Daily Radial Stress Exposure and M7+ Earthquakes: An Observational Study on SeismoAlert from 2015–2025

ABSTRACT

Background. Whether small periodic gravitational stresses influence earthquake occurrence has been debated for more than a century. This study examines whether M7+ earthquakes are preferentially observed during exposure to a moving geographical belt centered on the apparent geocentric lunar declination. Methods. The SeismoAlert T13 screening covers 20 selected tectonic corridors from 1 January 2015 through 31 December 2025 (96,432 h). Historical lunar declination and a ±20° latitude-belt criterion define hourly exposure in 1° geographical cells. Observed M7+ events are classified by origin time, and exposed versus unexposed event rates are compared using accumulated cell-hours, crude rate ratios, and cell-adjusted conditional estimates. T14 provides magnitude-stratified, leave-one-region-out, and belt-boundary sensitivity audits. Results. Among 99 M7+ earthquakes, 48 were exposed and 51 unexposed. Across the screened cells, 152.58 million exposed and 237.68 million unexposed cell-hours yielded crude rates of 0.315 versus 0.215 events per million cell-hours (RR 1.466). The geographically adjusted RR was 1.392 (95% CI 0.867–2.265; two-sided p=0.174). M6+ (n=889) had adjusted RR 1.093 (p=0.256), whereas M8+ (n=7) had RR 4.513 (p=0.153), with large uncertainty. Conclusions. A positive point estimate for M7+ events appears in the predefined T13 computational screen but is not statistically decisive. Because the exposure is geometric, the selected corridors are approximate rectangles, and clustering and post hoc selection are not fully addressed, the finding motivates preregistered replication and direct fault-resolved tidal-stress analysis rather than causal inference.

Keywords: SeismoAlert; lunar declination; Earth tides; tidal stress belt; M7+ earthquakes; exposure-normalized seismicity; conditional rate ratio; global tectonic corridors.

1. INTRODUCTION

Large earthquakes arise principally from the progressive accumulation of tectonic stress and the eventual rupture of faults [1]. Superimposed on these processes, the Earth–Moon–Sun system generates small, periodically varying tidal forces that may modulate the stress state of faults already approaching failure. Establishing whether such forcing is associated with a detectable change in major-earthquake occurrence remains challenging, however, because tectonic hazard varies substantially across regions and observed earthquake sequences are affected by clustering, catalogue characteristics, and random variability. The central scientific issue is therefore not the existence of astronomical tides, but whether a clearly defined and reproducible measure of lunar exposure is associated with a measurable difference in seismicity rates.

The SeismoAlert research programme addresses this question through a moving, latitude-based tidal-stress-belt (TSB) exposure framework. Successive investigations refined the alignment of earthquake origin times with lunar positions, introduced geographically differentiated comparisons, and accounted for the unequal durations of exposure and non-exposure. In particular, comparisons based only on the proportion of earthquakes occurring inside the belt may misrepresent the association when the two states occupy different amounts of observation time. The T13 Global Faults analysis therefore evaluates earthquake occurrence relative to accumulated geographical cell-time, while T14 examines the stability of the resulting estimates through additional sensitivity analyses. In this framework, TSB exposure is an operational astronomical–geographical indicator rather than a direct measurement of stress resolved on individual fault planes.

The primary objective of the present study is to determine whether the occurrence rate of magnitude 7.0 and greater (M ≥ 7.0) earthquakes was higher during defined TSB exposure than during non-exposure across selected global seismic corridors from 2015 through 2025, after accounting for unequal exposure durations and geographical differences among study cells. Secondary objectives are to characterize regional variation in the observed association, investigate its dependence on earthquake magnitude, and assess the sensitivity of the findings to the selection of seismic corridors. Together, these analyses provide an exposure-normalized observational test of the SeismoAlert hypothesis and a basis for subsequent validation using independent earthquake samples and physically resolved tidal-stress calculations.

2. LITERATURE REVIEW AND BOOKS

2.1 Historical statistical debate

Schuster (1897) framed the fundamental statistical difficulty in searches for lunar and solar earthquake periodicities: apparent periodicity can arise by chance. Later, Vidale et al. (1998) reported an absence of correlation in a well-characterized California sample, providing an essential counterpoint to positive studies. Both caution against treating a phase coincidence as sufficient evidence of physical triggering [2,3].

2.2 Observational evidence for tidal modulation

Tanaka, Ohtake and Sato (2002) analyzed 9,350 global earthquakes using theoretically computed tidal stresses and Schuster phase tests; their overall sample did not show a significant correlation, although subsets warranted attention [4]. Cochran, Vidale and Tanaka (2004) reported correlation of strong tides with shallow thrust earthquakes [5]. Tanaka (2010) described a time-dependent association preceding major Sumatra megathrust events [6]. Ide, Yabe and Tanaka (2016) examined how tidal influence might appear in earthquake size–frequency behavior, while Scholz, Tan and Albino (2019) demonstrated the importance of local physical mechanisms at mid-ocean ridges [7,8]. These studies use stress, phase, fault or setting-specific quantities that differ from the present latitude-only proxy.

2.3 Books and foundational theory

The physical framework is informed by Melchior’s The Tides of the Planet Earth (1983), which develops tidal potential and deformation, and Scholz’s The Mechanics of Earthquakes and Faulting (3rd ed., 2019), which develops friction, fault stress and earthquake mechanics [9,10]. These works provide background theory; neither is evidence that the present TSB geometry accurately represents fault-resolved Coulomb stress.

2.4 Research gap

Published tidal-triggering studies frequently calculate a tidal stress or phase at the earthquake hypocenter and use focal-mechanism information. A simple moving latitude belt offers a transparent, reproducible screening exposure that does not require complete focal mechanisms, but this simplicity entails physical approximation. Its statistical behavior, especially when normalized by local exposure time, is the subject of this study.

3. THEORETICAL FRAMEWORK

3.1 Astronomical and gravitational background

The lunar gravitational potential contains a spatially varying tidal component; the resulting solid-Earth deformation and stress depend on Earth structure, ocean loading, depth, and fault orientation. A resolved Coulomb stress perturbation is often represented schematically as ΔCFS=Δτ+μ′Δσn under a specified normal-stress sign convention, where Δτ is fault-parallel shear traction and μ′ is effective friction. The sign and amplitude require a specified fault plane and a physical tide model. This study does not calculate ΔCFS.

3.2 Operational daily radial-stress exposure proxy

For a geographical cell centered at latitude φ and historical geocentric apparent lunar declination δ(t), define the indicator E(φ,t)=1 if |φ−δ(t)|≤20°, and E(φ,t)=0 otherwise. The belt has a total latitude width of 40°. This operational choice follows the archived T13 methodology; it should not be interpreted as a calibrated physical threshold in tidal traction. Longitude is not used in E, even though actual lunar hour angle and local tidal stresses depend on longitude. The term “daily” describes the repeatedly changing exposure; event classification is performed at exact earthquake UTC times against the lunar ephemeris.

For each cell c, T_in,c=Σ_t E(φc,t)Δt and T_out,c=T_total−T_in,c, using hourly midpoints. Over the 2015–2025 interval T_total=96,432 hours per cell. Aggregated cell-hours are sums over cells, not elapsed hours experienced by a single fault. Accordingly, T_in may exceed T_out at some low latitudes under this broad belt. This is a mathematical property of the chosen definition, not proof of physically longer fault loading.

3.3 Rate comparison and null hypothesis

Let N_in,c and N_out,c be earthquake counts assigned to each cell under the two exposure states. The pooled rates are λ_in=ΣN_in,c/ΣT_in,c and λ_out=ΣN_out,c/ΣT_out,c, with crude RR=λ_in/λ_out. Because seismic activity is highly uneven geographically, the main inference uses a within-cell adjusted RR rather than treating every cell-hour as interchangeable. The null hypothesis is equal conditional earthquake intensity between the two states (RR=1); the alternative is unequal intensity, with interest in RR>1.

This hypothesis concerns association. Even a robust association would not alone demonstrate lunar triggering, since lunar declination is a proxy for a multidimensional tidal-stress field and earthquakes are not independent, identically distributed arrivals.

3.4. Original daily astronomical and stress-data generation workflow

The original SeismoAlert production script, daily_tidal_stress.py (supplied by the investigator; source-code audit for this revision), constructs a daily astronomical and stress-index dataset. It is distinct from the later T13 hourly latitude-cell exposure analysis. The script specifies a UTC date range from 1 January 1970 to 31 December 2100, the JPL DE433 planetary ephemeris (de433.bsp), and Skyfield for time scales and celestial positions. These choices describe the source-code configuration, not an independent verification that every historical output was successfully generated.

For each calendar date, the script evaluates an astronomical snapshot at 00:00 in Makkah (UTC+03:00), represented as 21:00 UTC on the preceding calendar day. Skyfield computes the Moon’s geocentric direction as observed from the Earth and projects that direction onto the WGS84 terrestrial ellipsoid to obtain the sublunar latitude and longitude. The antipodal coordinates are generated by reversing latitude and shifting longitude by 180° with wraparound. A date-label caveat is important: the exported Date field stores the actual UTC instant (usually 21:00 UTC of the previous day), not a local-date string.

The script assigns broad descriptive seismic-zone labels by testing whether each preset latitude interval overlaps a ±15° latitude band centered on the sublunar latitude (and separately on the antipodal latitude). This overlap is a zone-label lookup, not a spatial fault-polygon intersection. The six broad latitude bands and their descriptive fault/country strings are hard-coded. Crucially, the ±15° zone-screening band in this original script is different from the ±20° hourly TSB exposure threshold used in T13; the manuscript must not treat them as interchangeable.

The stress-index calculation first obtains instantaneous Earth–Moon and Earth–Sun distances and defines the scalar potential-like amplitude U(t) = G M_M R_E² / r_M(t)³ + G M_S R_E² / r_S(t)³. The source code uses G = 6.67430×10⁻¹¹ SI, lunar mass 7.342×10²² kg, solar mass 1.989×10³⁰ kg, and Earth radius 6.371×10⁶ m. At a specified terrestrial latitude and longitude, angular separation θ from the sublunar point is calculated from spherical trigonometry: cos θ = sin φ sin φ_s + cos φ cos φ_s cos(λ−λ_s).

The script then computes radial_kPa = [Y h₂ U (3 cos²θ − 1)] / (g R_E × 1000) and shear_kPa = [μ l₂ U × 3 sin(2θ)] / (g R_E × 1000), followed by coulomb_kPa = shear_kPa + 0.6 radial_kPa. Here h₂ = 0.6, l₂ = 0.084, Y = 7.0×10¹⁰ Pa, μ = 3.0×10¹⁰ Pa, and g = 9.81 m s⁻² are the values encoded in the program. These are simplified, model-dependent stress proxies, not a full elastic-Earth or fault-resolved Coulomb failure stress calculation. The sign and physical interpretation of the combined index require additional validation.

Two implementation features constrain interpretation. First, the code evaluates the radial and Coulomb indices only at the sublunar point and its antipode, rather than at each earthquake hypocenter or fault plane. At either idealized point, θ is 0 or π, so sin(2θ) = 0 and the implemented shear term vanishes; the radial term is identical at both points because it depends on cos²θ. Second, the solar contribution enters U through the Earth–Sun distance, but the angular factor θ is referenced only to the Moon. Consequently, the implemented expression is not a full vector superposition of lunar and solar tidal potentials at their respective sky directions. No inference about local fault stress should be drawn from these two reported indices alone.

The script also computes astronomical event annotations: new and full Moon times using Skyfield almanac; approximate perigee candidates as local minima in Moon–Earth distance sampled every three hours; a fixed January 3 annual perihelion label; and Moon–Mars and Moon–Venus longitude conjunction samples within 2° evaluated every six hours. For each daily record, it stores the nearest such event and its absolute time separation. These annotations are contextual descriptors, not demonstrated earthquake-triggering events. Fixed-date perihelion is an approximation; sampled conjunction windows can produce repeated event labels.

The exported fields are Date, Nearest_Event, Sublat, Sublon, Faults, Countries, Radial_kPa, Coulomb_kPa, Antipode_Lat, Antipode_Lon, Antipode_Faults, and Antipode_Countries. The program writes daily_tidal_stress.csv and daily_tidal_stress.json. These outputs describe daily snapshots and regional labels; they do not themselves provide the hourly exposed and unexposed denominators or event-time assignments required for the T13 conditional rate-ratio analysis.

3.5. Relationship between the original daily data and the T13–T14 test

T13 instead uses an exact-time earthquake catalogue, an hourly lunar-declination time series and a 1° geographic cell grid. Its exposure indicator is E(φ,t) = 1 if |φ − δ_Moon(t)| ≤ 20°, and 0 otherwise. The denominator for each cell is the sum of hourly exposure states over the observation period; event exposure is assigned at earthquake time using the corresponding lunar declination. The T13 methodology records DE421-based lunar positions, whereas the original daily script names DE433. Thus the two products are related conceptually through lunar astronomy, but are not numerically identical pipelines and should not be described as if the daily stress CSV was directly transformed into the T13 cell-hour table.

The original daily script provides historical context and a reproducible description of SeismoAlert’s daily sublunar/antipodal and simplified stress-index calculations. The quantitative results in Tables 1–6 remain attributable to the separately documented T13/T14 hourly exposure analyses. A future integrated test should evaluate the corrected lunar and solar stress tensors at event locations and specified fault geometries, and compare those stress amplitudes with the present latitude-only exposure proxy.

Table 7. Data products and definitions in the SeismoAlert analysis

Feature	Original daily_tidal_stress.py	T13/T14 earthquake-rate analysis
Temporal sampling	One snapshot per Makkah calendar day	Hourly exposure grid; earthquake event-time classification
Astronomical kernel	DE433 specified in script	DE421 stated in T13 methodology
Spatial basis	Sublunar and antipodal points; six descriptive latitude zones	20 seismic rectangles, 1° cells, overlap priority
Belt definition	±15° for zone-label overlap	±20° around lunar declination for hourly exposure
Stress metric	Simplified radial and Coulomb indices at sublunar/antipodal points	Binary geographical exposure; no fault-resolved stress
Principal files	daily_tidal_stress.csv and .json	T13 cell exposure, events, statistics, methodology; T14 sensitivity outputs

4. DATA, STUDY AREA AND MATERIALS

4.1 Catalog and observational window

The event input to T13 is the corrected T8B exact-time catalog derived from the USGS earthquake catalog, with UTC origin times, epicentral positions and reported magnitudes. The screened period is 2015-01-01 00:00 UTC through 2026-01-01 00:00 UTC (end exclusive), including three leap days. ComCat is an authoritative source of catalog earthquake parameters but the present study does not independently audit every event’s magnitude-type harmonization or later catalog revision [11].

4.2 Seismic corridor selection

Twenty geographical rectangles approximate global fault or plate-boundary corridors. They are screening regions, not fault polygons. When rectangles overlap, events and cells are assigned using the fixed priority sequence recorded in the methodology JSON, preventing duplicate counting. Spatial coverage is selected rather than a uniform worldwide sampling frame; results therefore generalize to these selected corridors, not automatically to all global M7+ earthquakes.

Table 1. Original T13 geographical screening rectangles (degrees; overlapping rectangles resolved by priority).

Region	Longitude (°)	Latitude (°)
Indonesia	95 to 141	-11 to 6
Papua New Guinea	141 to 156	-11 to 0
Philippines	116 to 127	5 to 21
Japan Trench	135 to 150	30 to 46
Kuril Kamchatka	150 to 165	43 to 57
Himalayan Belt	70 to 100	25 to 37
Aleutian West	170 to 180	48 to 56
Aleutian East	-180 to -165	48 to 56
Alaska Margin	-165 to -135	52 to 63
Cascadia	-131 to -121	40 to 51
San Andreas	-125 to -114	31 to 40
Mexico	-108 to -92	13 to 22
Central America	-92 to -77	6 to 16
Peru	-84 to -68	-19 to 0
Northern Chile	-76 to -66	-33 to -19
Southern Chile	-77 to -69	-47 to -33
Tonga	-180 to -170	-26 to -14
Kermadec	-180 to -174	-37 to -26
New Zealand	165 to 180	-48 to -34
Sumatra Andaman	90 to 100	0 to 17

 

4.3 Exposure construction and quality controls

The T8B workflow corrected an earlier interpolation error that had produced effectively constant lunar declination. T13 uses historical geocentric apparent lunar declination sampled at hourly midpoints for exposure duration, and exact event-time declination for event classification. The original audit reported maximum interpolation discrepancy of approximately 0.0004084°. The one-degree cell-center exposure approximation remains a distinct source of boundary uncertainty; T14 counts events close to the ±20° boundary.

5. METHODS AND STATISTICAL ANALYSIS

First, each catalog earthquake with magnitude at least 6 is assigned to one selected corridor and one geographical cell. Second, cell exposure hours are accumulated separately for the inside and outside states over the complete observational window. Third, M7+ event origin times are classified against the belt criterion. Fourth, crude pooled rates and within-cell conditional rate-ratio estimates are computed. Fifth, M6+, M7+, M8+, and mutually exclusive magnitude groups are compared, and each region is removed in turn to test dependence on one corridor.

The reported 95% confidence intervals and two-sided p-values are reproduced from T13/T14 output files; they are not re-estimated here using a different model. The within-cell estimator excludes events in cells with no variation in exposure, which affects the number of informative events. The present analyses do not include declustering, spatially clustered standard errors, multiple-comparison correction, or preregistered held-out testing; those are needed before confirmatory claims.

6. RESULTS

6.1 Global exposure-normalized M7+ result

Table 2. T13 combined M7+ events and accumulated geographical cell-time (2015–2025).

Measure	Exposed	Unexposed
M7+ events	48	51
Accumulated cell-hours	152,579,770	237,680,534
M7+ events per million cell-hours	0.3146	0.2146
Fraction of all cell-hours	39.1%	60.9%

 

The crude pooled rate ratio is 1.466, corresponding to approximately 46.6% higher observed M7+ event frequency per exposed cell-hour. The cell-adjusted RR is 1.392 (95% CI 0.867–2.265, p=0.174). Thus the point estimate is positive, but the interval includes unity and the conventional null is not rejected. The adjusted and crude estimates differ because the distribution of cell-hours does not match the spatial distribution of seismic hazard.

6.2 Region-level M7+ findings

Table 3. Complete T13 regional M7+ comparison. Boundary RR values (0 or ∞) reflect sparse counts; “—” indicates not estimable.

Region	M7+ n	In / out	Adjusted RR	p (2-sided)
Indonesia	17	12/5	1.113	0.840
Papua New Guinea	12	9/3	1.447	0.577
Philippines	5	5/0	∞	0.092
Japan Trench	6	2/4	2.583	0.268
Kuril Kamchatka	8	0/8	0.000	0.962
Himalayan Belt	5	1/4	0.503	0.533
Aleutian West	0	0/0	—	—
Aleutian East	0	0/0	—	—
Alaska Margin	9	0/9	—	—
Cascadia	1	0/1	0.000	0.692
San Andreas	1	0/1	0.000	0.557
Mexico	6	5/1	4.225	0.152
Central America	0	0/0	—	—
Peru	10	7/3	1.402	0.624
Northern Chile	3	1/2	0.843	0.890
Southern Chile	1	0/1	0.000	0.770
Tonga	6	2/4	0.479	0.386
Kermadec	6	4/2	3.779	0.099
New Zealand	3	0/3	0.000	0.424
Sumatra Andaman	0	0/0	—	—

 

Mexico (5/6 exposed; adjusted RR 4.225) and Kermadec (4/6; RR 3.779) have elevated estimates, but with only six events each. The Philippines has 5/5 exposed, producing a boundary estimate rather than a stable finite effect size. Kuril–Kamchatka and Alaska show no exposed M7+ events under the belt criterion; Alaska has no informative exposed cell-hours in its screening rectangle. These contrasts underscore the danger of selecting only positive regions.

6.3 Magnitude thresholds and non-overlapping bins

Table 4. T14 combined magnitude-stratified results, including mutually exclusive classes.

Magnitude group	Events	In / out	Adjusted RR	95% CI	p
M6+	889	414/475	1.093	0.938–1.274	0.256
M7+	99	48/51	1.392	0.867–2.265	0.174
M8+	7	4/3	4.513	0.630–90.421	0.153
M6.0-6.9	790	366/424	1.062	0.904–1.249	0.462
M7.0-7.9	92	44/48	1.293	0.794–2.134	0.306

 

The apparent increase in the point estimate at higher magnitudes is not evidence of a monotonic magnitude response: the M8+ result rests on seven events (five informative) and has a very wide interval. M7.0–7.9 excludes M8+ and has a smaller estimate than the inclusive M7+ group.

6.4 Leave-one-region-out sensitivity

For the M7+ group, the leave-one-region-out adjusted RR ranged from 1.267 to 1.542 across the available exclusions. All point estimates remained above one, indicating that no single selected region alone reversed the sign of the pooled association. This does not guarantee statistical significance or eliminate regional dependence.

Table 5. T14 M7+ leave-one-region-out sensitivity (full set of regional exclusions).

Excluded region	Remaining M7+	Adjusted RR	p
Alaska Margin	90	1.392	0.174
Aleutian East	99	1.392	0.174
Aleutian West	99	1.392	0.174
Cascadia	98	1.407	0.163
Central America	99	1.392	0.174
Himalayan Belt	94	1.487	0.118
Indonesia	82	1.471	0.154
Japan Trench	93	1.332	0.252
Kermadec	93	1.267	0.349
Kuril Kamchatka	91	1.392	0.174
Mexico	93	1.283	0.325
New Zealand	96	1.451	0.134
Northern Chile	96	1.423	0.157
Papua New Guinea	87	1.384	0.215
Peru	89	1.391	0.205
Philippines	94	1.271	0.337
San Andreas	98	1.420	0.153
Southern Chile	98	1.401	0.168
Sumatra Andaman	99	1.392	0.174
Tonga	93	1.542	0.092

 

6.5 Boundary audit and informative sample

T14 found 5 of 99 M7+ events within 0.5° of the ±20° belt boundary, and 8 within 1°. No M8+ event lay within 1° of the boundary. For M7+, 83 of 99 events were in cells informative for within-cell rate estimation; 16 occurred in cells without both exposure states. These figures show where the geometric proxy provides limited or boundary-sensitive information.

6.6 Earlier SeismoAlert test sequence

Table 6. Development of the SeismoAlert observational testing program. Tests overlap in periods and events and are not independent replications.

Test	Scope / contribution	Relevant result
T8B	Corrected exact-time lunar declination interpolation	Validated event-time geometry; 2015–2025 catalog basis
T9B	Indonesia, PNG, Philippines; 2015–2025	M7+ 26/34 exposed; adjusted RR 1.575, p=0.258
T10	Mexico, San Andreas, Cascadia	Mexico M7+ 5/6 exposed; RR approximately 4.23
T11	Peru and Chile regional replication	Recent Peru M7+ 7/10 exposed; adjusted RR 1.402
T12	Independent replication of T9B with T11 method	Reproduced regional estimates to reported precision
T13	Twenty-region global fault-corridor screen	M7+ 48/99 exposed; adjusted RR 1.392
T14	Magnitude, regional exclusion, boundary audits	M7+ leave-one-out estimates remain >1; 5 events within 0.5° boundary

 6.7 Temporal Enhancement of Major Earthquake Occurrence During Astronomical Event Windows 

To investigate whether major earthquake occurrence exhibits temporal associations with selected astronomical configurations, an additional analysis was performed using the SeismoAlert astronomical-event dataset and the USGS earthquake catalogue. The investigation focused on syzygy (New Moon and Full Moon), lunar perigee, and Earth perihelion. Each astronomical event was designated as the central day of a seven-day window, extending three calendar days before and after the event. A supplementary 12-hour buffer was applied at each end, producing an eight-day exposure interval. All dates were standardized to SeismoAlert’s UTC+3 forecasting convention, and overlapping event windows were merged to prevent duplicate counting of exposure time.

The analysis examined earthquakes of magnitude M ≥ 7.0 occurring within the 20 predefined seismic corridors during 2015–2025. Of the 99 recorded major earthquakes, 74 occurred within the combined astronomical-event windows, encompassing 2,540 forecast-days, whereas 25 occurred outside these windows, encompassing 1,478 forecast-days. Normalization by temporal exposure yielded earthquake occurrence rates of approximately 29.13 and 16.91 events per 1,000 forecast-days, respectively.

The corresponding incidence rate ratio was

RR=1.722

This result represents an estimated 72.2% higher occurrence rate of M ≥ 7.0 earthquakes during the designated astronomical-event windows compared with the remaining observation period. The approximate 95% confidence interval for the rate ratio was 1.095–2.710, indicating a positive association in this selected sample.

A within-year circular time-shift analysis, designed to preserve aspects of the observed earthquake clustering while altering the alignment between seismic activity and astronomical windows, yielded an exploratory one-sided probability of approximately p = 0.009. This finding suggests that the observed temporal concentration was uncommon under the specified randomization procedure.

7. DISCUSSION

7.1 Interpretation of the positive M7+ estimate

The observed M7+ rate per accumulated exposed cell-hour exceeds the corresponding unexposed rate in the T13 screening sample. This supports further testing of the operational association. The cell-adjusted estimate, smaller than the crude estimate, illustrates why spatial exposure normalization is necessary. Nevertheless, its confidence interval is compatible with both a modest reduction and a substantial increase in rate, and its p-value does not meet a conventional significance threshold. The correct interpretation is an exploratory positive point estimate with material uncertainty.

7.2 Why event percentages alone are inadequate

The 48/99 exposed fraction is 48.5%, apparently below half. Yet exposed cell-time constitutes only 39.1% of the total sampled cell-time. An event fraction above the exposure-time fraction can yield a crude RR above one. Conversely, simply dividing the 99 events by the global 39.1% exposure fraction would assume uniform background earthquake risk across every cell, an implausible assumption. The conditional cell-adjusted estimate addresses this particular spatial imbalance, although other biases remain.

7.3 Geographical heterogeneity and fault mechanics

The large contrast between low-latitude regions and high-latitude regions arises partly from the geometry of the 40° moving latitude belt. Because the indicator does not use lunar hour angle, local tidal potential, ocean loading, focal depth or fault orientation, the exposed state cannot be equated with increased positive Coulomb stress. Indeed, the physical direction of tidal modulation may differ among thrust, normal and strike-slip faults, as earlier studies demonstrate [5,8].

7.4 Comparison with prior literature

The SeismoAlert finding is broadly consistent with the proposition that lunar-related variables deserve testing, but it is not directly comparable in magnitude to stress-resolved tidal triggering estimates. Tanaka et al. (2002) showed that even a large catalog can have an overall null result [4]; Vidale et al. (1998) found no clear correlation in a California fault sample [3]. Cochran et al. (2004) and Tanaka (2010) provide positive setting-specific results [5,6]. Together these publications favor a mechanism-aware, conditional interpretation over any claim of universal lunar earthquake triggering.

7.5 Selection, multiple testing and clustering

The research program developed across multiple tests, regions, thresholds and time windows. Therefore, T13 should not be described as a fully independent preregistered confirmatory test. Regional comparisons are multiple correlated examinations of the same underlying event catalog. Mainshock–aftershock sequences further violate simple independent-event assumptions. Future uncertainty estimation should use declustering or cluster-robust resampling, and a held-out period or prospectively fixed spatial sample.

7.6 Why a physically resolved next test matters

A decisive follow-up should compute astronomical tidal potential and Earth response at each hypocenter, then resolve shear and normal traction on the earthquake fault plane using focal mechanisms, depth, local geometry and ocean-loading corrections. A preregistered analysis could compare the current latitude proxy with fault-resolved ΔCFS, lunar hour-angle and tidal-phase alternatives. Improvement beyond the geometric baseline would help determine whether the proxy reflects a physical stress mechanism or a sampling artifact.

8. STUDY LIMITATIONS

The principal limitations are: (i) an operational belt half-width of 20° not independently calibrated to physical stress; (ii) rectangular corridors instead of fault-trace or rupture polygons; (iii) hourly cell-center exposure approximation rather than continuous exact-location integration; (iv) lack of fault-resolved tidal stress, lunar hour angle and local ocean-loading models; (v) earthquake clustering and spatial heterogeneity; (vi) a limited M7+ sample and extremely small M8+ sample; (vii) regional and magnitude analyses explored during model development; (viii) no independent catalog revalidation or prospective out-of-sample confirmation. The reported uncertainty may be optimistic if temporal clustering is material.

9. SUMMARY OF PRINCIPAL FINDINGS

Over 2015–2025, T13 recorded 99 M7+ earthquakes across 20 selected seismic corridors. Forty-eight occurred in the operational lunar-declination belt and 51 outside. After normalizing by 152.58 million exposed and 237.68 million unexposed geographical cell-hours, crude M7+ event rates were 0.315 and 0.215 per million cell-hours. The crude RR was 1.466 and the within-cell adjusted RR 1.392 (95% CI 0.867–2.265; p=0.174). T14 leave-one-region-out checks did not reverse the sign of the M7+ point estimate, while the M8+ analysis remained highly uncertain. These are observational associations within the selected screening design, not direct stress measurements or demonstrated causal effects.

10. FINAL CONCLUSION

This expanded SeismoAlert study establishes a reproducible framework for comparing large-earthquake occurrence with a moving lunar-declination latitude-belt exposure using the correct denominator of accumulated geographical cell-time. The M7+ data show a positive but statistically inconclusive adjusted association in the selected 2015–2025 corridors. The finding warrants a preregistered replication with independent data and a physically resolved tidal-stress model. At present, it does not support deterministic earthquake prediction, causal attribution, or claims that exposure necessarily increases the stress promoting slip on a particular fault.

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