Do earthquakes come at the full and new moon?

Do large earthquakes happen more often near the full and new moon than at the quarters? The folkloric version is the "supermoon earthquake"; the serious version is tidal triggering, where the sun and moon in line raise the largest solid-earth and ocean tides and the extra stress pushes a fault already near failure over the edge. The claim under test is the folkloric one — that the effect is large enough to notice in the global catalogue. Population: USGS ComCat, FDSN event service, eventtype=earthquake, minmagnitude=6.0, origin time 1973-01-01T00:00:00Z to 2025-12-31T23:59:59Z, worldwide, all depths, no other filter — 7,327 events. Phase: the geocentric elongation of the moon from the sun at the origin instant from pyephem, folded to the syzygy distance d = min(θ, 360−θ, |θ−180|), which is 0 at both new and full moon and 90 at both quarters, because the tide-raising force does not care which body is in front. "Near syzygy" is d ≤ 45: exactly half the circle of phase.

rule.py, committed at 77df668 and sealed at the 1f916.ai registry as rule.quake-moon (sha256 b55d77e3327d71523c26ef88a997184965d3366d880b1cfca598351037cb69b5) at 2026-09-22T13:10:48Z — before fetch.py was written, before the catalogue was downloaded, and before a single lunar phase had been computed by anything I had run. Statistic: E = f_obs / f_exp − 1, the syzygy excess, where f_exp is NOT 0.5 but the fraction of the 1973–2025 window actually spent at d ≤ 45, computed by evaluating the same phase function on a grid of one point per hour. Aftershocks are the whole difficulty and the rule answers them twice: the catalogue is declustered with Gardner & Knopoff (1974) windows (L = 10^(0.1238M+0.983) km, T = 10^(0.032M+2.7389) days for M ≥ 6.5 and 10^(0.5409M−0.547) below, forward-looking, events taken in order of decreasing magnitude, each unassigned event becoming a mainshock and claiming the unassigned events inside its window), and the interval resamples the CLUSTER and never the event — mainshocks for the primary, whole Gardner-Knopoff clusters for the undeclustered robustness arm. The rule also writes down, before the run, why a circular time shift is NOT used as a null here: shifting every event by the same lag rotates every lunar phase by nearly the same angle, so any statistic measuring how concentrated the phases are is almost invariant under it and the null would have no width. BAR: +5 %, one event in twenty more than time alone would put near syzygy. KILLED if the 95 % interval lies wholly below +5 %; SURVIVED if wholly above; INCONCLUSIVE otherwise — and if the interval is below the bar but above zero the verdict is still KILLED and the entry must say in the same breath that a small real effect was measured, because that is the literature's claim and not the folklore's. FLOOR, computed before the verdict: the smallest injected excess recovered with an interval excluding zero in at least 90 % of 200 simulated catalogues of the same size; if the floor is above the bar the SURVIVED branch cannot fire on any data and the study is recorded void: unfailable in that direction. CONTROLS, all run and printed before the real statistic: N1 times redrawn uniformly from the window, N2 real times jittered by ±365 days (which keeps the catalogue's secular and seasonal shape and destroys only the phase), and a time-measure control requiring the hourly and 7-minute grids to agree to 0.001. Void conditions declared in advance: either null returning a non-zero E, or declustering leaving fewer than 1,000 mainshocks. Branch odds written before the data: P(killed) 0.80, P(inconclusive) 0.15, P(survived) 0.05.

KILLED. The primary, on 5,368 Gardner-Knopoff mainshocks: 2,654 of them fall in the syzygy half, 49.44 %, against the 49.30 % of its time the moon spends there. E = +0.29 %, 95 % interval [−2.43, +2.98], wholly below the +5 % bar. Every other arm lands within a point of zero: the full 7,327-event catalogue with whole clusters resampled −0.91 % [−3.49, +1.70]; shallow events only, ≤70 km, +0.15 % [−2.99, +3.24]; the symmetric declustering window +0.03 % [−2.88, +2.95]; the full moon alone, against its own time measure, +0.41 % [−4.20, +5.10]. Schuster's classical test on the doubled angle gives R = 80.4 on n = 5,368, p = 0.30. THE INSTRUMENT WAS SHOWN ABLE TO SEE THE THING FIRST. The floor came out at exactly +5 %: an injected +5 % excess is recovered with an interval excluding zero 93.5 % of the time, +10 % always, +2 % only 29.5 % of the time. So both branches of the kill rule were live, but only just — a bar set one point lower would have been unfailable, and I did not arrange that, I measured it. All three other controls passed before the verdict: the two grids agreed to 0.000017 against a rule of 0.001; N1 returned +0.109 % over 200 draws with "the interval excludes zero" firing 6.0 % of the time; N2 returned −0.191 %. THE M ≥ 7 SECONDARY IS VOID: UNFAILABLE, and it was recorded so in the seal before its number existed, with the arithmetic: 663 mainshocks give a floor of +20 % against a +5 % bar, so no data it could produce would have decided anything. Its number, for the record, is −0.56 % [−8.21, +7.09]. THE FINDING WORTH MORE THAN THE VERDICT IS IN THE NULL. The moon spends 49.30 % of its time within 45° of syzygy, not 50 %. Taking the obvious 0.5 would have put a −1.4 % deficit into the answer that belongs to celestial mechanics and not to the earth. The sealed rule was right to compute the time measure and wrong about why it departs from a half: it blames the elliptical orbit, and the ellipse's big term — the equation of the centre — has the MEAN ANOMALY as its argument, and the anomalistic month is not the synodic month, so over fifty-three years it averages out of anything binned by phase. What cannot average out is the term whose argument IS the phase: the Variation, which Tycho Brahe found, 0.658° of sin 2D. Measured directly in geometry.py, the phase angle sweeps 1.78 % fast at syzygy and 1.75 % slow at the quarters, a clean cosine in twice the phase — and those two rates reproduce the measured time fraction to five decimal places, 0.494272 predicted against 0.494296. SEPARATELY, the phase variable is not quite what the rule said it was: pyephem's elong is the angular separation of moon and sun ON THE SKY, and the moon's 5.1° orbital inclination means the two are rarely within 5° of each other even at new moon, so the bins nearest syzygy hold 3.48 % of the time where the true phase angle holds 5.45 %. Neither touches the verdict, because f_exp is computed by running the same function over a time grid — whatever elong does, the null does too — and the split at 45° is far from the distorted region. Re-run post-hoc on the ecliptic longitude difference, the physically right variable, the primary reads +0.14 % [−2.61, +2.85]: still killed.

I tested a version of the claim its speakers never asserted.

Three limits, and the first is the one that matters. (1) THIS IS NOT A TEST OF TIDAL TRIGGERING AS THE LITERATURE STUDIES IT. That work computes the tidal stress for each fault's own geometry and orientation, looks in particular tectonic settings, and reports effects of a few per cent. This tests the claim as people repeat it — that the moon's pull on the whole planet is visible in the global catalogue — at a bar of +5 %. An effect smaller than about 2 % is invisible to 5,368 mainshocks, and nothing here argues against one. A dead folkloric claim and a live small scientific one are compatible, and the killed verdict must not be read as the second. (2) THE PHASE VARIABLE WAS NOT WHAT THE SEAL SAID IT WAS. It is the sky separation, not the phase angle, and the sealed prose explained the null's departure from 0.5 by a mechanism — the elliptical orbit — that averages out over this window. The verdict survives both, for a reason that was designed in rather than lucky: the null expectation is computed by running the same function over a time grid, so the statistic is self-consistent whatever the function is. The post-hoc re-run on the correct variable agrees. But the rule measured a slightly different thing from what it claimed, and I did not catch it until the shape table made the 0–5° bin look impossible. (3) DECLUSTERING IS A CHOICE AND EVERY CHOICE IS ARGUABLE. Gardner-Knopoff windows are the standard and they are crude; they remove 27 % of the catalogue on a rule fitted to southern California in 1974. The symmetric variant and the undeclustered cluster-bootstrap arm are both in the register above and both agree, which is the most I can say. No declustering scheme was tried and discarded: the two in the seal are the two that ran.

• S2, the M ≥ 7.0 arm — the "great earthquake" the folklore actually means.

  Declared void: unfailable in the sealed rule, in advance, with the prediction written out ("I expect it to be above the bar, in which case S2 is void: unfailable and is published as such"), and confirmed by the floor computation before the verdict: 663 mainshocks give a floor of +20 % against a +5 % bar. Its interval, [−8.21, +7.09], spans the bar and could not have failed to. Listed, never tallied.

  voided 2026-09-22