Out-of-sample test · Solar polar fields and earthquakes
In 2015, a paper reported that 26 of 33 great earthquakes struck inside “Significant Windows” drawn from the Sun’s polar magnetic field [2]. We rebuilt its rules, froze them, and tested them on the nine M8+ earthquakes that came after [1].
This page summarizes our study [1] of a 2015 paper [2]. Our analysis marks reasoning that goes beyond the study, and the verdicts are our assessment.
Read the study (PDF)The 2015 paper (PDF)Code and dataSourcesHow this was checkedCorrections
4 of 9
M8+ earthquakes since January 2014 fell inside the frozen windows [1 §4.2]
2.5
hits expected by chance, because the windows covered 27.8% of days [1 §4.2]
p = 0.22
Consistent with chance. Had the windows kept the paper’s 78.8% hit rate, about 7 of the 9 (78.8% of 9) would have been inside [1 §4.2].
The 2015 paper’s claims
The paper: 26 of 33, or 78.8%, from 1976 to 2014 [2 p. 313]
That was in the record the rules were developed on. Of the nine M8+ earthquakes since, the frozen windows caught four. Had they kept catching 78.8%, four or fewer would happen only 2.5% of the time, and the data favor chance over that rate by about 7 to 1 [1 §4.2]. See section 4.
The paper: “very strong evidence against the null hypothesis” [2 p. 314]
The authors also called their p-value “likely heavily biased,” because the rules were refined on the same polar-field record [2 p. 313]. Our rebuild still finds a signal in that record (p = 0.003, or 0.010 allowing for clustered earthquakes), but not in the years since [1 §4.1, §4.2].
The paper’s abstract [2 p. 310]
On new data the windows showed no significant link, though nine earthquakes can’t rule out a weak effect; the signal before 2014 comes from the record the rules were developed on [1 §5.1]. The electrical stresses on offer are at least seven orders of magnitude below tidal stresses, which modulate earthquakes only modestly [1 §5.2][6]. See section 6.
1 · What the 2015 paper claimed
Ben Davidson, Kongpop U-Yen and Christopher Holloman used 13 rules to draw windows about 20 to 50 days wide around peaks and polarity reversals in the Wilcox Solar Observatory’s record of the Sun’s polar magnetic fields [2 pp. 312–313, 319–322][1 §3.1].
Days inside windows
41.6%
of all days, so chance alone predicts about 14 hits (41.6% of 33) [2 p. 313]
As reported
p = 0.000015
but computed on the same polar-field record used to design the rules, as the authors noted [2 p. 313]
SPF is the paper’s abbreviation for the solar polar fields.
“Although the p-value is small, it is likely heavily biased since it is calculated against the SPF dataset that was used to refine the theoretical development of the algorithm.”
“The SPF data set was used to formulate the descriptions of the Significant Windows but was done so independent of the seismic event catalogue.”
“…the analysis was performed retrospectively, meaning that the model currently lacks a predictive element, and must [be] assessed by examining how well it predicts large earthquakes in the future.”
| Rule | Window centered on | Phase required | Half-width |
|---|---|---|---|
| C1 | Primary, peaked spike in a single or double half-cycle | Polar maximum | 20 d |
| C2–C4 | Spikes when fields are very strong: above 175 µT in the spike, its neighboring half-cycles or the other pole | Polar maximum | 25 d |
| C5, C6 | Primary, peaked spike in a triple or quadruple half-cycle | Polar maximum | 15 d, 10 d |
| C7, C8, C9 | Semi-flat, flat or secondary spike | Any | 10 d, 15 d, 10 d |
| C10 | Zero crossing of one pole’s field, with excursions above 15 µT on both sides | Any | 15 d |
| C11 | First zero crossing of a pole during a polar maximum | Polar maximum | 15 d |
| C12 | End of a polar minimum | Any | 15 d |
| C13 | Zero crossing of the average field, (N + S)/2 | Maximum, or excursions above 50 µT | 15 d |
Spike windows (C1–C9) also need a half-cycle that doesn’t cross zero and whose peak differs by at least 40 µT from both neighbors. Under the delay rule, a window that starts within 30 days after an M8+ earthquake, or after the fourth M7.5+ earthquake within 100 days, moves 20 days later, or by its half-width if that’s less; one starting 31–100 days after moves 10 days [1 §3.1][2 p. 313]. The paper splits the polar-field cycle into a polar maximum, when the fields are strong; a polar minimum, while they reverse; and a polar recovery of about 18 months as they strengthen again [2 p. 311].
2 · How we tested it
Twelve years of new data now allow the test the authors called for. Nine M8+ earthquakes have struck since January 2014, and the observatory’s polar-field record runs to January 2026 [1 §1].
We reimplemented all 13 window rules from the paper’s appendix. The authors’ own code survives only in a web archive we couldn’t reach [1 §3].
For 1976–2014, the rebuild covers 43.2% of days, against the paper’s 41.6%, and places 21 of 30 earthquakes inside windows (p = 0.003): a comparable signal [1 §4.1].
We settled each ambiguous rule, picking the reading closest to the paper’s own statistics where readings differed, and locked them all before any earthquake after 2014 was scored [1 §3.2, §3.3].
We scored the nine M8+ earthquakes from January 18, 2014, to January 9, 2026, against the frozen windows [1 §3.4].
Like the paper’s, our smoothing uses data from both sides of each date, so these windows couldn’t have been drawn in real time. That favors the hypothesis [1 §3.4].
| Statistic | Paper | Rebuild |
|---|---|---|
| Days inside windows | 41.6% | 43.2% |
| Days inside windows, polar maximum | 46.5% | 48.7% |
| Days inside windows, polar minimum | 27.9% | 39.3% |
| Days inside windows, polar recovery | 25.2% | 16.6% |
| Half-minicycles, north / south | 79 / 75 | 76 / 68 |
| M8+ earthquakes inside windows | 26 of 33 (78.8%) | 21 of 30 (70.0%) |
| Binomial p | 1.5 × 10−5 | 0.003 |
| Largest events in the paper’s Fig. 4 classified as it reported | — | 5 of 6 |
The study’s Table 1 [1 §4.1], with the paper’s figures from its pages 313, 315 and 320 [2]. The one Fig. 4 disagreement is the September 12, 2007, M8.4 southern Sumatra earthquake, 14 days from the nearest window in the rebuild. Coverage by phase differs most around the 2012–2014 reversal, which the rebuild, with data ending in January 2014, classifies as recovery rather than minimum [1 §4.1].
3 · Fifty years of windows and earthquakes
Gray stripes are days inside a window. Filled marks are M8+ earthquakes that struck inside a window; open marks struck outside [1 §4.1, §4.2].
| Date (UTC) | Earthquake | Magnitude | Polar phase | Result |
|---|---|---|---|---|
| 1976–2014: the record the rules were developed on | ||||
| Sumba, Indonesia | 8.3 | Maximum | Inside (C7) | |
| Valparaíso, Chile | 8.0 | Maximum | Outside, 3 d | |
| Michoacán, Mexico | 8.0 | Maximum | Inside (C1, C3, C8) | |
| Atka, Alaska | 8.0 | Maximum | Outside, 43 d | |
| Macquarie Ridge | 8.0 | Maximum | Inside (C10, C13) | |
| Bolivia (deep) | 8.2 | Maximum | Outside, 27 d | |
| Shikotan, Kuril Islands | 8.3 | Maximum | Inside (C7) | |
| Antofagasta, Chile | 8.0 | Maximum | Inside (C7) | |
| Colima–Jalisco, Mexico | 8.0 | Maximum | Inside (C5) | |
| Biak, Indonesia | 8.1 | Maximum | Inside (C1) | |
| Balleny Islands | 8.1 | Maximum | Inside (C1) | |
| New Ireland, Papua New Guinea | 8.0 | Minimum | Inside (C9, C13) | |
| Southern Peru | 8.4 | Minimum | Inside (C12) | |
| Tokachi-oki, Japan | 8.2 | Maximum | Inside (C7) | |
| Tasman Sea | 8.1 | Maximum | Inside (C1, C9, C13) | |
| Sumatra–Andaman Islands | 9.1 | Maximum | Inside (C1, C9, C13) | |
| Nias, Indonesia | 8.6 | Maximum | Inside (C1, C7) | |
| Tonga | 8.0 | Maximum | Outside, 11 d | |
| Kuril Islands | 8.3 | Maximum | Outside, 35 d | |
| Kuril Islands | 8.1 | Maximum | Inside (C13) | |
| Solomon Islands | 8.1 | Maximum | Inside (C8) | |
| Pisco, Peru | 8.0 | Maximum | Inside (C7) | |
| Southern Sumatra (Bengkulu) | 8.4 | Maximum | Outside, 14 d | |
| Samoa | 8.1 | Maximum | Inside (C7) | |
| Maule, Chile | 8.8 | Maximum | Inside (C1, C7) | |
| Tōhoku, Japan | 9.1 | Maximum | Inside (C1) | |
| Wharton Basin, Indian Ocean | 8.6 | Maximum | Outside, 9 d | |
| Wharton Basin, aftershock | 8.2 | Maximum | Outside, 9 d | |
| Santa Cruz Islands | 8.0 | Maximum | Outside, 60 d | |
| Sea of Okhotsk (deep) | 8.3 | Maximum | Inside (C10, C11, C12) | |
| 2014–2026: new data, scored with the frozen rules | ||||
| Iquique, Chile | 8.2 | Minimum | Outside, 256 d | |
| Illapel, Chile | 8.3 | Recovery | Outside, 247 d | |
| Chiapas, Mexico | 8.2 | Maximum | Inside (C7) | |
| Fiji (deep) | 8.2 | Maximum | Inside (C7) | |
| Northern Peru | 8.0 | Maximum | Inside (C13) | |
| Kermadec Islands | 8.1 | Maximum | Inside (C7) | |
| Chignik, Alaska | 8.2 | Maximum | Outside, 5 d | |
| South Sandwich Islands | 8.1 | Maximum | Outside, 19 d | |
| Kamchatka, Russia | 8.8 | Minimum | Outside, 104 d | |
Results from our rebuild [1]. “Inside” names the rules whose windows cover the date; “outside” gives the days to the nearest window. Names are short forms of the USGS place names or the earthquakes’ common names [4].
Coverage within polar maxima was similar before and after 2014 (48.7% and 45.1%), but 45% of the later days fell in the long polar minima and recoveries of solar cycles 24 and 25, where coverage was only 7–8%. Weaker fields also failed the rules’ 40 µT amplitude test more often [1 §4.3].
Thinner windows don’t bias the comparison with chance, which uses the windows’ own coverage in the same years [1 §3.5]. In polar maxima alone, where the windows were nearly as dense as before, 4 of 6 earthquakes fell inside against 45.1% coverage, not significantly more than chance (p = 0.26) [1 §4.2].
Outside · 256 days from a window
Outside · 247 days from a window
Inside a window (C7)
Inside a window (C7)
Inside a window (C13)
Inside a window (C7)
Outside · 5 days from a window
Outside · 19 days from a window
Outside · 104 days from a window
C7 is a window on a semi-flat spike in one pole’s field, and C13 a window on a zero crossing of the average field; see the rules [1 §3.1]. Phases are the paper’s stages of the polar-field cycle [2 p. 311]. Dates are UTC [4].
The two largest, Kamchatka (M8.8) and Illapel (M8.3), fell 104 and 247 days from the nearest window [1 §4.2].
4 · The statistics
The bars show how likely each number of hits out of nine would be by chance, and how likely it would be if the paper’s 78.8% hit rate were real [1 §3.5, §4.2].
The figures above hold the windows to the paper’s 78.8% hit rate, but the windows covered less time after 2014. Suppose instead that earthquakes were about five times likelier inside a window than outside, as 26 of 33 in 41.6% of days implies. At 27.8% coverage that predicts about 6 of the 9. Four falls short of that, but not by enough to rule it out (p = 0.14), and the data favor chance only slightly, by about 1.5 to 1. In polar maxima, where coverage was close to the paper’s, 4 of 6 fits both chance and the paper’s rate; the shortfall comes from the three earthquakes in polar minima and recoveries, all outside windows. Either way, the new data don’t show the effect.
| Test | Result |
|---|---|
| Binomial, against 27.8% coverage (2.5 hits expected) | P(≥ 4) = 0.22 |
| Phase-stratified (2.9 expected) | P(≥ 4) = 0.32 |
| Keeping earthquakes clustered, over 4,375 shifts (2.4 expected on average) | P(≥ 4) = 0.21 |
| Polar maximum only: 4 of 6, against 45.1% coverage | P(≥ 4) = 0.26 |
| Likelihood ratio, claimed rate against chance | 0.14, or about 7 to 1 for chance |
| Hits needed for p < 0.05 | 6 of 9 |
The clustering test shifts all the earthquakes together by every possible offset, wrapping around within the period, and reapplies the delay rule each time [1 §3.5].
| C13 spacing | Date offset | Days inside | Hits of 9 | P(≥ hits) |
|---|---|---|---|---|
| At least 90 days (primary) | 0 d | 27.8% | 4 | 0.22 |
| At least 90 days | +4 d | 27.7% | 3 | 0.47 |
| Within 90 days (as printed) | 0 d | 22.4% | 3 | 0.33 |
| Within 90 days | +4 d | 22.2% | 2 | 0.63 |
| None | 0 d | 29.1% | 4 | 0.25 |
| None | +4 d | 28.9% | 3 | 0.51 |
The paper’s formula for rule C13 appears to contradict its text, and its dates run 4 days later than the observatory’s current table [1 §2.1, §3.2].
Across six readings of the paper’s ambiguous rules, hits ranged from 2 to 4, and no p-value fell below 0.2 [1 §4.3].
5 · Why it didn’t hold
The 2015 association behaves like an overfit: strong in the record used to build the rules, not detectable in new data [1 §5].
Thirteen conditions, thresholds from 3 to 175 µT, windows 20 to 50 days wide and a delay rule, all developed on the 1976–2014 record [1 §5.1]. The paper also proposed widening the windows to take in near-misses [2 pp. 314–315].
Sixteen of the 30 earthquakes from 1976 to 2014 struck in 2004–2013, so a few well-placed windows could catch many of them. Allowing for clustering weakens the rebuild’s p-value for those years from 0.003 to 0.010 [1 §5.1].
The rules were developed on the 1976–2014 polar-field record and scored on earthquakes from the same years. The authors say they wrote the rules without reference to the earthquake catalog, but they called their p-value “likely heavily biased” and asked for a test on future earthquakes [2 pp. 313–314].
6 · Mechanism
Our test is about timing: it would pick up any effect that follows the windows, whether magnetic, electric or carried by solar particles. It rejects the strong effect the 2015 paper reported, though nine earthquakes can’t rule out a weak one [1 §5.1, §5.2]. Physically, the electrical stresses on offer are also tiny.
About 10−12 PaFair-weather current of the global electric circuit
Below 10−4 PaCurrents induced by a strong geomagnetic storm
About 103 PaSolid-Earth tides, which modulate earthquakes only modestly
At least 7 orders of magnitude
Stress on a fault, in pascals (log scale)
The paper proposed treating the Earth as a capacitor that stores energy until changes in the polar fields trigger its release, perhaps by way of the solar wind, with piezoelectric effects amplifying stress on faults [2 p. 315]. Amplifiers like these haven’t been shown to bridge the gap at the scale of a fault [1 §5.2].
They’re the observatory’s measurements of the line-of-sight field poleward of about 55° on the Sun, averaged over 30 days: an index that depends on the instrument [3][8][1 §5.2]. The Sun’s field reaches Earth only as an interplanetary field of a few nanotesla, thousands of times weaker than Earth’s own [1 §5.2].
Tides push on faults far harder than these electrical effects could, and they shift the odds of earthquakes only modestly [6]. A large study of solar activity and global seismicity found no significant triggering [5].
7 · Limits
Our version differs from the authors’ in half-cycle counts and coverage by phase. It comes within 1.6 points of their overall coverage and finds a comparable, weaker signal in the 1976–2014 record [1 §4.1, §5.3].
Three of the paper’s 33 earthquakes are no longer rated M8.0 or above, so our comparison with its result uses 30 [1 §5.3].
It favors the hypothesis, and windows near the end of the record, including those around the 2025 Kamchatka earthquake, rest on truncated fits [1 §5.3].
At 27.8% coverage, detecting a true hit rate of 60% with 80% power would take about 16 M8+ earthquakes, roughly two decades of data; a rate of 50% would take about 30 [1 §5.3].
The observatory’s polar-field table ends in January 2026. Future tests need a continuation calibrated to it, chosen before any new earthquake is scored [1 §5.3].
Solar effects with other timing, such as storms from coronal mass ejections or the solar cycle as a whole, are separate hypotheses this test doesn’t address. Evidence on them is mixed: studies have linked earthquakes to geomagnetic storms [9] and to cosmic-ray rates that vary with the solar cycle [10], while a large survey found no significant link [5][1 §5.2].
Freeze the rules, data versions and code before scoring any event, and publish them.
Test hit rates against the share of time the windows cover, using a null model that keeps earthquakes clustered.
Hold back part of the record, or wait for new events, before claiming significance.
These are the study’s lessons [1 §5.4]. What would change our verdicts on the hit rate and on the polar fields modulating earthquakes: future M8+ earthquakes falling inside windows computed by these frozen rules, from a continuation of the record chosen before scoring, significantly more often than the windows’ share of days (at about 28% coverage, 6 or more of 9).
8 · Read it yourself
Everything behind this page, so you can check our work, or extend the test once a calibrated continuation of the polar-field record is chosen.
Our study, October 6, 2026 · 14 pages · 612 KB [1]
The 2015 paper, New Concepts in Global Tectonics Journal 3(3) · 13 pages · 4.1 MB · © NCGT Group, a copy for review [2]
The 13 window rules, rebuilt from the paper’s Appendix A · 12 KB
The test: hits, chance, the clustering and likelihood tests, the 1976–2014 comparison and the six readings of the rules · 5 KB
Coverage by phase, the amplitude test, distances to the nearest window, the phase-stratified test and power · 5 KB
The polar-field table and the earthquake list as we saved them on October 11, 2026, with their sources · 39 KB [3][4]
Put the three scripts and the two files from the zip in one folder, then run python3 davidson_out_of_sample.py and python3 supporting_numbers.py. They need Python 3 and NumPy. The first takes about a minute, mostly for its clustering tests, which shift the earthquakes 4,375 and 13,711 times. Together they print the study’s results.
Bracketed numbers refer to this list; § marks a section of [1], and p. a page of [2]. Links checked October 11, 2026.
Martin, B. (October 6, 2026). An Out-of-Sample Test of the Proposed Link Between Solar Polar Magnetic Fields and M8+ Earthquakes. Study, PDF, 14 pages. Its code and data are under Read it yourself.
Davidson, B., U-Yen, K., and Holloman, C. (2015). Relationship between M8+ earthquake occurrences and the solar polar magnetic fields. New Concepts in Global Tectonics Journal 3(3), 310–322. Copy for review (PDF, © NCGT Group); page numbers are the journal’s.
Wilcox Solar Observatory, Stanford University. WSO polar field observations, 1976–present. Retrieved October 6 and 11, 2026; last updated August 10, 2026.
U.S. Geological Survey. ANSS Comprehensive Earthquake Catalog (ComCat): every M7.5+ earthquake from January 1, 1976, to October 6, 2026, from its FDSN event service, as CSV.
Love, J. J., and Thomas, J. N. (2013). Insignificant solar-terrestrial triggering of earthquakes. Geophysical Research Letters 40(6), 1165–1170.
Ide, S., Yabe, S., and Tanaka, Y. (2016). Earthquake potential revealed by tidal influence on earthquake size–frequency statistics. Nature Geoscience 9, 834–837.
Rycroft, M. J., Israelsson, S., and Price, C. (2000). The global atmospheric electric circuit, solar activity and climate change. Journal of Atmospheric and Solar-Terrestrial Physics 62(17–18), 1563–1576.
Svalgaard, L., Duvall, T. L., and Scherrer, P. H. (1978). The strength of the Sun’s polar fields. Solar Physics 58, 225–239.
Chen, H., Wang, R., Miao, M., et al. (2020). A statistical study of the correlation between geomagnetic storms and M ≥ 7.0 global earthquakes during 1957–2020. Entropy 22(11), 1270.
Homola, P., Marchenko, V., Napolitano, A., et al. (2023). Observation of large scale precursor correlations between cosmic rays and earthquakes with a periodicity similar to the solar cycle. Journal of Atmospheric and Solar-Terrestrial Physics 247, 106068.
Method
On October 11, 2026, we downloaded the polar-field table and the earthquake list again and re-ran the study’s code. Every result reproduced exactly: the hits, the coverage, each statistical test and each alternative reading of the rules. We checked each statement about the 2015 paper against its text, and compared the rebuilt rules line by line with its Appendix A [1][2].
Apart from the interpretation choices the study describes and tests (see section 4), the rebuild departs from Appendix A in one small way: rule C2 doesn’t check that a spike is primary. Adding the check changes the rebuild’s 1976–2014 coverage from 43.25% to 43.18%, with the same hits, and changes nothing after 2014. The authors’ own R code, which the paper cites, is preserved only in a web archive our tools couldn’t reach, so we couldn’t compare the rebuild with it [2 p. 318].
The verdicts and the items tagged “Our analysis” are our own assessment, built on the study and the cited sources. The force estimates are order-of-magnitude figures. Ben Davidson, the 2015 paper’s lead author, also produced the presentation in our Disaster Cycle check; see Related checks.
The study’s code and first draft were prepared with Claude, an AI assistant made by Anthropic, as the study acknowledges [1]. This page was also researched and written with Claude, then re-checked against its sources in a separate verification pass.
Corrections
If we get something wrong, we fix it and record the change below with the date. If a correction changes a verdict, the log says what the old verdict was.