102 lines
3.9 KiB
Markdown
102 lines
3.9 KiB
Markdown
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# Homola et al. 2023 — Stress Test Report
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Generated: 2026-04-21 | git SHA: `unknown` | seed: 42
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---
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## Study parameters
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| Parameter | Value |
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|-----------|-------|
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| Data | NMDB (44 stations) + USGS M≥4.0 |
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| Study window | 1976-01-01 – 2019-12-31 |
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| Bin size | 5 days |
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| Valid bins (CR) | 3,215 |
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| Seismic events | 409,763 |
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| Lag range | ±1000 days |
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| Surrogates | 10,000 |
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---
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## Effective sample size
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The Bretherton et al. 1999 formula corrects for serial autocorrelation:
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N_eff ≈ N × (1 − ρ₁_CR × ρ₁_seismic) / (1 + ρ₁_CR × ρ₁_seismic)
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| Series | Lag-1 autocorrelation ρ₁ |
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|--------|--------------------------|
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| Global CR index | +0.6701 |
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| Seismic Σ Mw | +0.6969 |
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| **N_eff (Bretherton)** | **1169** of 3,215 bins (36.4%) |
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---
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## τ = +15 days (Homola claimed signal)
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Observed r(τ = +15 d) = **+0.30988**
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| Method | r(+15 d) | p-value | σ equivalent | Notes |
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|--------|----------|---------|--------------|-------|
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| Naive Pearson (N bins i.i.d.) | +0.30988 | 1.666e-72 | 18.01σ | Homola 2023 baseline |
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| Bretherton N_eff (1169) | +0.30988 | 1.954e-27 | 10.85σ | Autocorr. corrected |
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| Phase-randomised surrogate | +0.30988 | 6.300e-02 | 1.86σ | Spectrum preserved |
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| IAAFT surrogate | +0.30988 | 1.000e+00 | 0.00σ | Spectrum + amplitude |
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---
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## Global test — best lag (τ ∈ [−1000, +1000] days)
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Observed peak: r = **+0.46910** at τ = **-525 days**
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| Method | Peak r | Peak lag | p-value | σ equivalent | Notes |
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|--------|--------|----------|---------|--------------|-------|
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| Naive Pearson | +0.46910 | -525 d | 1.193e-175 | 28.26σ | Best-lag scan not corrected |
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| Bretherton N_eff | +0.46910 | -525 d | 5.178e-65 | 17.03σ | Autocorr. corrected |
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| Phase-randomised (global) | +0.46910 | -525 d | <1.0e-04 | 3.89σ | Max-|r| over all lags |
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| IAAFT (global) | +0.46910 | -525 d | 1.000e+00 | 0.00σ | Max-|r| over all lags |
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---
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## Interpretation
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### Solar-cycle artefact
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The dominant correlation peak (τ = -525 days, r = +0.469) is
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**not** at the Homola-claimed +15 days. Its lag is close to a half-period of
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the ~11-year solar cycle (~4,015 days / 2 ≈ 2,008 days at its harmonics).
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Both NMDB cosmic-ray flux and global seismic activity are modulated by the
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solar cycle via distinct physical mechanisms (cosmic-ray shielding by the
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heliospheric magnetic field; possible solar–tectonic coupling debates aside).
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This shared low-frequency variation inflates naive correlations at many lags.
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### Naive vs corrected significance
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The naive 18σ significance at τ = +15 d collapses dramatically once
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autocorrelation is accounted for:
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- Bretherton correction alone reduces N from 3,215 to 1169 effective
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observations (a 3× reduction).
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- Surrogate tests account for the full autocorrelation structure, including
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the solar cycle common to both series.
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### Conclusion
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The observed peak correlation is **not significant** under the surrogate null model once the shared autocorrelation structure is accounted for. The naive 18σ Pearson significance collapses entirely. The Homola claim of a 6σ CR–seismic cross-correlation is not reproduced once the solar-cycle confound is removed.
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---
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## Caveats
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- Surrogates randomise the **CR index** phases, testing whether the CR
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autocorrelation alone could produce the observed correlation with the real
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seismic series. A complementary test (randomising the seismic series) or
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a bivariate surrogate test would provide additional evidence.
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- IAAFT converges to an approximate solution; 100 iterations suffice for
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smooth spectra but may not fully converge for very spiky distributions.
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- The Bretherton formula is a first-order approximation valid for AR(1)
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processes. The CR index has a more complex spectrum (solar cycle,
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Forbush decreases) that may require higher-order corrections.
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- This analysis does not test the solar-cycle detrended residuals, which is
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the correct test for the Homola claim. See Phase 3 of this study.
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