the answer depends on which threshold is used. The notebook estimated Mc separately in each stratum with maximum curvature, a mode estimator that moves in 0.1-magnitude steps; it landed on 4.4 for day and 4.5 for night. Give both strata the same Mc and the difference falls from +0.106 to **+0.0017** (z = +0.08). There is no day/night effect to explain. ## Result ### 1. The published numbers reproduce | Stratum | Mc (own) | N | b | |---|---:|---:|---:| | Day, 06–18 JST | 4.4 | 5,329 | 1.167 | | Night, 18–06 JST | 4.5 | 4,830 | 1.272 | | Difference | | | +0.106 | These match the notebook's 1.167 (N = 5,329) and 1.272 (N = 4,830) to three decimals, from an independently pulled catalogue. The published result is not a data error. ### 2. One threshold instead of two | Stratum | Mc (shared) | N | b | |---|---:|---:|---:| | Day | 4.4 | 5,329 | 1.1668 | | Night | 4.4 | 5,876 | 1.1685 | | Difference | | | **+0.0017** (SE 0.0221, z = +0.08) | The entire published effect comes from the 0.1-magnitude offset between the two Mc estimates. The sweep below moves the night Mc in 0.1 steps and shows Δb tracking it almost exactly: | Night Mc offset | b(night) | Δb | z | |---:|---:|---:|---:| | -0.1 | 1.0411 | -0.1256 | -6.16 | | +0.0 | 1.1685 | +0.0017 | +0.08 | | +0.1 | 1.2723 | +0.1055 | +4.34 | | +0.2 | 1.3254 | +0.1586 | +5.88 | | +0.3 | 1.3107 | +0.1439 | +4.83 | ### 3. It replicates in five other regions Same test, independent catalogues, each with a single shared Mc: | Region | Mc | N day | N night | b day | b night | Δb (common Mc) | z | Δb (separate Mc) | |---|---:|---:|---:|---:|---:|---:|---:|---:| | japan | 4.4 | 5,329 | 5,876 | 1.167 | 1.168 | +0.0017 | +0.08 | +0.105 | | chile | 4.3 | 3,153 | 3,403 | 1.326 | 1.324 | -0.0019 | -0.06 | -0.002 | | california | 3.5 | 816 | 999 | 0.975 | 0.997 | +0.0216 | +0.46 | -0.039 | | iceland | 4.5 | 74 | 101 | 1.509 | 1.616 | +0.1068 | +0.45 | +0.107 | | newzealand | 4.3 | 707 | 753 | 1.223 | 1.122 | -0.1006 | -1.63 | -0.101 | | oklahoma | 2.5 | 3,866 | 3,570 | 1.084 | 1.092 | +0.0081 | +0.32 | +0.008 | With a common Mc no region reaches |z| = 2; with separate Mcs several differences appear that are not there under a consistent threshold. ### 4. The rate by hour is flat enough that a real cycle would be surprising χ² over 24 hourly bins = 30.5, df = 23, p = 0.13. Earthquake origin times in this catalogue are effectively uniform across the local day, which is what a tectonic catalogue should look like: faults do not know what time it is. The b-value difference never had a mechanism because there was never a signal. ### 5. Declustered, still nothing Removing aftershocks within three days and 0.1 magnitude of a larger event leaves 7,920 events: Δb = -0.0367, z = -1.39. ## Why the original reasoning could not see this The notebook checked one consequence of detection bias (Mc should fall at night) and, finding it did not, concluded the mechanism was something else. But separate Mc estimation is a *second* channel through which detection differences enter the estimate, and moving Mc *up* also moves b *up* when the extra events are the small ones. The test that separates the two is not "did Mc move the way I expected" but "does the result survive one threshold for both strata". ## What this test cannot see This says nothing about whether real day/night differences exist in *induced* seismicity or in catalogues built from human reports; it tests the Japan tectonic catalogue only. A regional network with magnitude-dependent daytime noise could still produce a genuine effect at low magnitudes, which the common-Mc test at M >= 4.4 would miss by design. The b estimator itself (Aki maximum likelihood with Utsu binning) is standard but sensitive to magnitude rounding. ## Files `run.py` reproduces everything from `../../data/quakes_japan.csv` and the other regional pulls; `data.csv` is the per-region summary; `results.json` holds every number above.
hypothesis.md
# Hypothesis — Is there a day/night difference in the b-value? ## The claim as published The notebook's `seismicity/DIURNAL.md` reports, in a Japan box (30–46°N, 128–146°E) with M ≥ 3.5 for 2010–2025: | Window | Mc | N | b | SE | |---|---:|---:|---:|---:| | Day (06–18 JST) | 4.4 | 5,329 | 1.167 | 0.016 | | Night (18–06 JST) | 4.5 | 4,830 | 1.272 | 0.018 | Difference (night − day): **+0.105 ± 0.024, z = 4.36**, described as "significant and the mechanism is not". ## The decisive comparison, fixed in advance **Decisive comparison, fixed in advance:** b is estimated above a magnitude of completeness. The question is whether the day/night difference survives when both strata use the *same* Mc. - **Support for a real effect**: the difference remains ≥ 0.05 with one shared Mc, and the same sign appears in independent regions. - **Refute (method artefact)**: the difference falls below 0.05 with one shared Mc, and a sweep of the night Mc by 0.1 reproduces the published value exactly. A secondary prediction: if a real diurnal process existed, origin times would also depart from uniform, so a χ² test over 24 hourly bins is reported as context. ## Support and refutation No separate support criteria: the decisive comparison above is the criterion.