great-earthquakes-lunar-phase-statistics

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great-earthquakes-lunar-phase-statistics

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Statistical analysis of the largest earthquakes (M≥8.5, 365–2025) and their proximity to the four cardinal lunar phases. Shows a significant deficit of events in the lunar mid-cycle (4 observed vs 12 expected within 2.95 days). Includes offsets, binomial tests, and figures.

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- eclipses.py
- lunar-distance-m85.py
- lunar-phase-offset.py
- magnitude-trend.py
- phasenergy.py
- phasetype-offset.py
- phasetype.py
- 0365-2025-lunar-phases-m85p.txt
- 1904-2021-lunar-phases-m80p.txt
- 1904-2021-lunar-phases-m82p.txt
- eclipses.png
- lunar-distance-m85.png
- lunar-phase-offset.png
- magnitude-trend.png
- phasenergy.png
- phasetype-offset.png
- phasetype.png
LICENSE
README.md

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// repository documentation

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**Table of Contents**
- [Main result](#main-result-295-days-window)
- [By phase type](#by-phase-type)
- [Progressive strengthening](#progressive-strengthening)
- [Near-phase percentage and relative energy release](#near-phase-percentage-and-relative-energy-release)
- [Offsets by individual cardinal phase](#offsets-by-individual-cardinal-phase)
- [Lunar distance](#lunar-distance)
- [Eclipse conditions among syzygies](#eclipse-conditions-among-syzygies)
- [Implications for mechanism](#implications-for-mechanism)
- [The Moon as a stabilizer for Earth's environment](#the-moon-as-a-stabilizer-for-earths-environment)

This repository presents a statistical analysis of the temporal relationship between the largest known earthquakes (~ M ≥ 8.5) and the four cardinal lunar phases (New Moon, First Quarter, Full Moon, and Third Quarter). To our knowledge this study is unique due to the focus on these lunar phases and emphasis on magnitude dependence. The results and conclusion do not conflict with earlier studies, like Dr. Hough's 2018 study of M ≥ 8.0 earthquakes, but rather extend them.

The presented catalog spans more than 1,660 years, from the 365 CE Crete earthquake to the 2025 Kamchatka event, and comprises a total of 59 great earthquakes for which reliable origin times and well-constrained longitude-based UTC equivalents are available. Some events with unknown origin times are still included, such as the 869 Japan event, if their calendar date places them so close to a cardinal lunar phase that any plausible longitudinal offset keeps them firmly inside the pre-defined near-phase window. Lunar phases and geocentric distances were computed with the ELP-MPP02 theory as implemented in [Solpage](https://www.ssgeos.org/solpage.htm).

### Main result (±2.95 days window)

The central result is a clear deficit of events in the true mid-cycle between cardinal phases. Using a window of ±2.95 days around each of the four phases:

- 55 events fall inside the near-phase windows,
- only 4 events fall in the mid-cycle gaps.

Under the null hypothesis of temporal uniformity across the synodic month, approximately 47 and 12 events, respectively, would be expected. A one-sided binomial test yields p ≈ 0.0044. [See figure](/figures/lunar-phase-offset.png "lunar phase offsets").

| Category              | Observed | Expected |
|-----------------------|----------|----------|
| Near cardinal phase   | 55       | 47.2     |
| Mid-cycle             | 4        | 11.8     |
| **Total**             | **59**   | **59**   |

- One-sided binomial p-value (excess of near-phase events): **≈ 0.0044**
- Mean closest offset to nearest cardinal phase: **1.70 days**

### By phase type

Both syzygy (New/Full) and quadrature (First/Third Quarter) contribute to the near-phase excess; the data show a slight preference for syzygy (56%), but quadrature is well represented (44%). There's a minimal tendency for events to occur before (29) rather than after (26) the nearest cardinal phase. [See figure](/figures/phasetype.png "phase type distribution").

| Type          | Count | Percentage |
|---------------|-------|------------|
| Syzygy (New/Full) | 31  | 56%      |
| Quadrature (Q1/Q3)| 24  | 44%      |

### Progressive strengthening

A progressive strengthening of the signal with magnitude is observed when the same ±2.95-day window is applied to successively higher thresholds. For this comparison a dataset of M ≥ 8.0 earthquakes is used from the ISC-GEM catalog covering the period 1904-2021 listing 108 events. [See figure](/figures/magnitude-trend.png "progressive strengthening by magnitude").

| Magnitude threshold | Sample size (n) | Near-phase | Near-phase % | One-sided p-value |
|---------------------|-----------------|------------|--------------|-------------------|
| M ≥ 8.0             | 108             | 87         | 80.6%        | 0.490             |
| M ≥ 8.2             | 51              | 44         | 86.3%        | 0.169             |
| M ≥ 8.5             | 59              | 55         | 93.2%        | 0.004             |
| M ≥ 8.8             | 22              | 21         | 95.5%        | 0.047             |

The proportion of events falling inside the near-phase windows rises from 80.6 % at M 8.0 to 95.5 % at M 8.8, while the mid-cycle population shrinks to a handful of outliers. The p-value for the M 8.8 threshold rises due to the reduced sample size (22). This magnitude dependence is consistent with a modulating influence that becomes detectable only among the largest, most critically stressed faults.

### Near-phase percentage and relative energy release

There is a close parallel between the increase in seismic energy release (E ∝ 10¹·⁵ᴹ) and the rising near-phase fraction. Relative to an M 8.0 event, energy release is roughly 2× higher at M 8.2, 5.6× higher at M 8.5, and nearly 16× higher at M 8.8. When the near-phase percentage and relative energy are plotted together, the two curves rise in a strikingly parallel fashion [See figure](/figures/phasenergy.png "near phase percentage versus seismic energy release").

| Magnitude threshold | Sample size (n) | Near-phase % | Relative energy<br>(normalized to M 8.0) |
|---------------------|-----------------|--------------|------------------------------------------|
| M ≥ 8.0             | 108             | 80.6 %       | 1.0×                                     |
| M ≥ 8.2             | 51              | 86.3 %       | 2.0×                                     |
| M ≥ 8.5             | 59              | 93.2 %       | 5.6×                                     |
| M ≥ 8.8             | 22              | 95.5 %       | 15.8×                                    |

This parallel rise is consistent with the idea that any modulating influence becomes more detectable — or more effective — on the largest, most critically stressed faults that release the greatest amounts of energy. In other words, the rise in near-phase percentage is not merely a statistical curiosity; it closely tracks the steep increase in energy release. This strengthens the case that the lunar-phase preference is related to the readiness of a fault to fail in a very large event.

### Offsets by individual cardinal phase

When each event is assigned to its nearest cardinal phase, Full Moon dominates both in frequency and in tightness of clustering. [See figure](/figures/phasetype-offset.png "phase type offsets by nearest cardinal phase").

| Nearest phase   | Events | Mean offset | Median offset | Closest event |
|-----------------|--------|-------------|---------------|---------------|
| Full Moon       | 20     | 1.41 d      | 1.34 d        | 0.01 d        |
| Third Quarter   | 10     | 1.65 d      | 1.45 d        | 0.18 d        |
| First Quarter   | 15     | 1.91 d      | 2.17 d        | 0.11 d        |
| New Moon        | 14     | 1.91 d      | 2.21 d        | 0.11 d        |

Full Moon accounts for the largest share of events and shows the smallest average offset. Grouping the phases into the two halves of the synodic cycle (waxing versus waning) yields a further asymmetry:

- First Quarter + Full Moon (Q1 + Q2): **35 events** (59.3 %)
- Third Quarter + New Moon (Q3 + Q4): **24 events** (40.7 %)

The preference for the waxing-to-opposition segment (especially Full Moon) is one of the clearer secondary patterns in the n = 59 catalog.

### Lunar distance

Geocentric lunar distances at the time of the M ≥ 8.5 events were also examined. No significant preference for perigee (or “super moon”) conditions was found. Events occur across a wide range of distances, with many taking place when the Moon is near or beyond its mean distance (~384,000 km) and a substantial fraction occurring closer to apogee. [See figure](/figures/lunar-distance-m85.png "lunar distance at time of M ≥ 8.5 earthquakes").

| Statistic                          | Value            |
|------------------------------------|------------------|
| Mean distance                      | 382.813 km       |
| Median distance                    | 383.898 km       |
| Reference mean Earth–Moon distance | ≈ 384.400 km     |
| Events below sample mean           | 29               |
| Events at/above sample mean        | 30               |
| Minimum                            | 356.837 km       |
| Maximum                            | 406.335 km       |
| Standard deviation                 | 15.640 km        |

In contrast to the clear clustering with respect to the four cardinal phases, lunar distance shows no comparable statistical signal. This suggests that the phase geometry itself (syzygy or quadrature) is the more relevant factor, while the instantaneous Earth–Moon distance appears to play no systematic role among these great earthquakes.

### Eclipse conditions (among syzygies)

Solar and lunar eclipses are possible only at New Moon and Full Moon, respectively, and only when the Moon is sufficiently close to the ecliptic plane. In this catalog an eclipse label is applied whenever the absolute ecliptic latitude of the Moon satisfies |β| < 1.6° at the moment of syzygy (the same geometric criterion used by the [Solpage](https://www.ssgeos.org/solpage.htm) labeling function). This means that the label “eclipse” is applied to any eclipse type (total, annular, partial, etc.). [See figure](/figures/eclipses.png "eclipse geometry among the syzygies").

| Category                        | Observed | Expected (p ≈ 0.202) |
|---------------------------------|----------|----------------------|
| Eclipse syzygies (≤ 2.95 d)     | 5        | 6.9                  |
| Non-eclipse syzygies            | 29       | 27.1                 |
| **Total nearest-phase syzygies**| **34**   | **34**               |

- Observed fraction: 14.7 %
- One-sided binomial p-value (greater): ≈ 0.84
- Two-sided p-value: ≈ 0.55

With the applied tolerance (< 1.6°) there is no excess of eclipses (5 versus ~6.5 expected under null). Combined with the neutral lunar-distance result, this further indicates that the cardinal-phase preference is not driven by special geometric conditions that produce eclipses or “super moon” distances.

### Implications for mechanism

Three independent features of the catalog sit uncomfortably with a purely gravitational-tidal explanation:

1. No preference for perigee — The mean lunar distance at the time of the M ≥ 8.5 events is essentially neutral (≈ 382.813  km versus a conventional mean of ≈ 384.400 km), and a secondary peak occurs near 390–400 000 km. Classic “Super Moon” arguments would have predicted the opposite.
2. Quadrature phases are well represented — First and Third Quarter events form a substantial fraction of the near-phase population. Standard solid-Earth tide models predict maximum stress modulation at syzygy (New/Full Moon) and a minimum at quadrature.
3. Asymmetry between the two syzygies and between the two halves of the synodic cycle - Simple tidal-stress models treat New Moon and Full Moon nearly equivalently (both are spring-tide syzygies) and do not predict a systematic preference for the waxing-to-opposition segment.

The mid-cycle deficit itself is statistically significant, yet the most straightforward gravitational expectations — a stronger effect near perigee, a stronger effect at syzygy and near equivalence of the two syzygies, and symmetry between the two halves of the synodic cycle — are not supported by the data. This suggests that if lunar geometry exerts a modulating influence on the largest earthquakes, the relevant physics is unlikely to be the simple inverse-cube (1/R³) tidal stress that is commonly invoked.

These findings are offered as an empirical observation. They indicate that the largest earthquakes on record are not randomly distributed with respect to the lunar cycle and preferentially avoid the mid-points between the principal lunar phases. The result is consistent with a modulating influence of lunar geometry at 0/90/180° on faults that are already under critical stress.

### The Moon as a stabilizer for Earth's environment

The magnitude-dependent concentration of the largest earthquakes near the four cardinal lunar phases could be most economically explained by treating the Moon as a seismic modulator or regulator rather than a simple trigger. As magnitude increases, events become progressively more tightly clustered around the four cardinal phases — the geometrically and dynamically most distinct nodes of the lunar cycle — while mid-cycle intervals are strongly depleted.

This behavior would be continuous with the Moon’s already-recognized long-term stabilizing roles in Earth’s obliquity, rotation and climate. Once it is accepted that the Moon exerts a persistent stabilizing constraint on the planet, it may not be surprising that the same coupling could also impose a detectable monthly modulation on the timing of the largest seismic ruptures. The observations therefore appear as a shorter-timescale expression of a single, deep Earth–Moon interaction rather than an isolated or mysterious anomaly.

In this light the Moon might function as a regulator of when critically stressed faults are permitted to fail, with the effect becoming clearer the closer a large fault system is to catastrophic failure.

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