Add seven additional robustness checks (3a–3g) and update paper
3a Block-bootstrap surrogates (B=804 bins≈11 yr, n=5000): raw r(+15d)
p=0.022 — marginally significant on undetrended series, driven by
the shared solar-cycle trend not a causal signal.
3b Partial correlation (sunspot-regressed, no filter): r(+15d) drops
from 0.079 to 0.029 (63%) — confirms solar-cycle confounding without
preprocessing circularity.
3c Spectral coherence in solar-cycle band = 0.840 (>0.776 threshold);
kNN mutual information at τ=+15d = 0.000 nats (p=1.000) — no
nonlinear dependence at the claimed lag.
3d Missing-data impact: 0% NaN at station thresholds 2/3/5; r(+15d)
unchanged — missing data is not a confound.
3e Bin-size sensitivity: dominant peak at τ≈-520d for 1/5/27-day bins;
r at +15d scales with bin size (solar-cycle leakage, not physical).
3f GK declustering removes 28.4% of events as aftershocks; r(+15d)
changes by only Δ=0.014 — aftershock clustering not a confound.
3g Per-solar-cycle analysis (cycles 21–24): r(+15d) all positive
(0.018–0.073) but dominant peak lags scattered (-65/-125/+125/-125d)
— phase-drifting solar-cycle artefact, not physical precursor.
Script fixes: vectorised block bootstrap (401×5000 → NumPy matmul),
kNN MI with sorted searchsorted (O(N log N), no inflated values),
coherence nperseg 512→2048 (resolves solar-cycle band), axhspan→axvspan.
Paper: new Methods subsections (block bootstrap, partial correlation,
nonlinear dependence); new Results subsections for each check; updated
Conclusions with 7-item robustness summary; Kraskov2004 and
GardnerKnopoff1974 added to refs.bib; Homola2023 updated to arXiv
preprint 2204.12310; eq:energy duplicate label fixed. PDF: 35 pages.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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\newlabel{fig:geoheatmap}{{4}{13}{Heatmap of BH-significant station--grid-cell pairs ($q = 0.05$). Each row is an NMDB station; each column is a $10° \times 10°$ seismic grid cell. Significant pairs (455/7{,}037) are scattered without obvious geographic clustering, inconsistent with a local coupling mechanism.\relax }{figure.caption.6}{}}
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\newlabel{fig:geodistlag}{{5}{14}{Optimal lag $\tau ^*(s,g)$ vs.\ great-circle distance $d(s,g)$ for all 7{,}037 station--cell pairs (grey) and BH-significant pairs (coloured by peak $|r|$). The OLS regression line (red) has slope $\beta = -0.45$~days/1000\,km ($p=0.21$), consistent with zero. A local propagation mechanism would predict a positive slope.\relax }{figure.caption.7}{}}
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\newlabel{fig:oosxcorr}{{6}{14}{Out-of-sample cross-correlation function (2020--2025, $T=390$ bins, $10^5$ phase surrogates). The observed $r(\tau )$ (black) lies entirely within the surrogate 95th-percentile envelope (grey shading). The claimed signal at $\tau = +15$~d (vertical line) is $r = 0.045$ --- below the surrogate 95th percentile of 0.136.\relax }{figure.caption.8}{}}
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\newlabel{fig:rolling}{{7}{15}{Rolling $r(+15\,\text {d})$ in 18-month overlapping windows across the out-of-sample period. Error bars are bootstrap 95\% confidence intervals. The grey horizontal band shows the surrogate 95th percentile. The signal shows no consistent sign or trend.\relax }{figure.caption.10}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Annual rolling $r(+15\,\text {d})$ across the full 1976--2025 period (grey points with 95\% bootstrap CI). The sinusoidal best-fit (red curve, $P = 9.95$\nobreakspace {}yr) closely tracks the oscillatory pattern, confirming that the CR--seismic correlation is modulated by the solar cycle. The vertical dashed line marks the in-sample/out-of-sample split (2020).\relax }}{15}{figure.caption.11}\protected@file@percent }
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\newlabel{fig:combined}{{8}{15}{Annual rolling $r(+15\,\text {d})$ across the full 1976--2025 period (grey points with 95\% bootstrap CI). The sinusoidal best-fit (red curve, $P = 9.95$~yr) closely tracks the oscillatory pattern, confirming that the CR--seismic correlation is modulated by the solar cycle. The vertical dashed line marks the in-sample/out-of-sample split (2020).\relax }{figure.caption.11}{}}
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\citation{Jeffreys1961}
|
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\newlabel{tab:rawcorr}{{1}{14}{Raw pairwise correlation statistics across three time windows. Bonferroni correction applied for $3 \times 3 = 9$ tests. CR uses the per-bin station-median index ($\hat {x}^{(50)}$). Seismic energy is $\log _{10}\!\left (\sum 10^{1.5 M_W}\right )$. Sunspot is the 365-day smoothed daily count. $^{*}p_\text {Bonf}<0.05$, $^{**}p_\text {Bonf}<0.01$, $^{***}p_\text {Bonf}<0.001$.\relax }{table.caption.7}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Raw pairwise scatter plots for the in-sample window (1976--2019, $N = 3{,}215$ five-day bins). \textbf {Left}: CR station-median index vs $\log _{10}$ seismic energy; horizontal error bars span the station $[\hat {x}^{(5)}, \hat {x}^{(95)}]$ spread. \textbf {Centre}: CR index vs 365-day smoothed sunspot number; the strong anti-correlation ($r = -0.82$) reflects the Forbush decrease mechanism. \textbf {Right}: Smoothed sunspot number vs $\log _{10}$ seismic energy; thin horizontal error bars show the daily sunspot spread within each 5-day bin. All points are coloured by decimal year (plasma colormap), revealing the solar-cycle drift: successive cycles trace the same anti-correlated arc in the centre panel. Black curves are LOWESS trend lines ($f = 0.4$).\relax }}{15}{figure.caption.8}\protected@file@percent }
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\newlabel{fig:rawinsample}{{1}{15}{Raw pairwise scatter plots for the in-sample window (1976--2019, $N = 3{,}215$ five-day bins). \textbf {Left}: CR station-median index vs $\log _{10}$ seismic energy; horizontal error bars span the station $[\hat {x}^{(5)}, \hat {x}^{(95)}]$ spread. \textbf {Centre}: CR index vs 365-day smoothed sunspot number; the strong anti-correlation ($r = -0.82$) reflects the Forbush decrease mechanism. \textbf {Right}: Smoothed sunspot number vs $\log _{10}$ seismic energy; thin horizontal error bars show the daily sunspot spread within each 5-day bin. All points are coloured by decimal year (plasma colormap), revealing the solar-cycle drift: successive cycles trace the same anti-correlated arc in the centre panel. Black curves are LOWESS trend lines ($f = 0.4$).\relax }{figure.caption.8}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Raw pairwise scatter plots for the out-of-sample window (2020--2025, $N = 390$ bins, 27 NMDB stations). Layout identical to Figure\nobreakspace {}\ref {fig:rawinsample}. The CR--sunspot anti-correlation strengthens to $r = -0.939$ during Solar Cycle\nobreakspace {}25, which had a particularly wide dynamic range. The CR--seismicity correlation ($r = 0.046$, $p_\text {Bonf} = 1.0$) is indistinguishable from zero.\relax }}{15}{figure.caption.9}\protected@file@percent }
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\newlabel{fig:rawoos}{{2}{15}{Raw pairwise scatter plots for the out-of-sample window (2020--2025, $N = 390$ bins, 27 NMDB stations). Layout identical to Figure~\ref {fig:rawinsample}. The CR--sunspot anti-correlation strengthens to $r = -0.939$ during Solar Cycle~25, which had a particularly wide dynamic range. The CR--seismicity correlation ($r = 0.046$, $p_\text {Bonf} = 1.0$) is indistinguishable from zero.\relax }{figure.caption.9}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Raw pairwise scatter plots for the full combined window (1976--2025, $N = 3{,}604$ bins). The multi-decadal colour gradient in the centre panel shows CR and sunspot oscillating in anti-phase across four complete solar cycles. The overall CR--seismicity Pearson correlation ($r = 0.055$, $\rho = 0.065$) is statistically significant ($p_\text {Bonf} = 0.008$) but quantitatively negligible, and its sign follows directly from the confounding triangle described in the text.\relax }}{16}{figure.caption.10}\protected@file@percent }
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\newlabel{fig:rawcombined}{{3}{16}{Raw pairwise scatter plots for the full combined window (1976--2025, $N = 3{,}604$ bins). The multi-decadal colour gradient in the centre panel shows CR and sunspot oscillating in anti-phase across four complete solar cycles. The overall CR--seismicity Pearson correlation ($r = 0.055$, $\rho = 0.065$) is statistically significant ($p_\text {Bonf} = 0.008$) but quantitatively negligible, and its sign follows directly from the confounding triangle described in the text.\relax }{figure.caption.10}{}}
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\newlabel{fig:homola}{{4}{16}{Cross-correlation function $r(\tau )$ for the raw (undetrended) CR index and global seismic metric, 1976--2019. The dominant peak at $\tau = -525$~days (vertical dashed line, red) corresponds to a half-solar-cycle lag; the claimed $\tau = +15$~days is marked with a vertical solid line (blue). The horizontal shaded band shows the na\"ive $\pm 2\sigma $ confidence interval (ignoring autocorrelation); the narrower band is the Bretherton-corrected interval.\relax }{figure.caption.11}{}}
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\newlabel{fig:stress}{{5}{17}{Null distribution of the peak cross-correlation statistic from 10{,}000 IAAFT surrogates for the raw (blue) and HP-detrended (orange) CR--seismic series. Vertical dashed lines mark the observed peak for each case. While the raw peak is improbably large under the null, the detrended peak is only marginally significant, and the correlation at the claimed $\tau =+15$~d is not.\relax }{figure.caption.12}{}}
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\newlabel{fig:detrended}{{6}{19}{Cross-correlation functions for the raw (blue) and HP-detrended (orange) series. The dominant peak at $\tau = -525$~days in the raw data (dashed blue) is absent after detrending, confirming it is a solar-cycle artefact. Neither series exhibits a significant peak at $\tau = +15$~days (vertical grey line).\relax }{figure.caption.14}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Cross-correlation $r(\tau )$ under three detrending approaches (HP filter, Butterworth highpass, rolling-mean subtraction) for the raw CR index vs.\ log$_{10}$ seismic energy, 1976--2019. The vertical grey line marks the claimed $\tau = +15$\nobreakspace {}days. No method produces a positive feature at this lag.\relax }}{19}{figure.caption.15}\protected@file@percent }
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\newlabel{fig:detrend_robust}{{7}{19}{Cross-correlation $r(\tau )$ under three detrending approaches (HP filter, Butterworth highpass, rolling-mean subtraction) for the raw CR index vs.\ log$_{10}$ seismic energy, 1976--2019. The vertical grey line marks the claimed $\tau = +15$~days. No method produces a positive feature at this lag.\relax }{figure.caption.15}{}}
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\newlabel{tab:neff}{{3}{20}{Comparison of $N_\text {eff}$ estimators for raw in-sample series at $\tau = +15$~days ($N = 3{,}214$, $r = 0.079$).\relax }{table.caption.16}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Cross-correlation $r(\tau )$ for three magnitude cutoffs ($M \geq 4.5$, blue; $M \geq 5.0$, orange; $M \geq 6.0$, green), in-sample window 1976--2019. The vertical grey line marks $\tau = +15$\nobreakspace {}days. All three cutoffs yield similar, small correlations at the claimed lag, and the dominant peak location ($\tau = -525$\nobreakspace {}days) is stable.\relax }}{20}{figure.caption.17}\protected@file@percent }
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\newlabel{fig:mag_threshold}{{8}{20}{Cross-correlation $r(\tau )$ for three magnitude cutoffs ($M \geq 4.5$, blue; $M \geq 5.0$, orange; $M \geq 6.0$, green), in-sample window 1976--2019. The vertical grey line marks $\tau = +15$~days. All three cutoffs yield similar, small correlations at the claimed lag, and the dominant peak location ($\tau = -525$~days) is stable.\relax }{figure.caption.17}{}}
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\newlabel{sec:res:blockbootstrap}{{4.8}{20}{Block-Bootstrap Surrogate Comparison}{subsection.4.8}{}}
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\newlabel{fig:blockbootstrap}{{9}{21}{Block-bootstrap null distributions for the raw CR--seismic pair ($B = 804$ bins $\approx 11$~yr, $S = 5{,}000$ surrogates). \textbf {Left}: distribution of $r(+15\,\text {d})$ under the CBB null; observed value $r = 0.079$ (red) lies at the $p = 0.022$ tail. \textbf {Right}: distribution of the peak $|r|$; observed peak $0.135$ at $\tau = -525$~d lies at $p = 0.008$. Grey dashed lines mark the 95\% CI of the null.\relax }{figure.caption.18}{}}
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|
||||
\newlabel{fig:partialcorr}{{10}{22}{Cross-correlation $r(\tau )$ for the raw seismic metric (blue) and the sunspot-regressed seismic residual (orange), both against the CR index, on the raw (unfiltered) in-sample series. The claimed $\tau = +15$~d (grey dashed line) shows $r_\text {raw} = 0.079$ vs.\ $r_\text {partial} = 0.029$, a 63\% reduction once the shared solar-cycle component is regressed out.\relax }{figure.caption.19}{}}
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\newlabel{sec:res:missing}{{4.11}{22}{Missing-Data Sensitivity}{subsection.4.11}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces \textbf {Left}: Magnitude-squared coherence between the CR index and seismic metric (blue), with the solar-cycle band shaded (orange, 0.08--0.115 cycles\nobreakspace {}yr$^{-1}$) and the 95\% significance level (red dashed). The mean coherence in the SC band is 0.840, confirming a strong shared solar-cycle component. \textbf {Right}: kNN mutual information ($k = 5$) at lag $\tau = 0$ (blue) and $\tau = +15$\nobreakspace {}d (orange) vs.\ their respective shuffle-null distributions. Both observed MI values are indistinguishable from zero; $p(+15\,\text {d}) = 1.000$.\relax }}{23}{figure.caption.22}\protected@file@percent }
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\newlabel{fig:coherence}{{11}{23}{\textbf {Left}: Magnitude-squared coherence between the CR index and seismic metric (blue), with the solar-cycle band shaded (orange, 0.08--0.115 cycles~yr$^{-1}$) and the 95\% significance level (red dashed). The mean coherence in the SC band is 0.840, confirming a strong shared solar-cycle component. \textbf {Right}: kNN mutual information ($k = 5$) at lag $\tau = 0$ (blue) and $\tau = +15$~d (orange) vs.\ their respective shuffle-null distributions. Both observed MI values are indistinguishable from zero; $p(+15\,\text {d}) = 1.000$.\relax }{figure.caption.22}{}}
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\newlabel{tab:missing}{{4}{23}{Missing-data sensitivity: global CR index and correlation at $\tau = +15$~days for three station-threshold values.\relax }{table.caption.23}{}}
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\citation{GardnerKnopoff1974}
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\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Cross-correlation $r(\tau )$ for three bin sizes: 1-day (left), 5-day (centre), 27-day (right). The dominant peak (red dotted) consistently falls near $\tau \approx -520$\nobreakspace {}days across all bin sizes. The correlation at the claimed $\tau = +15$\nobreakspace {}days (grey dashed) increases from 0.036 to 0.123 as bin size increases, consistent with increasing solar-cycle leakage rather than a physical short-lag signal.\relax }}{24}{figure.caption.24}\protected@file@percent }
|
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\newlabel{fig:binsize}{{12}{24}{Cross-correlation $r(\tau )$ for three bin sizes: 1-day (left), 5-day (centre), 27-day (right). The dominant peak (red dotted) consistently falls near $\tau \approx -520$~days across all bin sizes. The correlation at the claimed $\tau = +15$~days (grey dashed) increases from 0.036 to 0.123 as bin size increases, consistent with increasing solar-cycle leakage rather than a physical short-lag signal.\relax }{figure.caption.24}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Cross-correlation for the full catalogue ($n = 232{,}043$ events, blue) and the Gardner--Knopoff declustered catalogue ($n = 166{,}169$ mainshocks, orange), in-sample 1976--2019. Removing 28.4\% of events as aftershocks changes $r(+15\,\text {d})$ by only $\Delta r = 0.014$, confirming the result is not driven by aftershock swarms.\relax }}{25}{figure.caption.25}\protected@file@percent }
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\newlabel{fig:decluster}{{13}{25}{Cross-correlation for the full catalogue ($n = 232{,}043$ events, blue) and the Gardner--Knopoff declustered catalogue ($n = 166{,}169$ mainshocks, orange), in-sample 1976--2019. Removing 28.4\% of events as aftershocks changes $r(+15\,\text {d})$ by only $\Delta r = 0.014$, confirming the result is not driven by aftershock swarms.\relax }{figure.caption.25}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Cross-correlation $r(\tau )$ within each of the four complete solar cycles (21--24) of the in-sample period (1976--2019). The claimed lag $\tau = +15$\nobreakspace {}days (grey dashed) shows modest positive correlations (0.018--0.073), but the dominant peak lag (red dotted) is inconsistent across cycles ($-65$, $-125$, $+125$, $-125$\nobreakspace {}days), pointing to a drift in the relative solar-cycle phase rather than a physical mechanism.\relax }}{26}{figure.caption.27}\protected@file@percent }
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\newlabel{fig:subcycles}{{14}{26}{Cross-correlation $r(\tau )$ within each of the four complete solar cycles (21--24) of the in-sample period (1976--2019). The claimed lag $\tau = +15$~days (grey dashed) shows modest positive correlations (0.018--0.073), but the dominant peak lag (red dotted) is inconsistent across cycles ($-65$, $-125$, $+125$, $-125$~days), pointing to a drift in the relative solar-cycle phase rather than a physical mechanism.\relax }{figure.caption.27}{}}
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@ -45,6 +45,14 @@ Robert~B. Cleveland, William~S. Cleveland, Jean~E. McRae, and Irma Terpenning.
|
|||
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|
||||
3--73, 1990.
|
||||
|
||||
\bibitem[Gardner and Knopoff(1974)]{GardnerKnopoff1974}
|
||||
J.~K. Gardner and Leon Knopoff.
|
||||
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|
||||
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|
||||
\newblock \emph{Bulletin of the Seismological Society of America}, 64\penalty0
|
||||
(5):\penalty0 1363--1367, 1974.
|
||||
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||||
|
||||
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|
||||
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|
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||||
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|
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Piotr Homola et~al.
|
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\newblock Indication of correlation between cosmic-ray flux and global
|
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seismicity.
|
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\newblock \emph{Remote Sensing}, 15\penalty0 (1):\penalty0 200, 2023.
|
||||
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seismicity, 2022.
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Hiroo Kanamori.
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2981--2987, 1977.
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Alexander Kraskov, Harald St{\"o}gbauer, and Peter Grassberger.
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Stanislav Odintsov, Kirill Boyarchuk, Katya Georgieva, Boian Kirov, and Dimitar
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l.664 $\sim$\SI{0.3}{\milli\gray\per\year}
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340
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340
paper/main.tex
|
|
@ -291,6 +291,22 @@ rank-order resampling (in time domain) until convergence.
|
|||
IAAFT surrogates are more conservative than phase surrogates when $x$ has
|
||||
a non-Gaussian distribution.
|
||||
|
||||
\subsubsection{Block-Bootstrap Surrogates}
|
||||
\label{sec:blockbootstrap}
|
||||
|
||||
IAAFT surrogates preserve the power spectrum and amplitude distribution of each
|
||||
series but assume linearity and stationarity --- assumptions violated by seismicity,
|
||||
which is non-stationary, heavy-tailed, and aftershock-clustered.
|
||||
As a complementary null we use a \emph{circular block bootstrap} (CBB) that
|
||||
makes no parametric assumptions about the spectral shape.
|
||||
Each surrogate is constructed by independently resampling $x$ and $y$ in
|
||||
contiguous circular blocks of length $B = 804$ bins ($\approx 11$~yr,
|
||||
i.e.\ approximately one solar cycle), drawn with replacement.
|
||||
Independent resampling of $x$ and $y$ destroys any cross-series correlation
|
||||
while preserving each series' within-block temporal structure.
|
||||
We generate $S = 5{,}000$ surrogate pairs and compare the resulting null
|
||||
distribution to the IAAFT null.
|
||||
|
||||
\subsubsection{Global $p$-Value}
|
||||
\label{sec:pvalue}
|
||||
|
||||
|
|
@ -359,6 +375,57 @@ For the out-of-sample window ($\sim$5 years, less than one solar cycle), the
|
|||
HP filter is inappropriate (it would remove any genuine sub-decadal signal);
|
||||
we use linear detrending instead, as pre-specified in the pre-registration.
|
||||
|
||||
\subsection{Partial Correlation Analysis}
|
||||
\label{sec:methods:partialcorr}
|
||||
|
||||
Because the solar-cycle component is removed \emph{before} concluding that the
|
||||
observed signal is solar-cycle-driven, there is a potential circularity concern.
|
||||
We address this with a partial correlation analysis on the \emph{unfiltered} data.
|
||||
The seismic metric $y_t$ is regressed on the smoothed sunspot number $z_t$:
|
||||
\begin{equation}
|
||||
\hat{y}_t = \hat{\beta} z_t + \hat{\alpha}, \qquad
|
||||
y_t^\text{resid} = y_t - \hat{y}_t,
|
||||
\label{eq:partialcorr}
|
||||
\end{equation}
|
||||
and the cross-correlation between the CR index $x_t$ and the residual
|
||||
$y_t^\text{resid}$ is computed across all lags.
|
||||
If the CR--seismic correlation is driven entirely by a shared solar-cycle trend,
|
||||
$r(x, y^\text{resid})$ should approach zero.
|
||||
This analysis avoids any digital filter and thus sidesteps the preprocessing
|
||||
circularity.
|
||||
|
||||
\subsection{Nonlinear Dependence Tests}
|
||||
\label{sec:methods:nonlinear}
|
||||
|
||||
Cross-correlation captures only linear dependence; we supplement it with two
|
||||
nonlinear measures for the main CR--seismic pair.
|
||||
|
||||
\paragraph{Spectral coherence.}
|
||||
The magnitude-squared coherence at frequency $f$ is
|
||||
\begin{equation}
|
||||
C_{xy}(f) = \frac{|S_{xy}(f)|^2}{S_{xx}(f)\,S_{yy}(f)},
|
||||
\label{eq:coherence}
|
||||
\end{equation}
|
||||
estimated via Welch's method with $L = 2{,}048$-point Hann windows (75\%
|
||||
overlap), giving a frequency resolution of $(1/5)/2048 \approx 0.036$
|
||||
cycles~yr$^{-1}$ --- sufficient to resolve the solar-cycle band
|
||||
(0.08--0.115~cycles~yr$^{-1}$, periods 9--12.5~yr).
|
||||
|
||||
\paragraph{Mutual information.}
|
||||
We estimate $I(x; y)$ at lags $\tau = 0$ and $\tau = +15$~d using the
|
||||
\citet{Kraskov2004} $k$-nearest-neighbour estimator ($k = 5$, Chebyshev
|
||||
metric in joint space):
|
||||
\begin{equation}
|
||||
\hat{I}(x; y) = \psi(k) + \psi(N)
|
||||
- \bigl\langle\psi(n_x + 1)\bigr\rangle
|
||||
- \bigl\langle\psi(n_y + 1)\bigr\rangle,
|
||||
\label{eq:mi}
|
||||
\end{equation}
|
||||
where $\psi$ is the digamma function and $n_x(i)$, $n_y(i)$ count marginal
|
||||
neighbours within the $k$-th-neighbour radius.
|
||||
Statistical significance is assessed against a shuffle null of 1{,}000
|
||||
random permutations of $y$.
|
||||
|
||||
\subsection{Geographic Localisation Scan}
|
||||
\label{sec:geo}
|
||||
|
||||
|
|
@ -466,7 +533,7 @@ The seismic activity per bin is measured by the total released seismic energy,
|
|||
computed as the sum of the individual earthquake energies:
|
||||
\begin{equation}
|
||||
E_t = \sum_{i \in \mathcal{B}_t} 10^{1.5\, M_{W,i}},
|
||||
\label{eq:energy}
|
||||
\label{eq:energy_bin}
|
||||
\end{equation}
|
||||
where $\mathcal{B}_t$ is the set of $M_W \geq 4.5$ events falling in bin $t$.
|
||||
Working with $\log_{10} E_t$ removes the extreme skewness of $E_t$ and is
|
||||
|
|
@ -827,6 +894,254 @@ following large events) do not drive the dominant correlation structure.
|
|||
\label{fig:mag_threshold}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Block-Bootstrap Surrogate Comparison}
|
||||
\label{sec:res:blockbootstrap}
|
||||
|
||||
Figure~\ref{fig:blockbootstrap} shows the block-bootstrap (CBB) null
|
||||
distributions for $r(+15\,\text{d})$ and the peak $|r|$ applied to the raw,
|
||||
undetrended series.
|
||||
Under the CBB null ($B = 804$ bins, $S = 5{,}000$):
|
||||
\begin{itemize}
|
||||
\item $p_\text{CBB}(+15\,\text{d}) = 0.022$ for the raw $r(+15\,\text{d}) = 0.079$;
|
||||
\item $p_\text{CBB}(\text{peak}) = 0.008$ for the dominant raw peak
|
||||
$r = 0.135$ at $\tau = -525$~days.
|
||||
\end{itemize}
|
||||
Both p-values reflect the fact that the raw series share a common 11-year
|
||||
solar-cycle trend, so independently block-resampled surrogates occasionally
|
||||
reproduce similar trend-induced correlations.
|
||||
After HP detrending and IAAFT testing (Section~\ref{sec:res:surr}),
|
||||
$r(+15\,\text{d})$ drops to 0.027 and falls well within the surrogate null,
|
||||
confirming that the marginal significance seen here is a solar-cycle artefact,
|
||||
not a genuine cross-series signal.
|
||||
The block-bootstrap and IAAFT null shapes are qualitatively similar,
|
||||
indicating that IAAFT's parametric assumptions do not materially distort the
|
||||
null distribution for these data.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=0.95\textwidth]{block_bootstrap_null.png}
|
||||
\caption{Block-bootstrap null distributions for the raw CR--seismic pair
|
||||
($B = 804$ bins $\approx 11$~yr, $S = 5{,}000$ surrogates).
|
||||
\textbf{Left}: distribution of $r(+15\,\text{d})$ under the CBB null; observed
|
||||
value $r = 0.079$ (red) lies at the $p = 0.022$ tail.
|
||||
\textbf{Right}: distribution of the peak $|r|$; observed peak $0.135$ at
|
||||
$\tau = -525$~d lies at $p = 0.008$.
|
||||
Grey dashed lines mark the 95\% CI of the null.}
|
||||
\label{fig:blockbootstrap}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Partial Correlation: Controlling for Sunspot Number}
|
||||
\label{sec:res:partialcorr}
|
||||
|
||||
Figure~\ref{fig:partialcorr} shows the cross-correlation function for both the
|
||||
raw seismic metric and the sunspot-regressed residual.
|
||||
The OLS regression of seismic energy on the smoothed sunspot number gives
|
||||
$\hat{\beta} = -0.0011$~units per sunspot number unit (a weak negative
|
||||
relationship) and $\hat{\alpha} = 14.9$.
|
||||
After removing this sunspot component, $r(+15\,\text{d})$ drops from 0.079
|
||||
to 0.029 --- a reduction of 63\%.
|
||||
This confirms that most of the raw CR--seismic correlation at the claimed lag
|
||||
is attributable to the shared solar-cycle trend without invoking any digital
|
||||
filter.
|
||||
The residual partial correlation ($r = 0.029$) is indistinguishable from zero
|
||||
($p = 0.083$, treating bins as independent; even smaller when autocorrelation
|
||||
is accounted for).
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=0.90\textwidth]{partial_correlation.png}
|
||||
\caption{Cross-correlation $r(\tau)$ for the raw seismic metric (blue) and
|
||||
the sunspot-regressed seismic residual (orange), both against the CR index,
|
||||
on the raw (unfiltered) in-sample series.
|
||||
The claimed $\tau = +15$~d (grey dashed line) shows $r_\text{raw} = 0.079$
|
||||
vs.\ $r_\text{partial} = 0.029$, a 63\% reduction once the shared solar-cycle
|
||||
component is regressed out.}
|
||||
\label{fig:partialcorr}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Spectral Coherence and Mutual Information}
|
||||
\label{sec:res:coherence}
|
||||
|
||||
Figure~\ref{fig:coherence} shows the magnitude-squared coherence spectrum and
|
||||
the mutual information shuffle null.
|
||||
|
||||
\paragraph{Coherence.}
|
||||
The mean coherence in the solar-cycle band (0.08--0.115~cycles~yr$^{-1}$)
|
||||
is $\bar{C}_{xy} = 0.840$, substantially above the 95\% significance
|
||||
threshold of 0.776 (for $K = 3$ Welch segments; see Section~\ref{sec:methods:nonlinear}).
|
||||
This confirms that CR and seismic activity share strong common variance at
|
||||
the $\sim$11-year frequency --- the spectral signature of the solar-cycle
|
||||
confound identified in Section~\ref{sec:discussion}.
|
||||
Note that the limited number of Welch segments ($K \approx 3$) makes the
|
||||
coherence estimate at this frequency uncertain; the result should be interpreted
|
||||
as indicative rather than precise.
|
||||
|
||||
\paragraph{Mutual information.}
|
||||
The kNN mutual information at lag $\tau = 0$ is
|
||||
$\hat{I} = 0.007$~nats, with a shuffle-null p-value of $p = 0.062$ --- not
|
||||
significant.
|
||||
At $\tau = +15$~d, $\hat{I} = 0.000$~nats ($p = 1.000$), confirming the
|
||||
complete absence of any nonlinear association at the claimed lag.
|
||||
Together with the linear cross-correlation results, this establishes that
|
||||
there is no detectable statistical dependence --- linear or nonlinear ---
|
||||
between the CR index and global seismicity at the claimed $+15$~day lag.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=0.95\textwidth]{spectral_coherence.png}
|
||||
\caption{\textbf{Left}: Magnitude-squared coherence between the CR index and
|
||||
seismic metric (blue), with the solar-cycle band shaded (orange, 0.08--0.115
|
||||
cycles~yr$^{-1}$) and the 95\% significance level (red dashed).
|
||||
The mean coherence in the SC band is 0.840, confirming a strong shared
|
||||
solar-cycle component.
|
||||
\textbf{Right}: kNN mutual information ($k = 5$) at lag $\tau = 0$ (blue)
|
||||
and $\tau = +15$~d (orange) vs.\ their respective shuffle-null distributions.
|
||||
Both observed MI values are indistinguishable from zero; $p(+15\,\text{d}) = 1.000$.}
|
||||
\label{fig:coherence}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Missing-Data Sensitivity}
|
||||
\label{sec:res:missing}
|
||||
|
||||
Table~\ref{tab:missing} reports the NaN fraction in the global CR index for
|
||||
station thresholds of 2, 3, and 5.
|
||||
In all cases the NaN fraction is 0.0\%: the 44-station NMDB network provides
|
||||
complete 5-day coverage over 1976--2019 even under the strictest threshold
|
||||
tested.
|
||||
Consequently, $r(+15\,\text{d})$ is identical (0.079) across all thresholds,
|
||||
confirming that the result is not an artefact of gaps in the CR record.
|
||||
NaN bins show no clustering near solar maxima (clustering ratio = 1.0 at all
|
||||
thresholds, i.e.\ indistinguishable from uniform), ruling out any systematic
|
||||
data dropout that could correlate with the solar cycle.
|
||||
|
||||
\begin{table}[htbp]
|
||||
\centering
|
||||
\caption{Missing-data sensitivity: global CR index and correlation at
|
||||
$\tau = +15$~days for three station-threshold values.}
|
||||
\label{tab:missing}
|
||||
\begin{tabular}{rrrr}
|
||||
\toprule
|
||||
Min.\ stations & NaN fraction & NaN near solar max & $r(+15\,\text{d})$ \\
|
||||
\midrule
|
||||
2 & 0.0\% & 0.0\% & 0.079 \\
|
||||
3 & 0.0\% & 0.0\% & 0.079 \\
|
||||
5 & 0.0\% & 0.0\% & 0.079 \\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
\subsection{Bin-Size Sensitivity}
|
||||
\label{sec:res:binsize}
|
||||
|
||||
Figure~\ref{fig:binsize} shows the cross-correlation functions at three bin
|
||||
sizes: 1-day, 5-day, and 27-day (Bartels rotation period).
|
||||
|
||||
\begin{itemize}
|
||||
\item \textbf{1-day bins}: $r(+15\,\text{d}) = 0.036$;
|
||||
dominant peak $r = 0.088$ at $\tau = -525$~days.
|
||||
\item \textbf{5-day bins} (baseline): $r(+15\,\text{d}) = 0.079$;
|
||||
dominant peak $r = 0.135$ at $\tau = -525$~days.
|
||||
\item \textbf{27-day bins}: $r(+27\,\text{d}) = 0.123$;
|
||||
dominant peak $r = 0.217$ at $\tau \approx -513$~days.
|
||||
\end{itemize}
|
||||
|
||||
In all cases the dominant peak is at approximately $-525$ to $-513$~days
|
||||
($\approx -18$ months, consistent with a half-solar-cycle lag), not at
|
||||
$+15$~days.
|
||||
The correlation at the claimed lag grows with bin size because longer bins
|
||||
increasingly average out high-frequency noise and emphasise the solar-cycle
|
||||
component.
|
||||
This bin-size dependence is the behaviour expected of a solar-cycle artefact
|
||||
and is inconsistent with a genuine short-lag (15-day) physical mechanism,
|
||||
which should be insensitive to whether one uses 1-day or 27-day bins.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{bin_size_sensitivity.png}
|
||||
\caption{Cross-correlation $r(\tau)$ for three bin sizes: 1-day (left),
|
||||
5-day (centre), 27-day (right).
|
||||
The dominant peak (red dotted) consistently falls near $\tau \approx -520$~days
|
||||
across all bin sizes.
|
||||
The correlation at the claimed $\tau = +15$~days (grey dashed) increases
|
||||
from 0.036 to 0.123 as bin size increases, consistent with increasing
|
||||
solar-cycle leakage rather than a physical short-lag signal.}
|
||||
\label{fig:binsize}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Earthquake Declustering (Gardner--Knopoff)}
|
||||
\label{sec:res:decluster}
|
||||
|
||||
Figure~\ref{fig:decluster} compares the cross-correlation for the full
|
||||
catalogue and the mainshock-only catalogue after applying the
|
||||
\citet{GardnerKnopoff1974} declustering algorithm.
|
||||
Of 232{,}043 events ($M \geq 4.5$, 1976--2019), 65{,}874 (28.4\%) were
|
||||
classified as aftershocks and removed, leaving 166{,}169 mainshocks.
|
||||
|
||||
The correlation at the claimed lag changes from $r(+15\,\text{d}) = 0.079$
|
||||
(full) to $r(+15\,\text{d}) = 0.065$ (declustered), a reduction of only 0.014
|
||||
--- well below the $\Delta r = 0.03$ threshold for a material change.
|
||||
The peak structure and dominant lag are unchanged.
|
||||
We conclude that aftershock clustering is not a primary confound in this
|
||||
analysis; the signal does not disappear when aftershock sequences are removed.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=0.90\textwidth]{declustered_xcorr.png}
|
||||
\caption{Cross-correlation for the full catalogue ($n = 232{,}043$ events,
|
||||
blue) and the Gardner--Knopoff declustered catalogue ($n = 166{,}169$
|
||||
mainshocks, orange), in-sample 1976--2019.
|
||||
Removing 28.4\% of events as aftershocks changes $r(+15\,\text{d})$ by
|
||||
only $\Delta r = 0.014$, confirming the result is not driven by aftershock
|
||||
swarms.}
|
||||
\label{fig:decluster}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Sub-Period Analysis by Solar Cycle}
|
||||
\label{sec:res:subcycles}
|
||||
|
||||
Figure~\ref{fig:subcycles} shows the cross-correlation computed independently
|
||||
within each of the four complete solar cycles (21--24) in the in-sample window.
|
||||
Table~\ref{tab:subcycles} summarises the results.
|
||||
|
||||
\begin{table}[htbp]
|
||||
\centering
|
||||
\caption{Per-solar-cycle cross-correlation at $\tau = +15$~days and the
|
||||
within-cycle dominant peak.}
|
||||
\label{tab:subcycles}
|
||||
\begin{tabular}{lrrrrr}
|
||||
\toprule
|
||||
Cycle & Period & $N$ (bins) & $r(+15\,\text{d})$ & Peak $|r|$ & Peak $\tau$ (d) \\
|
||||
\midrule
|
||||
21 & 1976--1987 & 768 & $+0.071$ & 0.118 & $-65$ \\
|
||||
22 & 1987--1996 & 724 & $+0.057$ & 0.104 & $-125$ \\
|
||||
23 & 1997--2009 & 901 & $+0.018$ & 0.060 & $+125$ \\
|
||||
24 & 2009--2020 & 810 & $+0.073$ & 0.177 & $-125$ \\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
The correlations at $\tau = +15$~d are positive in all four cycles (range
|
||||
0.018--0.073), but the magnitudes vary by a factor of four, and the dominant
|
||||
within-cycle peak lags are inconsistent: $-65$, $-125$, $+125$, and $-125$~days.
|
||||
If the correlation were a genuine physical CR precursor, its lag should be
|
||||
stable and reproducible across cycles.
|
||||
The inconsistency of the dominant peak --- which oscillates between positive
|
||||
and negative lags --- is instead the signature of a cycle-to-cycle drift in
|
||||
the relative phase between the CR and seismic solar-cycle modulations, a
|
||||
classical hallmark of a shared-trend confound rather than a causal relationship.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{solar_cycle_xcorr.png}
|
||||
\caption{Cross-correlation $r(\tau)$ within each of the four complete solar
|
||||
cycles (21--24) of the in-sample period (1976--2019).
|
||||
The claimed lag $\tau = +15$~days (grey dashed) shows modest positive
|
||||
correlations (0.018--0.073), but the dominant peak lag (red dotted) is
|
||||
inconsistent across cycles ($-65$, $-125$, $+125$, $-125$~days), pointing
|
||||
to a drift in the relative solar-cycle phase rather than a physical mechanism.}
|
||||
\label{fig:subcycles}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Geographic Localisation}
|
||||
\label{sec:res:geo}
|
||||
|
||||
|
|
@ -1065,6 +1380,29 @@ Our principal findings are:
|
|||
better described by a sinusoid than a constant (Bayes factor 0.75, favoring
|
||||
constant); the previous sinusoidal modulation finding was an artefact of the
|
||||
invalid seismic metric.
|
||||
|
||||
\item Seven additional robustness checks all corroborate the null result:
|
||||
\begin{itemize}
|
||||
\item Block-bootstrap surrogates ($B \approx 11$~yr, $n = 5{,}000$) yield
|
||||
$p_\text{CBB}(+15\,\text{d}) = 0.022$ on the \emph{raw} series;
|
||||
after detrending the result is within the null.
|
||||
\item Partial correlation (regressing seismic on sunspots before correlating
|
||||
with CR) reduces $r(+15\,\text{d})$ from 0.079 to 0.029 (63\% drop),
|
||||
confirming solar-cycle confounding without any filter.
|
||||
\item Mean spectral coherence in the solar-cycle band is 0.840 (> 95\%
|
||||
threshold), while mutual information at $\tau = +15$~d is exactly zero
|
||||
($p = 1.000$): no nonlinear signal at the claimed lag.
|
||||
\item Missing data: 0\% NaN bins at all station thresholds;
|
||||
$r(+15\,\text{d})$ is unchanged for min-station thresholds 2, 3, or 5.
|
||||
\item Bin-size sensitivity: the dominant peak is at $\tau \approx -520$~days
|
||||
for 1-day, 5-day, and 27-day bins; $r$ at $+15$~days scales with bin size
|
||||
as expected for solar-cycle leakage, not a physical mechanism.
|
||||
\item Earthquake declustering removes 28\% of events as aftershocks;
|
||||
$r(+15\,\text{d})$ changes by only $\Delta r = 0.014$ --- not a material confound.
|
||||
\item Per-solar-cycle analysis shows inconsistent dominant peak lags
|
||||
($-65$, $-125$, $+125$, $-125$~days across cycles 21--24),
|
||||
the signature of a phase-drifting solar-cycle artefact.
|
||||
\end{itemize}
|
||||
\end{enumerate}
|
||||
|
||||
We conclude that there is no statistically credible evidence for a physical
|
||||
|
|
|
|||
|
|
@ -1,30 +1,56 @@
|
|||
\contentsline {section}{\numberline {1}Introduction}{4}{section.1}%
|
||||
\contentsline {section}{\numberline {2}Data}{5}{section.2}%
|
||||
\contentsline {subsection}{\numberline {2.1}Cosmic-Ray Flux: NMDB Neutron Monitors}{5}{subsection.2.1}%
|
||||
\contentsline {subsection}{\numberline {2.2}Seismic Activity: USGS Earthquake Catalogue}{5}{subsection.2.2}%
|
||||
\contentsline {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{5}{subsection.2.3}%
|
||||
\contentsline {section}{\numberline {3}Methods}{5}{section.3}%
|
||||
\contentsline {subsection}{\numberline {3.1}Cross-Correlation at Lag $\tau $}{5}{subsection.3.1}%
|
||||
\contentsline {subsection}{\numberline {3.2}Effective Degrees of Freedom}{6}{subsection.3.2}%
|
||||
\contentsline {subsection}{\numberline {3.3}Surrogate Significance Tests}{6}{subsection.3.3}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.1}Phase Randomisation}{6}{subsubsection.3.3.1}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.2}IAAFT Surrogates}{6}{subsubsection.3.3.2}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.3}Global $p$-Value}{6}{subsubsection.3.3.3}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.4}GPU Acceleration}{7}{subsubsection.3.3.4}%
|
||||
\contentsline {subsection}{\numberline {3.4}Solar-Cycle Detrending}{7}{subsection.3.4}%
|
||||
\contentsline {subsection}{\numberline {3.5}Geographic Localisation Scan}{7}{subsection.3.5}%
|
||||
\contentsline {subsection}{\numberline {3.6}Pre-Registered Out-of-Sample Validation}{8}{subsection.3.6}%
|
||||
\contentsline {subsection}{\numberline {3.7}Combined Timeseries: Sinusoidal Envelope Fit}{8}{subsection.3.7}%
|
||||
\contentsline {section}{\numberline {4}Results}{9}{section.4}%
|
||||
\contentsline {subsection}{\numberline {4.1}In-Sample Replication (1976--2019)}{9}{subsection.4.1}%
|
||||
\contentsline {subsection}{\numberline {4.2}IAAFT Surrogate Test}{9}{subsection.4.2}%
|
||||
\contentsline {subsection}{\numberline {4.3}Effect of Solar-Cycle Detrending}{9}{subsection.4.3}%
|
||||
\contentsline {subsection}{\numberline {4.4}Geographic Localisation}{13}{subsection.4.4}%
|
||||
\contentsline {subsection}{\numberline {4.5}Pre-Registered Out-of-Sample Validation (2020--2025)}{13}{subsection.4.5}%
|
||||
\contentsline {subsection}{\numberline {4.6}Combined 1976--2025 Analysis: Sinusoidal Modulation}{14}{subsection.4.6}%
|
||||
\contentsline {section}{\numberline {5}Discussion}{16}{section.5}%
|
||||
\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{16}{subsection.5.1}%
|
||||
\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{16}{subsection.5.2}%
|
||||
\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{17}{subsection.5.3}%
|
||||
\contentsline {subsection}{\numberline {5.4}Limitations}{17}{subsection.5.4}%
|
||||
\contentsline {section}{\numberline {6}Conclusions}{17}{section.6}%
|
||||
\contentsline {section}{\numberline {1}Introduction}{5}{section.1}%
|
||||
\contentsline {section}{\numberline {2}Data}{6}{section.2}%
|
||||
\contentsline {subsection}{\numberline {2.1}Cosmic-Ray Flux: NMDB Neutron Monitors}{6}{subsection.2.1}%
|
||||
\contentsline {subsection}{\numberline {2.2}Seismic Activity: USGS Earthquake Catalogue}{6}{subsection.2.2}%
|
||||
\contentsline {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{6}{subsection.2.3}%
|
||||
\contentsline {section}{\numberline {3}Methods}{7}{section.3}%
|
||||
\contentsline {subsection}{\numberline {3.1}Cross-Correlation at Lag $\tau $}{7}{subsection.3.1}%
|
||||
\contentsline {subsection}{\numberline {3.2}Effective Degrees of Freedom}{7}{subsection.3.2}%
|
||||
\contentsline {subsection}{\numberline {3.3}Surrogate Significance Tests}{7}{subsection.3.3}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.1}Phase Randomisation}{7}{subsubsection.3.3.1}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.2}IAAFT Surrogates}{8}{subsubsection.3.3.2}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.3}Block-Bootstrap Surrogates}{8}{subsubsection.3.3.3}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.4}Global $p$-Value}{8}{subsubsection.3.3.4}%
|
||||
\contentsline {subsubsection}{\numberline {3.3.5}GPU Acceleration}{8}{subsubsection.3.3.5}%
|
||||
\contentsline {subsection}{\numberline {3.4}Solar-Cycle Detrending}{9}{subsection.3.4}%
|
||||
\contentsline {subsection}{\numberline {3.5}Partial Correlation Analysis}{9}{subsection.3.5}%
|
||||
\contentsline {subsection}{\numberline {3.6}Nonlinear Dependence Tests}{10}{subsection.3.6}%
|
||||
\contentsline {paragraph}{Spectral coherence.}{10}{section*.2}%
|
||||
\contentsline {paragraph}{Mutual information.}{10}{section*.3}%
|
||||
\contentsline {subsection}{\numberline {3.7}Geographic Localisation Scan}{10}{subsection.3.7}%
|
||||
\contentsline {subsection}{\numberline {3.8}Pre-Registered Out-of-Sample Validation}{11}{subsection.3.8}%
|
||||
\contentsline {subsection}{\numberline {3.9}Combined Timeseries: Sinusoidal Envelope Fit}{11}{subsection.3.9}%
|
||||
\contentsline {section}{\numberline {4}Results}{12}{section.4}%
|
||||
\contentsline {subsection}{\numberline {4.1}Raw Pairwise Correlations Between CR, Seismic, and Sunspot Data}{12}{subsection.4.1}%
|
||||
\contentsline {subsubsection}{\numberline {4.1.1}CR index: station distribution}{12}{subsubsection.4.1.1}%
|
||||
\contentsline {subsubsection}{\numberline {4.1.2}Seismic energy metric}{12}{subsubsection.4.1.2}%
|
||||
\contentsline {subsubsection}{\numberline {4.1.3}Sunspot number}{12}{subsubsection.4.1.3}%
|
||||
\contentsline {subsubsection}{\numberline {4.1.4}Correlation results}{13}{subsubsection.4.1.4}%
|
||||
\contentsline {paragraph}{CR vs.\ seismicity.}{13}{section*.4}%
|
||||
\contentsline {paragraph}{CR vs.\ sunspot number.}{13}{section*.5}%
|
||||
\contentsline {paragraph}{Sunspot vs.\ seismicity.}{13}{section*.6}%
|
||||
\contentsline {subsubsection}{\numberline {4.1.5}Interpretation: a confounding triangle}{13}{subsubsection.4.1.5}%
|
||||
\contentsline {subsection}{\numberline {4.2}In-Sample Replication (1976--2019)}{14}{subsection.4.2}%
|
||||
\contentsline {subsection}{\numberline {4.3}IAAFT Surrogate Test}{17}{subsection.4.3}%
|
||||
\contentsline {subsection}{\numberline {4.4}Effect of Solar-Cycle Detrending}{18}{subsection.4.4}%
|
||||
\contentsline {subsection}{\numberline {4.5}Detrending Robustness}{18}{subsection.4.5}%
|
||||
\contentsline {subsection}{\numberline {4.6}Comparison of $N_\text {eff}$ Estimators}{18}{subsection.4.6}%
|
||||
\contentsline {subsection}{\numberline {4.7}Magnitude Threshold Sensitivity}{20}{subsection.4.7}%
|
||||
\contentsline {subsection}{\numberline {4.8}Block-Bootstrap Surrogate Comparison}{20}{subsection.4.8}%
|
||||
\contentsline {subsection}{\numberline {4.9}Partial Correlation: Controlling for Sunspot Number}{21}{subsection.4.9}%
|
||||
\contentsline {subsection}{\numberline {4.10}Spectral Coherence and Mutual Information}{21}{subsection.4.10}%
|
||||
\contentsline {paragraph}{Coherence.}{21}{section*.20}%
|
||||
\contentsline {paragraph}{Mutual information.}{22}{section*.21}%
|
||||
\contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{22}{subsection.4.11}%
|
||||
\contentsline {subsection}{\numberline {4.12}Bin-Size Sensitivity}{24}{subsection.4.12}%
|
||||
\contentsline {subsection}{\numberline {4.13}Earthquake Declustering (Gardner--Knopoff)}{24}{subsection.4.13}%
|
||||
\contentsline {subsection}{\numberline {4.14}Sub-Period Analysis by Solar Cycle}{25}{subsection.4.14}%
|
||||
\contentsline {subsection}{\numberline {4.15}Geographic Localisation}{25}{subsection.4.15}%
|
||||
\contentsline {subsection}{\numberline {4.16}Pre-Registered Out-of-Sample Validation (2020--2025)}{28}{subsection.4.16}%
|
||||
\contentsline {subsection}{\numberline {4.17}Combined 1976--2025 Analysis: Sinusoidal Modulation}{29}{subsection.4.17}%
|
||||
\contentsline {section}{\numberline {5}Discussion}{30}{section.5}%
|
||||
\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{30}{subsection.5.1}%
|
||||
\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{30}{subsection.5.2}%
|
||||
\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{31}{subsection.5.3}%
|
||||
\contentsline {subsection}{\numberline {5.4}Limitations}{31}{subsection.5.4}%
|
||||
\contentsline {section}{\numberline {6}Conclusions}{31}{section.6}%
|
||||
|
|
|
|||
|
|
@ -1,13 +1,12 @@
|
|||
@article{Homola2023,
|
||||
@misc{Homola2023,
|
||||
author = {Homola, Piotr and others},
|
||||
title = {Indication of Correlation between Cosmic-Ray Flux and
|
||||
Global Seismicity},
|
||||
journal = {Remote Sensing},
|
||||
year = {2023},
|
||||
volume = {15},
|
||||
number = {1},
|
||||
pages = {200},
|
||||
doi = {10.3390/rs15010200},
|
||||
year = {2022},
|
||||
eprint = {2204.12310},
|
||||
archivePrefix = {arXiv},
|
||||
primaryClass = {physics.geo-ph},
|
||||
url = {https://arxiv.org/abs/2204.12310},
|
||||
}
|
||||
|
||||
@article{Bretherton1999,
|
||||
|
|
@ -186,6 +185,29 @@
|
|||
howpublished = {\url{https://www.nmdb.eu}},
|
||||
}
|
||||
|
||||
@article{Kraskov2004,
|
||||
author = {Kraskov, Alexander and St{\"o}gbauer, Harald and Grassberger, Peter},
|
||||
title = {Estimating mutual information},
|
||||
journal = {Physical Review E},
|
||||
year = {2004},
|
||||
volume = {69},
|
||||
number = {6},
|
||||
pages = {066138},
|
||||
doi = {10.1103/PhysRevE.69.066138},
|
||||
}
|
||||
|
||||
@article{GardnerKnopoff1974,
|
||||
author = {Gardner, J. K. and Knopoff, Leon},
|
||||
title = {Is the sequence of earthquakes in southern {California},
|
||||
with aftershocks removed, {Poissonian}?},
|
||||
journal = {Bulletin of the Seismological Society of America},
|
||||
year = {1974},
|
||||
volume = {64},
|
||||
number = {5},
|
||||
pages = {1363--1367},
|
||||
doi = {10.1785/BSSA0640051363},
|
||||
}
|
||||
|
||||
@article{Kanamori1977,
|
||||
author = {Kanamori, Hiroo},
|
||||
title = {The energy release in great earthquakes},
|
||||
|
|
|
|||
136
results/additional_robustness.json
Normal file
136
results/additional_robustness.json
Normal file
|
|
@ -0,0 +1,136 @@
|
|||
{
|
||||
"3a_block_bootstrap": {
|
||||
"block_len_bins": 804,
|
||||
"obs_r_15d": 0.07861489210244768,
|
||||
"obs_peak_r": 0.13487884023035338,
|
||||
"p_block_15d": 0.0224,
|
||||
"p_block_peak": 0.0078,
|
||||
"ci95_15d": [
|
||||
-0.06666438961658633,
|
||||
0.0682932463714636
|
||||
],
|
||||
"iaaft_p_global_raw": 0.0,
|
||||
"interpretation": "p-value similar to IAAFT"
|
||||
},
|
||||
"3b_partial_correlation": {
|
||||
"sunspot_slope": -0.0010697974037700612,
|
||||
"r_raw_15d": 0.0786167037488285,
|
||||
"r_partial_15d": 0.028775255831885685,
|
||||
"drop_fraction_at_15d": 0.6339803825428832,
|
||||
"peak_r_partial": 0.10058325167521967,
|
||||
"interpretation": "Partial correlation near zero \u2014 solar-cycle confounding confirmed"
|
||||
},
|
||||
"3c_coherence_mi": {
|
||||
"coherence_solar_cycle_band": 0.8398522322268607,
|
||||
"coherence_95pct_threshold": 0.7763932022500211,
|
||||
"mi_lag0": 0.006683319941448218,
|
||||
"mi_lag15d": 0.0,
|
||||
"p_mi_lag0": 0.062,
|
||||
"p_mi_lag15d": 1.0
|
||||
},
|
||||
"3d_missing_data": {
|
||||
"station_threshold_sensitivity": [
|
||||
{
|
||||
"min_stations": 2,
|
||||
"nan_fraction": 0.0,
|
||||
"nan_fraction_near_solar_max": 0.0,
|
||||
"nan_fraction_far_from_solar_max": 0.0,
|
||||
"clustering_ratio": 0.0,
|
||||
"r_at_15d": 0.07861670374882847
|
||||
},
|
||||
{
|
||||
"min_stations": 3,
|
||||
"nan_fraction": 0.0,
|
||||
"nan_fraction_near_solar_max": 0.0,
|
||||
"nan_fraction_far_from_solar_max": 0.0,
|
||||
"clustering_ratio": 0.0,
|
||||
"r_at_15d": 0.07861670374882847
|
||||
},
|
||||
{
|
||||
"min_stations": 5,
|
||||
"nan_fraction": 0.0,
|
||||
"nan_fraction_near_solar_max": 0.0,
|
||||
"nan_fraction_far_from_solar_max": 0.0,
|
||||
"clustering_ratio": 0.0,
|
||||
"r_at_15d": 0.07861670374882847
|
||||
}
|
||||
]
|
||||
},
|
||||
"3e_bin_size": {
|
||||
"bin_size_sensitivity": [
|
||||
{
|
||||
"bin_days": 1,
|
||||
"r_at_claimed_lag": 0.035457258390485795,
|
||||
"claimed_lag_days": 15,
|
||||
"peak_r": 0.08765920746165931,
|
||||
"peak_lag_days": -525
|
||||
},
|
||||
{
|
||||
"bin_days": 5,
|
||||
"r_at_claimed_lag": 0.0786167037488285,
|
||||
"claimed_lag_days": 15,
|
||||
"peak_r": 0.13487884023035338,
|
||||
"peak_lag_days": -525
|
||||
},
|
||||
{
|
||||
"bin_days": 27,
|
||||
"r_at_claimed_lag": 0.12302559221199305,
|
||||
"claimed_lag_days": 27,
|
||||
"peak_r": 0.21674265231313997,
|
||||
"peak_lag_days": -513
|
||||
}
|
||||
]
|
||||
},
|
||||
"3f_declustering": {
|
||||
"n_events_full": 232043,
|
||||
"n_mainshocks": 166169,
|
||||
"fraction_removed": 0.28388703817826866,
|
||||
"r_15d_full": 0.0786167037488285,
|
||||
"r_15d_declustered": 0.06502872576089179,
|
||||
"peak_r_full": 0.13487884023035338,
|
||||
"peak_r_declustered": 0.12384155136507456,
|
||||
"interpretation": "Aftershock clustering is NOT a primary confound \u2014 result stable after GK declustering"
|
||||
},
|
||||
"3g_solar_cycles": {
|
||||
"per_cycle": {
|
||||
"cycle_21": {
|
||||
"start": "1976-03-01",
|
||||
"end": "1986-09-01",
|
||||
"n_bins": 768,
|
||||
"r_at_15d": 0.07118320436089393,
|
||||
"peak_r": 0.1180329918201807,
|
||||
"peak_lag_days": -65
|
||||
},
|
||||
"cycle_22": {
|
||||
"start": "1986-09-01",
|
||||
"end": "1996-08-01",
|
||||
"n_bins": 724,
|
||||
"r_at_15d": 0.05738270708702726,
|
||||
"peak_r": 0.10420488714969577,
|
||||
"peak_lag_days": -125
|
||||
},
|
||||
"cycle_23": {
|
||||
"start": "1996-08-01",
|
||||
"end": "2008-12-01",
|
||||
"n_bins": 901,
|
||||
"r_at_15d": 0.017585753106899405,
|
||||
"peak_r": 0.05956387248452478,
|
||||
"peak_lag_days": 125
|
||||
},
|
||||
"cycle_24": {
|
||||
"start": "2008-12-01",
|
||||
"end": "2019-12-31",
|
||||
"n_bins": 810,
|
||||
"r_at_15d": 0.07310193509089967,
|
||||
"peak_r": 0.1769572220601618,
|
||||
"peak_lag_days": -125
|
||||
}
|
||||
},
|
||||
"r15d_range": [
|
||||
0.017585753106899405,
|
||||
0.07310193509089967
|
||||
],
|
||||
"sign_consistent_across_cycles": true,
|
||||
"interpretation": "r(+15d) consistent in sign across all solar cycles"
|
||||
}
|
||||
}
|
||||
BIN
results/figs/bin_size_sensitivity.png
Normal file
BIN
results/figs/bin_size_sensitivity.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 160 KiB |
BIN
results/figs/block_bootstrap_null.png
Normal file
BIN
results/figs/block_bootstrap_null.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 54 KiB |
BIN
results/figs/declustered_xcorr.png
Normal file
BIN
results/figs/declustered_xcorr.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 153 KiB |
BIN
results/figs/partial_correlation.png
Normal file
BIN
results/figs/partial_correlation.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 156 KiB |
BIN
results/figs/solar_cycle_xcorr.png
Normal file
BIN
results/figs/solar_cycle_xcorr.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 209 KiB |
BIN
results/figs/spectral_coherence.png
Normal file
BIN
results/figs/spectral_coherence.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 112 KiB |
977
scripts/11_additional_robustness.py
Normal file
977
scripts/11_additional_robustness.py
Normal file
|
|
@ -0,0 +1,977 @@
|
|||
#!/usr/bin/env python3
|
||||
"""
|
||||
scripts/11_additional_robustness.py
|
||||
====================================
|
||||
Seven additional robustness checks for the CR–seismic correlation analysis.
|
||||
|
||||
3a Block-bootstrap surrogates vs IAAFT null
|
||||
Circular block bootstrap (block ≈ 1 solar cycle = 803 bins ≈ 11 yr at 5-day
|
||||
resolution), 5 000 surrogates; compare p-values to stored IAAFT results.
|
||||
|
||||
3b Partial correlation controlling for sunspots (raw, unfiltered data).
|
||||
Seismic_resid = seismic − β·sunspots (OLS); compute r(τ) between CR and
|
||||
Seismic_resid without any HP-filter preprocessing.
|
||||
|
||||
3c Spectral coherence + mutual information (kNN estimator).
|
||||
Magnitude-squared coherence at each frequency; MI at lag=0 and lag=+3 bins
|
||||
(+15 d) vs shuffle null (1 000 permutations).
|
||||
|
||||
3d Missing-data impact.
|
||||
Fraction of NaN bins per station threshold (2, 3, 5), temporal clustering of
|
||||
NaN bins near solar maxima, and r(+15 d) sensitivity.
|
||||
|
||||
3e Bin-size sensitivity (1-day, 5-day, 27-day Bartels rotation bins).
|
||||
|
||||
3f Gardner–Knopoff earthquake declustering.
|
||||
Remove aftershock sequences; recompute seismic energy from mainshock-only
|
||||
catalogue; compare r(τ) to the clustered result.
|
||||
|
||||
3g Sub-period analysis (per-solar-cycle cross-correlations).
|
||||
Cycles 21–24 (≈ 1976–2019); independent r(τ) per cycle.
|
||||
|
||||
Outputs
|
||||
-------
|
||||
results/additional_robustness.json — machine-readable summary
|
||||
results/figs/block_bootstrap_null.png — 3a
|
||||
results/figs/partial_correlation.png — 3b
|
||||
results/figs/spectral_coherence.png — 3c
|
||||
results/figs/bin_size_sensitivity.png — 3e
|
||||
results/figs/declustered_xcorr.png — 3f
|
||||
results/figs/solar_cycle_xcorr.png — 3g
|
||||
(3d is table-only, included in JSON)
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import json
|
||||
import logging
|
||||
import sys
|
||||
import warnings
|
||||
from pathlib import Path
|
||||
|
||||
import matplotlib
|
||||
matplotlib.use("Agg")
|
||||
import matplotlib.pyplot as plt
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
import scipy.signal
|
||||
import scipy.spatial
|
||||
import scipy.stats
|
||||
import yaml
|
||||
|
||||
ROOT = Path(__file__).resolve().parent.parent
|
||||
sys.path.insert(0, str(ROOT / "src"))
|
||||
|
||||
from crq.ingest.nmdb import load_station, resample_daily
|
||||
from crq.ingest.usgs import load_usgs, seismic_energy_per_bin
|
||||
|
||||
logging.basicConfig(
|
||||
level=logging.INFO,
|
||||
format="%(asctime)s %(levelname)s %(message)s",
|
||||
datefmt="%H:%M:%S",
|
||||
)
|
||||
log = logging.getLogger(__name__)
|
||||
warnings.filterwarnings("ignore", category=RuntimeWarning)
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# Constants
|
||||
# ---------------------------------------------------------------------------
|
||||
STUDY_START = "1976-01-01"
|
||||
STUDY_END = "2019-12-31"
|
||||
BIN_DAYS = 5
|
||||
MIN_MAG = 4.5
|
||||
COV_THRESH = 0.60
|
||||
MIN_STATIONS = 3
|
||||
SEED = 42
|
||||
LAG_BINS = np.arange(-200, 205, 1) # ±1000 d in 5-d steps
|
||||
CLAIM_BIN = 3 # +15 d = bin 3
|
||||
|
||||
OUT_DIR = ROOT / "results"
|
||||
FIG_DIR = ROOT / "results" / "figs"
|
||||
NMDB_DIR = ROOT / "data" / "raw" / "nmdb"
|
||||
USGS_DIR = ROOT / "data" / "raw" / "usgs"
|
||||
CFG_FILE = ROOT / "config" / "stations.yaml"
|
||||
SN_FILE = ROOT / "data" / "raw" / "sidc" / "sunspots.csv"
|
||||
|
||||
FIG_DIR.mkdir(parents=True, exist_ok=True)
|
||||
|
||||
SOLAR_CYCLES = {
|
||||
21: ("1976-03-01", "1986-09-01"),
|
||||
22: ("1986-09-01", "1996-08-01"),
|
||||
23: ("1996-08-01", "2008-12-01"),
|
||||
24: ("2008-12-01", "2019-12-31"),
|
||||
}
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# Shared utilities
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def _station_names() -> list[str]:
|
||||
with open(CFG_FILE) as fh:
|
||||
return list(yaml.safe_load(fh)["stations"].keys())
|
||||
|
||||
|
||||
def _bin_daily(daily: pd.Series, t0: pd.Timestamp, bin_days: int,
|
||||
agg: str = "mean") -> pd.Series:
|
||||
days = (daily.index - t0).days
|
||||
bin_num = days // bin_days
|
||||
bin_dates = t0 + pd.to_timedelta(bin_num * bin_days, unit="D")
|
||||
g = daily.groupby(bin_dates)
|
||||
return g.sum() if agg == "sum" else g.mean()
|
||||
|
||||
|
||||
def _load_cr(study_start: str, study_end: str,
|
||||
bin_days: int = BIN_DAYS,
|
||||
min_stations: int = MIN_STATIONS) -> tuple[pd.Series, pd.DataFrame]:
|
||||
"""Return (cr_index, station_daily_norm)."""
|
||||
t0 = pd.Timestamp(study_start)
|
||||
t1 = pd.Timestamp(study_end)
|
||||
norm: dict[str, pd.Series] = {}
|
||||
for stn in _station_names():
|
||||
hourly = load_station(stn, t0.year, t1.year, NMDB_DIR)
|
||||
if hourly.empty:
|
||||
continue
|
||||
daily = resample_daily(hourly, stn, coverage_threshold=COV_THRESH)[stn]
|
||||
daily = daily.loc[study_start:study_end]
|
||||
if daily.notna().sum() < 30:
|
||||
continue
|
||||
mu = daily.mean()
|
||||
if not (np.isfinite(mu) and mu > 0):
|
||||
continue
|
||||
norm[stn] = daily / mu
|
||||
|
||||
if not norm:
|
||||
raise RuntimeError("No NMDB data.")
|
||||
|
||||
mat = pd.DataFrame(norm)
|
||||
n_valid = mat.notna().sum(axis=1)
|
||||
global_daily = mat.mean(axis=1)
|
||||
global_daily[n_valid < min_stations] = np.nan
|
||||
|
||||
cr = _bin_daily(global_daily, t0, bin_days)
|
||||
cr.name = "cr_index"
|
||||
log.info("CR (%d-d bins, min_stn=%d): %d bins, %d stations",
|
||||
bin_days, min_stations, len(cr), len(norm))
|
||||
return cr, mat
|
||||
|
||||
|
||||
def _load_seismic_events(study_start: str, study_end: str,
|
||||
min_mag: float = MIN_MAG) -> pd.DataFrame:
|
||||
"""Return raw USGS event DataFrame with latitude, longitude, mag columns."""
|
||||
t0 = pd.Timestamp(study_start)
|
||||
t1 = pd.Timestamp(study_end)
|
||||
ev = load_usgs(t0.year, t1.year, USGS_DIR)
|
||||
ev = ev.loc[study_start:study_end]
|
||||
ev = ev[ev["mag"] >= min_mag].copy()
|
||||
log.info("Events M≥%.1f: %d in %s–%s", min_mag, len(ev),
|
||||
study_start, study_end)
|
||||
return ev
|
||||
|
||||
|
||||
def _energy_metric(events: pd.DataFrame, study_start: str, study_end: str,
|
||||
bin_days: int, ref_index: pd.DatetimeIndex | None = None,
|
||||
min_mag: float = MIN_MAG) -> pd.Series:
|
||||
t0 = pd.Timestamp(study_start)
|
||||
s = seismic_energy_per_bin(events, study_start, study_end, bin_days, t0,
|
||||
min_mag=min_mag)
|
||||
if ref_index is not None:
|
||||
s = s.reindex(ref_index, fill_value=float(s.min()))
|
||||
else:
|
||||
s = s.fillna(float(s.min()))
|
||||
return s
|
||||
|
||||
|
||||
def _load_sunspots_binned(study_start: str, study_end: str,
|
||||
bin_days: int = BIN_DAYS) -> pd.Series:
|
||||
"""Parse the KSO comma-sep sunspot CSV → 5-day binned daily mean."""
|
||||
df = pd.read_csv(SN_FILE, header=0)
|
||||
df.columns = [c.strip() for c in df.columns]
|
||||
df["date"] = pd.to_datetime(df["Date"].str.strip(), errors="coerce")
|
||||
df = df.dropna(subset=["date"]).set_index("date")
|
||||
sn = pd.to_numeric(df["Total"].astype(str).str.strip(), errors="coerce")
|
||||
sn = sn.loc[study_start:study_end].rename("sunspot")
|
||||
# Resample to daily (data is already monthly-ish — forward-fill)
|
||||
daily_idx = pd.date_range(study_start, study_end, freq="D")
|
||||
sn = sn.reindex(daily_idx).interpolate("linear").ffill().bfill()
|
||||
t0 = pd.Timestamp(study_start)
|
||||
return _bin_daily(sn, t0, bin_days)
|
||||
|
||||
|
||||
def xcorr(x: np.ndarray, y: np.ndarray, lag_bins: np.ndarray) -> np.ndarray:
|
||||
"""Pearson r(τ) for each lag bin; τ>0 means x leads y."""
|
||||
N = len(x)
|
||||
rs = np.full(len(lag_bins), np.nan)
|
||||
for i, lag in enumerate(lag_bins):
|
||||
if lag >= 0:
|
||||
xa, ya = x[:N - lag], y[lag:]
|
||||
else:
|
||||
absl = -lag
|
||||
xa, ya = x[absl:], y[:N - absl]
|
||||
ok = np.isfinite(xa) & np.isfinite(ya)
|
||||
n = ok.sum()
|
||||
if n >= 10:
|
||||
xo = xa[ok] - xa[ok].mean()
|
||||
yo = ya[ok] - ya[ok].mean()
|
||||
denom = np.sqrt((xo ** 2).sum() * (yo ** 2).sum())
|
||||
if denom > 1e-12:
|
||||
rs[i] = np.dot(xo, yo) / denom
|
||||
return rs
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3a — Block-bootstrap surrogates
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def _circular_block_bootstrap(
|
||||
x: np.ndarray, y: np.ndarray,
|
||||
block_len: int,
|
||||
n_surr: int,
|
||||
lag_bins: np.ndarray,
|
||||
seed: int = SEED,
|
||||
) -> tuple[np.ndarray, np.ndarray]:
|
||||
"""
|
||||
Circular block bootstrap (CBB) null distribution.
|
||||
|
||||
Independently resample *x* and *y* with replacement using blocks of length
|
||||
*block_len* (circular, so the series wraps). Returns arrays of shape
|
||||
(n_surr,) containing the surrogate r(+15d) and peak |r| values.
|
||||
|
||||
Vectorised: all surrogates are built into a matrix (n_surr × N) and
|
||||
the correlation is computed for all surrogates simultaneously per lag,
|
||||
avoiding a 5000 × 401 = 2 M Python-loop iterations.
|
||||
"""
|
||||
rng = np.random.default_rng(seed)
|
||||
N = len(x)
|
||||
n_blocks = int(np.ceil(N / block_len))
|
||||
n_lags = len(lag_bins)
|
||||
|
||||
# Build surrogate matrices (n_surr × N) — Python loop only over n_surr
|
||||
log.info(" Building %d surrogate series (block_len=%d) …", n_surr, block_len)
|
||||
xs_mat = np.empty((n_surr, N), dtype=np.float64)
|
||||
ys_mat = np.empty((n_surr, N), dtype=np.float64)
|
||||
for i in range(n_surr):
|
||||
starts_x = rng.integers(0, N, size=n_blocks)
|
||||
starts_y = rng.integers(0, N, size=n_blocks)
|
||||
xs_mat[i] = np.concatenate([np.roll(x, -s)[:block_len] for s in starts_x])[:N]
|
||||
ys_mat[i] = np.concatenate([np.roll(y, -s)[:block_len] for s in starts_y])[:N]
|
||||
|
||||
# Vectorised xcorr: loop over lags only (all surrogates in parallel)
|
||||
log.info(" Vectorised xcorr over %d lags …", n_lags)
|
||||
rs_mat = np.full((n_surr, n_lags), np.nan, dtype=np.float64)
|
||||
for j, lag in enumerate(lag_bins):
|
||||
if lag >= 0:
|
||||
xa = xs_mat[:, :N - lag] if lag > 0 else xs_mat
|
||||
ya = ys_mat[:, lag:] if lag > 0 else ys_mat
|
||||
else:
|
||||
absl = -lag
|
||||
xa = xs_mat[:, absl:]
|
||||
ya = ys_mat[:, :N - absl]
|
||||
xm = xa - xa.mean(axis=1, keepdims=True)
|
||||
ym = ya - ya.mean(axis=1, keepdims=True)
|
||||
num = (xm * ym).sum(axis=1)
|
||||
denom = np.sqrt((xm ** 2).sum(axis=1) * (ym ** 2).sum(axis=1))
|
||||
valid = denom > 1e-12
|
||||
rs_mat[valid, j] = num[valid] / denom[valid]
|
||||
|
||||
claim_idx = np.where(lag_bins == CLAIM_BIN)[0]
|
||||
rs_15 = rs_mat[:, claim_idx[0]] if len(claim_idx) else np.full(n_surr, np.nan)
|
||||
rs_pk = np.nanmax(np.abs(rs_mat), axis=1)
|
||||
return rs_15, rs_pk
|
||||
|
||||
|
||||
def run_3a(cr: pd.Series, sei: pd.Series) -> dict:
|
||||
log.info("=== 3a: Block-bootstrap surrogates ===")
|
||||
x = cr.values.copy()
|
||||
y = sei.values.copy()
|
||||
|
||||
# Fill NaN with series mean for bootstrap (preserves length)
|
||||
x = np.where(np.isfinite(x), x, np.nanmean(x))
|
||||
y = np.where(np.isfinite(y), y, np.nanmean(y))
|
||||
|
||||
N = len(x)
|
||||
# Block length ≈ 1 solar cycle (11 yr ≈ 4016 d ÷ 5 d/bin = 803 bins)
|
||||
block_len = int(round(11 * 365.25 / BIN_DAYS))
|
||||
log.info(" N=%d block_len=%d bins (≈%.1f yr) surrogates=5000",
|
||||
N, block_len, block_len * BIN_DAYS / 365.25)
|
||||
|
||||
rs_15, rs_pk = _circular_block_bootstrap(x, y, block_len, 5000, LAG_BINS)
|
||||
|
||||
obs_rv = xcorr(x, y, LAG_BINS)
|
||||
obs_15 = obs_rv[LAG_BINS == CLAIM_BIN][0]
|
||||
obs_pk = np.nanmax(np.abs(obs_rv))
|
||||
|
||||
p_15 = float(np.mean(np.abs(rs_15) >= np.abs(obs_15)))
|
||||
p_pk = float(np.mean(rs_pk >= obs_pk))
|
||||
ci95_15 = (float(np.percentile(rs_15, 2.5)), float(np.percentile(rs_15, 97.5)))
|
||||
|
||||
log.info(" obs r(+15d)=%.4f block-bootstrap p(+15d)=%.4f p(peak)=%.4f",
|
||||
obs_15, p_15, p_pk)
|
||||
|
||||
# Load IAAFT p-value for comparison
|
||||
iaaft_raw = None
|
||||
try:
|
||||
with open(OUT_DIR / "detrended_results.json") as fh:
|
||||
det = json.load(fh)
|
||||
iaaft_raw = det["results"][0]["p_global_iaaft"]
|
||||
except Exception:
|
||||
pass
|
||||
|
||||
# Figure
|
||||
fig, axes = plt.subplots(1, 2, figsize=(11, 4))
|
||||
axes[0].hist(rs_15, bins=60, color="steelblue", alpha=0.7,
|
||||
label="Block-bootstrap null")
|
||||
axes[0].axvline(obs_15, color="red", lw=2, label=f"Observed r={obs_15:.3f}")
|
||||
axes[0].axvline(ci95_15[0], color="grey", ls="--")
|
||||
axes[0].axvline(ci95_15[1], color="grey", ls="--", label="95% CI")
|
||||
axes[0].set_xlabel("r(+15 d)")
|
||||
axes[0].set_title(f"Block bootstrap null\np(+15d) = {p_15:.3f}")
|
||||
axes[0].legend(fontsize=8)
|
||||
|
||||
axes[1].hist(rs_pk, bins=60, color="darkorange", alpha=0.7,
|
||||
label="Block-bootstrap null")
|
||||
axes[1].axvline(obs_pk, color="red", lw=2, label=f"Observed peak |r|={obs_pk:.3f}")
|
||||
axes[1].set_xlabel("Peak |r|")
|
||||
axes[1].set_title(f"Peak |r| null\np(peak) = {p_pk:.3f}")
|
||||
axes[1].legend(fontsize=8)
|
||||
|
||||
if iaaft_raw is not None:
|
||||
axes[0].set_xlabel("r(+15 d)" + f"\n(IAAFT p_global={iaaft_raw:.4f})")
|
||||
|
||||
fig.tight_layout()
|
||||
fig.savefig(FIG_DIR / "block_bootstrap_null.png", dpi=150, bbox_inches="tight")
|
||||
plt.close(fig)
|
||||
log.info("3a figure saved.")
|
||||
|
||||
return dict(
|
||||
block_len_bins=block_len,
|
||||
obs_r_15d=float(obs_15),
|
||||
obs_peak_r=float(obs_pk),
|
||||
p_block_15d=p_15,
|
||||
p_block_peak=p_pk,
|
||||
ci95_15d=list(ci95_15),
|
||||
iaaft_p_global_raw=iaaft_raw,
|
||||
interpretation=(
|
||||
"p-value similar to IAAFT" if iaaft_raw is None or abs(p_15 - iaaft_raw) < 0.1
|
||||
else "p-value changes materially vs IAAFT"
|
||||
),
|
||||
)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3b — Partial correlation controlling for sunspots (raw data)
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def run_3b(cr: pd.Series, sei: pd.Series) -> dict:
|
||||
log.info("=== 3b: Partial correlation (sunspot control) ===")
|
||||
sn = _load_sunspots_binned(STUDY_START, STUDY_END)
|
||||
|
||||
# Align all three series
|
||||
idx = cr.index.intersection(sei.index).intersection(sn.index)
|
||||
x = cr.reindex(idx).values.astype(float)
|
||||
y = sei.reindex(idx).values.astype(float)
|
||||
z = sn.reindex(idx).values.astype(float)
|
||||
|
||||
ok = np.isfinite(x) & np.isfinite(y) & np.isfinite(z)
|
||||
log.info(" Aligned N=%d, valid=%d", len(x), ok.sum())
|
||||
|
||||
# OLS: regress seismic on sunspot
|
||||
z_ok = z[ok]; y_ok = y[ok]; x_ok = x[ok]
|
||||
slope, intercept, *_ = scipy.stats.linregress(z_ok, y_ok)
|
||||
y_resid = y_ok - (slope * z_ok + intercept)
|
||||
log.info(" Sunspot regression on seismic: slope=%.4f intercept=%.4f", slope, intercept)
|
||||
|
||||
r_partial, pv = scipy.stats.pearsonr(x_ok, y_resid)
|
||||
log.info(" Partial r(CR, Seismic|Sunspot) at zero lag = %.4f p=%.4e",
|
||||
r_partial, pv)
|
||||
|
||||
# Full cross-correlation of CR vs seismic residual
|
||||
x_full = np.full(len(idx), np.nan)
|
||||
y_res_full = np.full(len(idx), np.nan)
|
||||
x_full[ok] = x_ok
|
||||
y_res_full[ok] = y_resid
|
||||
|
||||
rv_partial = xcorr(x_full, y_res_full, LAG_BINS)
|
||||
rv_raw = xcorr(x, y, LAG_BINS)
|
||||
|
||||
r_partial_15 = rv_partial[LAG_BINS == CLAIM_BIN][0]
|
||||
r_raw_15 = rv_raw[LAG_BINS == CLAIM_BIN][0]
|
||||
peak_partial = float(np.nanmax(np.abs(rv_partial)))
|
||||
log.info(" r(+15d) raw=%.4f partial=%.4f", r_raw_15, r_partial_15)
|
||||
|
||||
# Figure
|
||||
fig, ax = plt.subplots(figsize=(9, 4))
|
||||
lags_d = LAG_BINS * BIN_DAYS
|
||||
ax.plot(lags_d, rv_raw, color="steelblue", alpha=0.7, label="Raw seismic")
|
||||
ax.plot(lags_d, rv_partial, color="darkorange", lw=1.5,
|
||||
label="Seismic residual (sunspot removed)")
|
||||
ax.axhline(0, color="black", lw=0.6)
|
||||
ax.axvline(15, color="grey", ls="--", lw=1.2, label="+15 d")
|
||||
ax.set_xlabel("Lag τ (days)")
|
||||
ax.set_ylabel("Pearson r")
|
||||
ax.set_title(f"Partial correlation: CR vs seismic after sunspot regression\n"
|
||||
f"r_raw(+15d)={r_raw_15:.3f} r_partial(+15d)={r_partial_15:.3f}")
|
||||
ax.legend(fontsize=9)
|
||||
fig.tight_layout()
|
||||
fig.savefig(FIG_DIR / "partial_correlation.png", dpi=150, bbox_inches="tight")
|
||||
plt.close(fig)
|
||||
log.info("3b figure saved.")
|
||||
|
||||
drop_frac = (abs(r_raw_15) - abs(r_partial_15)) / max(abs(r_raw_15), 1e-9)
|
||||
return dict(
|
||||
sunspot_slope=float(slope),
|
||||
r_raw_15d=float(r_raw_15),
|
||||
r_partial_15d=float(r_partial_15),
|
||||
drop_fraction_at_15d=float(drop_frac),
|
||||
peak_r_partial=float(peak_partial),
|
||||
interpretation=(
|
||||
"Partial correlation near zero — solar-cycle confounding confirmed"
|
||||
if abs(r_partial_15) < 0.05 else
|
||||
"Partial correlation non-trivial — residual signal remains after sunspot control"
|
||||
),
|
||||
)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3c — Spectral coherence + mutual information
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def _mi_knn(x: np.ndarray, y: np.ndarray, k: int = 5) -> float:
|
||||
"""
|
||||
Kraskov et al. (2004) kNN mutual information estimator (estimator 1).
|
||||
Uses Chebyshev (L-inf) metric in joint space; marginal counts via
|
||||
vectorised searchsorted — O(N log N), no Python loop over points.
|
||||
Requires finite values only.
|
||||
"""
|
||||
from scipy.special import digamma
|
||||
N = len(x)
|
||||
x = (x - x.mean()) / (x.std() + 1e-12)
|
||||
y = (y - y.mean()) / (y.std() + 1e-12)
|
||||
xy = np.column_stack([x, y])
|
||||
|
||||
# k-NN in joint space using Chebyshev (L-inf) metric
|
||||
tree_xy = scipy.spatial.cKDTree(xy)
|
||||
dists, _ = tree_xy.query(xy, k=k + 1, p=np.inf, workers=-1)
|
||||
eps = dists[:, -1] # k-th neighbour Chebyshev distance
|
||||
|
||||
# Count marginal neighbours via sorted binary search — O(N log N), vectorised
|
||||
xs = np.sort(x)
|
||||
ys = np.sort(y)
|
||||
nx = (np.searchsorted(xs, x + eps, side="right")
|
||||
- np.searchsorted(xs, x - eps, side="left") - 1)
|
||||
ny = (np.searchsorted(ys, y + eps, side="right")
|
||||
- np.searchsorted(ys, y - eps, side="left") - 1)
|
||||
nx = np.maximum(nx, 0)
|
||||
ny = np.maximum(ny, 0)
|
||||
|
||||
mi = digamma(k) + digamma(N) - np.mean(digamma(nx + 1)) - np.mean(digamma(ny + 1))
|
||||
return float(max(mi, 0.0))
|
||||
|
||||
|
||||
def run_3c(cr: pd.Series, sei: pd.Series) -> dict:
|
||||
log.info("=== 3c: Spectral coherence + mutual information ===")
|
||||
rng = np.random.default_rng(SEED)
|
||||
|
||||
idx = cr.index.intersection(sei.index)
|
||||
x = cr.reindex(idx).values.astype(float)
|
||||
y = sei.reindex(idx).values.astype(float)
|
||||
ok = np.isfinite(x) & np.isfinite(y)
|
||||
xf, yf = x[ok], y[ok]
|
||||
|
||||
# --- Spectral coherence ---
|
||||
# nperseg=2048 gives freq. resolution (1/5)/2048 = 0.036 cycles/yr,
|
||||
# sufficient to resolve the solar-cycle band (0.08–0.115 cycles/yr).
|
||||
# nperseg=512 only gives 0.143 cycles/yr — no bins fall in the SC band.
|
||||
nperseg = 2048
|
||||
fs = 1.0 / BIN_DAYS # cycles per day
|
||||
f_d, Cxy = scipy.signal.coherence(xf, yf, fs=fs, nperseg=nperseg,
|
||||
window="hann", noverlap=nperseg * 3 // 4)
|
||||
f_yr = f_d * 365.25 # cycles per year
|
||||
|
||||
# Solar cycle band: 0.08–0.11 cycles/yr (9–12 year period)
|
||||
sc_mask = (f_yr >= 0.08) & (f_yr <= 0.115)
|
||||
coh_sc = float(np.mean(Cxy[sc_mask]))
|
||||
log.info(" Mean coherence in solar-cycle band: %.4f", coh_sc)
|
||||
|
||||
# Significance: 95th percentile of coherence for white-noise pairs
|
||||
noverlap_used = nperseg * 3 // 4
|
||||
step = nperseg - noverlap_used
|
||||
n_seg = max(1, (ok.sum() - nperseg) // step + 1)
|
||||
coh_95 = 1 - 0.05 ** (1.0 / (n_seg - 1)) if n_seg > 1 else np.nan
|
||||
log.info(" Coherence 95%% significance threshold (for %d segments): %.4f",
|
||||
n_seg, coh_95)
|
||||
|
||||
# --- Mutual information ---
|
||||
N = len(xf)
|
||||
mi_lag0 = _mi_knn(xf, yf)
|
||||
# MI at lag +15d (=+3 bins)
|
||||
lag15 = CLAIM_BIN
|
||||
xi15, yi15 = xf[:N - lag15], yf[lag15:]
|
||||
ok15 = np.isfinite(xi15) & np.isfinite(yi15)
|
||||
mi_lag15 = _mi_knn(xi15[ok15], yi15[ok15])
|
||||
log.info(" MI(lag=0)=%.4f MI(lag=+15d)=%.4f", mi_lag0, mi_lag15)
|
||||
|
||||
# Shuffle null for MI (1000 permutations)
|
||||
n_shuf = 1000
|
||||
mi_null_0 = np.empty(n_shuf)
|
||||
mi_null_15 = np.empty(n_shuf)
|
||||
for i in range(n_shuf):
|
||||
ys = rng.permutation(yf)
|
||||
mi_null_0[i] = _mi_knn(xf, ys)
|
||||
ys15 = rng.permutation(yf[lag15:])
|
||||
mi_null_15[i] = _mi_knn(xf[:N - lag15][ok15], ys15[ok15])
|
||||
|
||||
p_mi_0 = float(np.mean(mi_null_0 >= mi_lag0))
|
||||
p_mi_15 = float(np.mean(mi_null_15 >= mi_lag15))
|
||||
log.info(" p(MI lag=0)=%.4f p(MI lag=+15d)=%.4f", p_mi_0, p_mi_15)
|
||||
|
||||
# Figure
|
||||
fig, axes = plt.subplots(1, 2, figsize=(11, 4))
|
||||
|
||||
# Coherence panel
|
||||
ax = axes[0]
|
||||
ax.plot(f_yr, Cxy, color="steelblue", lw=1, label="Coherence")
|
||||
ax.axvspan(0.08, 0.115, alpha=0.15, color="orange", label="Solar-cycle band (0.08–0.115 yr⁻¹)")
|
||||
if np.isfinite(coh_95):
|
||||
ax.axhline(coh_95, color="red", ls="--", lw=1.2,
|
||||
label=f"95% sig. ({coh_95:.3f}, K={n_seg} seg.)")
|
||||
ax.set_xlim(0, 0.5)
|
||||
ax.set_ylim(0, 1.05)
|
||||
ax.set_xlabel("Frequency (cycles yr⁻¹)")
|
||||
ax.set_ylabel("Magnitude-squared coherence")
|
||||
coh_sc_str = f"{coh_sc:.3f}" if np.isfinite(coh_sc) else "N/A"
|
||||
ax.set_title(f"Spectral coherence (nperseg={nperseg})\nMean coh. in SC band: {coh_sc_str}")
|
||||
ax.legend(fontsize=8)
|
||||
|
||||
# MI panel
|
||||
ax = axes[1]
|
||||
ax.hist(mi_null_0, bins=40, color="steelblue", alpha=0.6, label="Shuffle null (lag=0)")
|
||||
ax.hist(mi_null_15, bins=40, color="darkorange", alpha=0.6, label="Shuffle null (lag=+15d)")
|
||||
ax.axvline(mi_lag0, color="steelblue", lw=2, ls="-", label=f"Obs MI(0)={mi_lag0:.3f}")
|
||||
ax.axvline(mi_lag15, color="darkorange", lw=2, ls="--",
|
||||
label=f"Obs MI(+15d)={mi_lag15:.3f}")
|
||||
ax.set_xlabel("Mutual information (nats)")
|
||||
ax.set_title(f"kNN mutual information\np(lag=0)={p_mi_0:.3f} p(lag=+15d)={p_mi_15:.3f}")
|
||||
ax.legend(fontsize=7)
|
||||
|
||||
fig.tight_layout()
|
||||
fig.savefig(FIG_DIR / "spectral_coherence.png", dpi=150, bbox_inches="tight")
|
||||
plt.close(fig)
|
||||
log.info("3c figure saved.")
|
||||
|
||||
return dict(
|
||||
coherence_solar_cycle_band=coh_sc,
|
||||
coherence_95pct_threshold=coh_95 if np.isfinite(coh_95) else None,
|
||||
mi_lag0=mi_lag0,
|
||||
mi_lag15d=mi_lag15,
|
||||
p_mi_lag0=p_mi_0,
|
||||
p_mi_lag15d=p_mi_15,
|
||||
)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3d — Missing-data sensitivity
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
SOLAR_MAXIMA = [1979.7, 1989.6, 2000.3, 2014.2] # approximate decimal years
|
||||
|
||||
|
||||
def _cr_nan_analysis(study_start: str, study_end: str,
|
||||
min_stations: int) -> dict:
|
||||
"""Return NaN stats and r(+15d) for the given station threshold."""
|
||||
cr, _ = _load_cr(study_start, study_end, bin_days=BIN_DAYS,
|
||||
min_stations=min_stations)
|
||||
ev = _load_seismic_events(study_start, study_end)
|
||||
sei = _energy_metric(ev, study_start, study_end, BIN_DAYS, cr.index)
|
||||
|
||||
nan_frac = float(cr.isna().mean())
|
||||
|
||||
# Are NaN bins concentrated near solar maxima?
|
||||
is_nan = cr.isna()
|
||||
bin_years = cr.index.year + cr.index.dayofyear / 365.25
|
||||
# Flag years within ±1.5 yr of any solar maximum
|
||||
near_max = np.zeros(len(cr), dtype=bool)
|
||||
for sm in SOLAR_MAXIMA:
|
||||
near_max |= np.abs(bin_years - sm) <= 1.5
|
||||
nan_near = float(is_nan[near_max].mean())
|
||||
nan_far = float(is_nan[~near_max].mean())
|
||||
|
||||
# r(+15d)
|
||||
ok = np.isfinite(cr.values) & np.isfinite(sei.values)
|
||||
x, y = cr.values[ok], sei.values[ok]
|
||||
r15, _ = scipy.stats.pearsonr(x, y) # zero-lag as proxy; lag-3 below
|
||||
# Actual lag-3
|
||||
N = len(cr)
|
||||
xa = cr.values[:N - CLAIM_BIN]; ya = sei.values[CLAIM_BIN:]
|
||||
ok2 = np.isfinite(xa) & np.isfinite(ya)
|
||||
r_15d, _ = scipy.stats.pearsonr(xa[ok2], ya[ok2])
|
||||
|
||||
return dict(
|
||||
min_stations=min_stations,
|
||||
nan_fraction=nan_frac,
|
||||
nan_fraction_near_solar_max=nan_near,
|
||||
nan_fraction_far_from_solar_max=nan_far,
|
||||
clustering_ratio=nan_near / max(nan_far, 1e-9),
|
||||
r_at_15d=float(r_15d),
|
||||
)
|
||||
|
||||
|
||||
def run_3d() -> dict:
|
||||
log.info("=== 3d: Missing-data sensitivity ===")
|
||||
results = []
|
||||
for thr in (2, 3, 5):
|
||||
log.info(" Station threshold = %d …", thr)
|
||||
res = _cr_nan_analysis(STUDY_START, STUDY_END, thr)
|
||||
results.append(res)
|
||||
log.info(" NaN=%.1f%% near-max=%.1f%% r(+15d)=%.4f",
|
||||
100 * res["nan_fraction"],
|
||||
100 * res["nan_fraction_near_solar_max"],
|
||||
res["r_at_15d"])
|
||||
return dict(station_threshold_sensitivity=results)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3e — Bin-size sensitivity
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def _run_for_bin_size(bin_days: int) -> dict:
|
||||
"""Load CR and seismic at *bin_days* resolution, compute r(τ)."""
|
||||
cr, _ = _load_cr(STUDY_START, STUDY_END, bin_days=bin_days)
|
||||
ev = _load_seismic_events(STUDY_START, STUDY_END)
|
||||
sei = _energy_metric(ev, STUDY_START, STUDY_END, bin_days, cr.index)
|
||||
|
||||
# Lag range: ±1000 days in steps of bin_days
|
||||
max_lag_bins = int(1000 / bin_days)
|
||||
lbs = np.arange(-max_lag_bins, max_lag_bins + 1)
|
||||
rv = xcorr(cr.values, sei.values, lbs)
|
||||
|
||||
# Find claimed lag bin (closest to +15d)
|
||||
claim_bin = int(round(15 / bin_days))
|
||||
r15 = rv[lbs == claim_bin][0] if np.any(lbs == claim_bin) else np.nan
|
||||
peak_idx = np.nanargmax(np.abs(rv))
|
||||
peak_r = rv[peak_idx]
|
||||
peak_lag = int(lbs[peak_idx]) * bin_days # days
|
||||
|
||||
log.info(" %d-d bins: r(+%dd)=%.4f peak r=%.4f @ τ=%dd",
|
||||
bin_days, claim_bin * bin_days, r15, peak_r, peak_lag)
|
||||
return dict(
|
||||
bin_days=bin_days,
|
||||
r_at_claimed_lag=float(r15),
|
||||
claimed_lag_days=claim_bin * bin_days,
|
||||
peak_r=float(peak_r),
|
||||
peak_lag_days=peak_lag,
|
||||
lag_bins=lbs.tolist(),
|
||||
r_values=rv.tolist(),
|
||||
)
|
||||
|
||||
|
||||
def run_3e() -> dict:
|
||||
log.info("=== 3e: Bin-size sensitivity ===")
|
||||
results = []
|
||||
rv_by_bin = {}
|
||||
for bd in (1, 5, 27):
|
||||
r = _run_for_bin_size(bd)
|
||||
results.append({k: v for k, v in r.items() if k not in ("lag_bins", "r_values")})
|
||||
rv_by_bin[bd] = (r["lag_bins"], r["r_values"])
|
||||
|
||||
# Figure: 3-panel
|
||||
fig, axes = plt.subplots(1, 3, figsize=(14, 4), sharey=False)
|
||||
colours = ["steelblue", "darkorange", "seagreen"]
|
||||
for ax, (bd, (lbs, rv)), col in zip(axes, rv_by_bin.items(), colours):
|
||||
lags_d = np.array(lbs) * bd
|
||||
rv = np.array(rv)
|
||||
ax.plot(lags_d, rv, color=col, lw=0.8)
|
||||
ax.axhline(0, color="black", lw=0.5)
|
||||
ax.axvline(15, color="grey", ls="--", lw=1, label="+15 d")
|
||||
closest = lbs[np.argmin(np.abs(np.array(lbs) - round(15 / bd)))]
|
||||
pk_d = lbs[np.nanargmax(np.abs(rv))] * bd
|
||||
ax.axvline(pk_d, color="red", ls=":", lw=1, label=f"Peak τ={pk_d}d")
|
||||
ax.set_title(f"{bd}-day bins\nr(+15d≈{int(round(15/bd)*bd)}d)="
|
||||
f"{rv[np.argmin(np.abs(np.array(lbs)-round(15/bd)))]:.3f}")
|
||||
ax.set_xlabel("Lag (days)")
|
||||
ax.set_ylabel("Pearson r")
|
||||
ax.legend(fontsize=7)
|
||||
fig.suptitle("Bin-size sensitivity: 1-day, 5-day, 27-day bins", fontsize=11)
|
||||
fig.tight_layout()
|
||||
fig.savefig(FIG_DIR / "bin_size_sensitivity.png", dpi=150, bbox_inches="tight")
|
||||
plt.close(fig)
|
||||
log.info("3e figure saved.")
|
||||
|
||||
return dict(bin_size_sensitivity=results)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3f — Gardner–Knopoff declustering
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def _gk_time_window(mag: float) -> float:
|
||||
"""After-shock time window T(M) in days (Gardner & Knopoff 1974)."""
|
||||
if mag < 6.5:
|
||||
return 10 ** (0.5 * mag - 1.8)
|
||||
else:
|
||||
return 10 ** (0.46 * mag - 2.31)
|
||||
|
||||
|
||||
def _gk_dist_window(mag: float) -> float:
|
||||
"""After-shock distance window L(M) in km (Gardner & Knopoff 1974)."""
|
||||
return 10 ** (0.1238 * mag + 0.983)
|
||||
|
||||
|
||||
def _haversine_km(lat1: np.ndarray, lon1: np.ndarray,
|
||||
lat2: float, lon2: float) -> np.ndarray:
|
||||
"""Vectorised haversine distance in km."""
|
||||
R = 6371.0
|
||||
dlat = np.radians(lat2 - lat1)
|
||||
dlon = np.radians(lon2 - lon1)
|
||||
a = (np.sin(dlat / 2) ** 2 +
|
||||
np.cos(np.radians(lat1)) * np.cos(np.radians(lat2)) *
|
||||
np.sin(dlon / 2) ** 2)
|
||||
return 2 * R * np.arcsin(np.sqrt(np.clip(a, 0, 1)))
|
||||
|
||||
|
||||
def _gardner_knopoff_decluster(events: pd.DataFrame) -> pd.DataFrame:
|
||||
"""
|
||||
Remove aftershocks from *events* using the Gardner-Knopoff (1974) algorithm.
|
||||
|
||||
Returns the mainshock-only DataFrame. Uses forward-only time windows
|
||||
(each mainshock's aftershock zone applies to all future events within T(M)).
|
||||
"""
|
||||
ev = events.dropna(subset=["latitude", "longitude", "mag"]).copy()
|
||||
ev = ev.sort_index()
|
||||
n = len(ev)
|
||||
|
||||
times = ev.index.values.astype("datetime64[ns]").astype(np.int64) / 1e9 / 86400 # days
|
||||
lats = ev["latitude"].values
|
||||
lons = ev["longitude"].values
|
||||
mags = ev["mag"].values
|
||||
is_as = np.zeros(n, dtype=bool)
|
||||
|
||||
log.info(" GK declustering: %d events …", n)
|
||||
for i in range(n):
|
||||
if is_as[i]:
|
||||
continue
|
||||
tw = _gk_time_window(mags[i])
|
||||
dw = _gk_dist_window(mags[i])
|
||||
# Forward window in time
|
||||
t_end = times[i] + tw
|
||||
j_lo = i + 1
|
||||
# Find j_hi via binary search (times is sorted)
|
||||
j_hi = np.searchsorted(times, t_end, side="right")
|
||||
if j_lo >= j_hi:
|
||||
continue
|
||||
cands = np.arange(j_lo, j_hi)
|
||||
cands = cands[~is_as[cands]] # skip already-flagged
|
||||
if len(cands) == 0:
|
||||
continue
|
||||
dists = _haversine_km(lats[cands], lons[cands], lats[i], lons[i])
|
||||
is_as[cands[dists <= dw]] = True
|
||||
|
||||
n_main = int((~is_as).sum())
|
||||
n_as = int(is_as.sum())
|
||||
log.info(" GK result: %d mainshocks %d aftershocks (%.1f%% removed)",
|
||||
n_main, n_as, 100 * n_as / max(n, 1))
|
||||
return ev[~is_as]
|
||||
|
||||
|
||||
def run_3f(cr: pd.Series) -> dict:
|
||||
log.info("=== 3f: Gardner–Knopoff declustering ===")
|
||||
events = _load_seismic_events(STUDY_START, STUDY_END, min_mag=MIN_MAG)
|
||||
sei_full = _energy_metric(events, STUDY_START, STUDY_END, BIN_DAYS, cr.index)
|
||||
|
||||
mainshocks = _gardner_knopoff_decluster(events)
|
||||
sei_decl = _energy_metric(mainshocks, STUDY_START, STUDY_END, BIN_DAYS, cr.index)
|
||||
|
||||
rv_full = xcorr(cr.values, sei_full.values, LAG_BINS)
|
||||
rv_decl = xcorr(cr.values, sei_decl.values, LAG_BINS)
|
||||
|
||||
r15_full = float(rv_full[LAG_BINS == CLAIM_BIN][0])
|
||||
r15_decl = float(rv_decl[LAG_BINS == CLAIM_BIN][0])
|
||||
pk_full = float(np.nanmax(np.abs(rv_full)))
|
||||
pk_decl = float(np.nanmax(np.abs(rv_decl)))
|
||||
log.info(" r(+15d) full=%.4f declustered=%.4f", r15_full, r15_decl)
|
||||
|
||||
n_removed_frac = float(1 - len(mainshocks) / len(events))
|
||||
|
||||
# Figure
|
||||
fig, ax = plt.subplots(figsize=(9, 4))
|
||||
lags_d = LAG_BINS * BIN_DAYS
|
||||
ax.plot(lags_d, rv_full, color="steelblue", alpha=0.8,
|
||||
label=f"Full catalogue (n={len(events):,})")
|
||||
ax.plot(lags_d, rv_decl, color="darkorange", lw=1.5,
|
||||
label=f"Declustered / mainshocks only (n={len(mainshocks):,})")
|
||||
ax.axhline(0, color="black", lw=0.5)
|
||||
ax.axvline(15, color="grey", ls="--", lw=1.2, label="+15 d")
|
||||
ax.set_xlabel("Lag τ (days)")
|
||||
ax.set_ylabel("Pearson r")
|
||||
ax.set_title(f"Gardner–Knopoff declustering\n"
|
||||
f"r(+15d): full={r15_full:.3f} declustered={r15_decl:.3f} "
|
||||
f"({100*n_removed_frac:.0f}% removed)")
|
||||
ax.legend(fontsize=9)
|
||||
fig.tight_layout()
|
||||
fig.savefig(FIG_DIR / "declustered_xcorr.png", dpi=150, bbox_inches="tight")
|
||||
plt.close(fig)
|
||||
log.info("3f figure saved.")
|
||||
|
||||
return dict(
|
||||
n_events_full=len(events),
|
||||
n_mainshocks=len(mainshocks),
|
||||
fraction_removed=n_removed_frac,
|
||||
r_15d_full=r15_full,
|
||||
r_15d_declustered=r15_decl,
|
||||
peak_r_full=pk_full,
|
||||
peak_r_declustered=pk_decl,
|
||||
interpretation=(
|
||||
"Aftershock clustering is NOT a primary confound — result stable after GK declustering"
|
||||
if abs(r15_full - r15_decl) < 0.03 else
|
||||
"Result changes after GK declustering — aftershock contamination is a concern"
|
||||
),
|
||||
)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# 3g — Sub-period analysis (per solar cycle)
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def run_3g(cr: pd.Series, sei: pd.Series) -> dict:
|
||||
log.info("=== 3g: Sub-period analysis (per solar cycle) ===")
|
||||
lag_range_bins = np.arange(-40, 41) # ±200 d in 5-d steps (short cycles)
|
||||
|
||||
fig, axes = plt.subplots(2, 2, figsize=(12, 8), sharey=True)
|
||||
results = {}
|
||||
|
||||
for ax, (cycle_num, (t_start, t_end)) in zip(axes.flat, SOLAR_CYCLES.items()):
|
||||
# Crop pre-aligned global CR/seismic series — avoids bin-date misalignment
|
||||
cr_c = cr.loc[t_start:t_end]
|
||||
sei_c = sei.loc[t_start:t_end]
|
||||
if len(cr_c) < 40:
|
||||
log.warning(" Cycle %d: insufficient data (%d bins)", cycle_num, len(cr_c))
|
||||
ax.set_title(f"Cycle {cycle_num}: insufficient data")
|
||||
results[f"cycle_{cycle_num}"] = None
|
||||
continue
|
||||
|
||||
rv = xcorr(cr_c.values, sei_c.values, lag_range_bins)
|
||||
|
||||
if np.all(np.isnan(rv)):
|
||||
log.warning(" Cycle %d: all-NaN xcorr — skipping", cycle_num)
|
||||
ax.set_title(f"Cycle {cycle_num}: all-NaN")
|
||||
results[f"cycle_{cycle_num}"] = None
|
||||
continue
|
||||
|
||||
r15 = float(rv[lag_range_bins == CLAIM_BIN][0]) if np.any(lag_range_bins == CLAIM_BIN) else np.nan
|
||||
pk_idx = np.nanargmax(np.abs(rv))
|
||||
pk_r = float(rv[pk_idx])
|
||||
pk_lag = int(lag_range_bins[pk_idx]) * BIN_DAYS
|
||||
n_bins = len(cr_c)
|
||||
log.info(" Cycle %d (%s–%s): N=%d r(+15d)=%.4f peak=%.4f@%dd",
|
||||
cycle_num, t_start, t_end, n_bins, r15, pk_r, pk_lag)
|
||||
|
||||
lags_d = lag_range_bins * BIN_DAYS
|
||||
ax.plot(lags_d, rv, color="steelblue", lw=1.2)
|
||||
ax.axhline(0, color="black", lw=0.5)
|
||||
ax.axvline(15, color="grey", ls="--", lw=1, label="+15 d")
|
||||
ax.axvline(pk_lag, color="red", ls=":", lw=1,
|
||||
label=f"Peak τ={pk_lag}d r={pk_r:.3f}")
|
||||
ax.set_title(f"Solar Cycle {cycle_num} ({t_start[:4]}–{t_end[:4]})\n"
|
||||
f"N={n_bins} bins r(+15d)={r15:.3f}")
|
||||
ax.set_xlabel("Lag (days)")
|
||||
ax.set_ylabel("Pearson r")
|
||||
ax.legend(fontsize=7)
|
||||
|
||||
results[f"cycle_{cycle_num}"] = dict(
|
||||
start=t_start, end=t_end,
|
||||
n_bins=n_bins,
|
||||
r_at_15d=r15,
|
||||
peak_r=pk_r,
|
||||
peak_lag_days=pk_lag,
|
||||
)
|
||||
|
||||
fig.suptitle("Cross-correlation per solar cycle (1976–2019)", fontsize=11)
|
||||
fig.tight_layout()
|
||||
fig.savefig(FIG_DIR / "solar_cycle_xcorr.png", dpi=150, bbox_inches="tight")
|
||||
plt.close(fig)
|
||||
log.info("3g figure saved.")
|
||||
|
||||
r15_vals = [v["r_at_15d"] for v in results.values() if v is not None]
|
||||
sign_consistent = all(r > 0 for r in r15_vals) or all(r < 0 for r in r15_vals)
|
||||
return dict(
|
||||
per_cycle=results,
|
||||
r15d_range=[float(min(r15_vals)), float(max(r15_vals))],
|
||||
sign_consistent_across_cycles=sign_consistent,
|
||||
interpretation=(
|
||||
"r(+15d) consistent in sign across all solar cycles"
|
||||
if sign_consistent else
|
||||
"r(+15d) sign INCONSISTENT across solar cycles — confirms solar-cycle artefact"
|
||||
),
|
||||
)
|
||||
|
||||
|
||||
# ---------------------------------------------------------------------------
|
||||
# Main
|
||||
# ---------------------------------------------------------------------------
|
||||
|
||||
def main() -> None:
|
||||
log.info("Loading base CR and seismic data …")
|
||||
cr, _stn = _load_cr(STUDY_START, STUDY_END)
|
||||
events = _load_seismic_events(STUDY_START, STUDY_END)
|
||||
sei = _energy_metric(events, STUDY_START, STUDY_END, BIN_DAYS, cr.index)
|
||||
|
||||
out = {}
|
||||
|
||||
log.info("Running 3a …")
|
||||
out["3a_block_bootstrap"] = run_3a(cr, sei)
|
||||
|
||||
log.info("Running 3b …")
|
||||
out["3b_partial_correlation"] = run_3b(cr, sei)
|
||||
|
||||
log.info("Running 3c …")
|
||||
out["3c_coherence_mi"] = run_3c(cr, sei)
|
||||
|
||||
log.info("Running 3d …")
|
||||
out["3d_missing_data"] = run_3d()
|
||||
|
||||
log.info("Running 3e …")
|
||||
out["3e_bin_size"] = run_3e()
|
||||
|
||||
log.info("Running 3f …")
|
||||
out["3f_declustering"] = run_3f(cr)
|
||||
|
||||
log.info("Running 3g …")
|
||||
out["3g_solar_cycles"] = run_3g(cr, sei)
|
||||
|
||||
# Save JSON
|
||||
out_path = OUT_DIR / "additional_robustness.json"
|
||||
with open(out_path, "w") as fh:
|
||||
json.dump(out, fh, indent=2, default=str)
|
||||
log.info("Results saved: %s", out_path)
|
||||
|
||||
# ── Summary printout ───────────────────────────────────────────────────
|
||||
print("\n" + "=" * 70)
|
||||
print(" ADDITIONAL ROBUSTNESS SUMMARY")
|
||||
print("=" * 70)
|
||||
r = out["3a_block_bootstrap"]
|
||||
print(f" 3a Block bootstrap p(+15d)={r['p_block_15d']:.4f} "
|
||||
f"p(peak)={r['p_block_peak']:.4f}")
|
||||
r = out["3b_partial_correlation"]
|
||||
print(f" 3b Partial corr r_raw(+15d)={r['r_raw_15d']:.4f} "
|
||||
f"r_partial={r['r_partial_15d']:.4f}")
|
||||
r = out["3c_coherence_mi"]
|
||||
print(f" 3c Coherence SC-band={r['coherence_solar_cycle_band']:.4f} "
|
||||
f"MI p(lag=0)={r['p_mi_lag0']:.3f} p(+15d)={r['p_mi_lag15d']:.3f}")
|
||||
for res in out["3d_missing_data"]["station_threshold_sensitivity"]:
|
||||
print(f" 3d min_stn={res['min_stations']} "
|
||||
f"NaN={100*res['nan_fraction']:.1f}% r(+15d)={res['r_at_15d']:.4f}")
|
||||
for res in out["3e_bin_size"]["bin_size_sensitivity"]:
|
||||
print(f" 3e {res['bin_days']:2d}-d bins "
|
||||
f"r(+{res['claimed_lag_days']}d)={res['r_at_claimed_lag']:.4f} "
|
||||
f"peak={res['peak_r']:.4f}@{res['peak_lag_days']}d")
|
||||
r = out["3f_declustering"]
|
||||
print(f" 3f Declustering removed={100*r['fraction_removed']:.0f}% "
|
||||
f"r_full={r['r_15d_full']:.4f} r_decl={r['r_15d_declustered']:.4f}")
|
||||
r = out["3g_solar_cycles"]
|
||||
print(f" 3g Solar cycles r(+15d) range={r['r15d_range']} "
|
||||
f"sign_consistent={r['sign_consistent_across_cycles']}")
|
||||
print("=" * 70)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
Loading…
Reference in a new issue