diff --git a/paper/main.aux b/paper/main.aux index 0e4b0c6..4cbd3d7 100644 --- a/paper/main.aux +++ b/paper/main.aux @@ -15,7 +15,6 @@ \providecommand\HyField@AuxAddToCoFields[2]{} \citation{Homola2023} \citation{Kanamori1977} -\citation{Homola2023} \citation{Stoupel1990,Urata2018} \citation{Homola2023} \citation{Bretherton1999} @@ -33,11 +32,11 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Seismic Activity: USGS Earthquake Catalogue}{6}{subsection.2.2}\protected@file@percent } \newlabel{sec:usgs}{{2.2}{6}{Seismic Activity: USGS Earthquake Catalogue}{subsection.2.2}{}} \newlabel{eq:energy}{{1}{6}{Seismic Activity: USGS Earthquake Catalogue}{equation.2.1}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{6}{subsection.2.3}\protected@file@percent } -\newlabel{sec:sidc}{{2.3}{6}{Solar Activity: SIDC Sunspot Number}{subsection.2.3}{}} \citation{Bartlett1946} \citation{Bretherton1999} \citation{Theiler1992,Schreiber2000} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{7}{subsection.2.3}\protected@file@percent } +\newlabel{sec:sidc}{{2.3}{7}{Solar Activity: SIDC Sunspot Number}{subsection.2.3}{}} \@writefile{toc}{\contentsline {section}{\numberline {3}Methods}{7}{section.3}\protected@file@percent } \newlabel{sec:methods}{{3}{7}{Methods}{section.3}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Cross-Correlation at Lag $\tau $}{7}{subsection.3.1}\protected@file@percent } @@ -47,11 +46,11 @@ \newlabel{sec:neff}{{3.2}{7}{Effective Degrees of Freedom}{subsection.3.2}{}} \newlabel{eq:neff_bartlett}{{3}{7}{Effective Degrees of Freedom}{equation.3.3}{}} \newlabel{eq:neff_breth}{{4}{7}{Effective Degrees of Freedom}{equation.3.4}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Surrogate Significance Tests}{7}{subsection.3.3}\protected@file@percent } -\newlabel{sec:surrogates}{{3.3}{7}{Surrogate Significance 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All points are coloured by decimal year (plasma colormap), revealing the solar-cycle drift: successive cycles trace the same anti-correlated arc in the centre panel. Black curves are LOWESS trend lines ($f = 0.4$).\relax }}{15}{figure.caption.8}\protected@file@percent } -\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. 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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}{}} -\@writefile{toc}{\contentsline {paragraph}{Mutual information.}{22}{section*.21}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{22}{subsection.4.11}\protected@file@percent } -\newlabel{sec:res:missing}{{4.11}{22}{Missing-Data Sensitivity}{subsection.4.11}{}} -\@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). 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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.9}{}} +\@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.10}\protected@file@percent } +\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.10}{}} +\@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 }}{16}{figure.caption.11}\protected@file@percent } +\newlabel{fig:rawoos}{{2}{16}{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. 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The horizontal shaded band shows the na\"ive $\pm 2\sigma $ confidence interval (ignoring autocorrelation); the narrower band is the Bretherton-corrected interval.\relax }}{17}{figure.caption.13}\protected@file@percent } +\newlabel{fig:homola}{{4}{17}{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.13}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}IAAFT Surrogate Test}{18}{subsection.4.3}\protected@file@percent } +\newlabel{sec:res:surr}{{4.3}{18}{IAAFT Surrogate Test}{subsection.4.3}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces 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. The raw peak is improbably large under the null; the detrended peak ($p < 10^{-4}$, $>3.9\sigma $) is nominally significant but sensitive to the choice of $N_\text {eff}$ estimator (see Table\nobreakspace {}\ref {tab:neff}), and occurs at a lag inconsistent with the claimed mechanism. 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The correlation at the claimed $\tau =+15$~d is not significant.\relax }{figure.caption.14}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Effect of Solar-Cycle Detrending}{19}{subsection.4.4}\protected@file@percent } +\newlabel{sec:res:detrend}{{4.4}{19}{Effect of Solar-Cycle Detrending}{subsection.4.4}{}} +\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Cross-correlation statistics at $\tau = +15$\nobreakspace {}days under four preprocessing conditions, in-sample window 1976--2019.\relax }}{19}{table.caption.15}\protected@file@percent } +\newlabel{tab:detrend}{{3}{19}{Cross-correlation statistics at $\tau = +15$~days under four preprocessing conditions, in-sample window 1976--2019.\relax }{table.caption.15}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Detrending Robustness}{19}{subsection.4.5}\protected@file@percent } +\newlabel{sec:detrend_robust}{{4.5}{19}{Detrending Robustness}{subsection.4.5}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Comparison of $N_\text {eff}$ Estimators}{19}{subsection.4.6}\protected@file@percent } +\newlabel{sec:neff_comparison}{{4.6}{19}{Comparison of $N_\text {eff}$ Estimators}{subsection.4.6}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Cross-correlation functions for the raw (blue) and HP-detrended (orange) series. 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The vertical grey line marks the claimed $\tau = +15$\nobreakspace {}days. No method produces a positive feature at this lag.\relax }}{20}{figure.caption.17}\protected@file@percent } +\newlabel{fig:detrend_robust}{{7}{20}{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. 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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 }}{21}{figure.caption.19}\protected@file@percent } +\newlabel{fig:mag_threshold}{{8}{21}{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. 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The claimed $\tau = +15$\nobreakspace {}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 }}{23}{figure.caption.21}\protected@file@percent } +\newlabel{fig:partialcorr}{{10}{23}{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.21}{}} +\@writefile{toc}{\contentsline {paragraph}{Mutual information.}{23}{section*.23}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{23}{subsection.4.11}\protected@file@percent } +\newlabel{sec:res:missing}{{4.11}{23}{Missing-Data Sensitivity}{subsection.4.11}{}} +\@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 }}{24}{figure.caption.24}\protected@file@percent } +\newlabel{fig:coherence}{{11}{24}{\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. 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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 } -\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. 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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 }}{26}{figure.caption.27}\protected@file@percent } +\newlabel{fig:decluster}{{13}{26}{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. 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The vertical dashed line marks the in-sample/out-of-sample split (2020).\relax }{figure.caption.35}{}} +\citation{KassRaftery1995} \citation{Homola2023} \citation{Odintsov2006} +\@writefile{toc}{\contentsline {section}{\numberline {5}Discussion}{31}{section.5}\protected@file@percent } +\newlabel{sec:discussion}{{5}{31}{Discussion}{section.5}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{31}{subsection.5.1}\protected@file@percent } \citation{Aplin2005} \citation{Pulinets2004} -\@writefile{toc}{\contentsline {section}{\numberline {5}Discussion}{30}{section.5}\protected@file@percent } -\newlabel{sec:discussion}{{5}{30}{Discussion}{section.5}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{30}{subsection.5.1}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{30}{subsection.5.2}\protected@file@percent } \citation{Homola2023} \citation{Urata2018} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{32}{subsection.5.2}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{32}{subsection.5.3}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Limitations}{32}{subsection.5.4}\protected@file@percent } \citation{Homola2023} \citation{Homola2023} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{31}{subsection.5.3}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Limitations}{31}{subsection.5.4}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusions}{31}{section.6}\protected@file@percent } -\newlabel{sec:conclusions}{{6}{31}{Conclusions}{section.6}{}} +\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusions}{33}{section.6}\protected@file@percent } +\newlabel{sec:conclusions}{{6}{33}{Conclusions}{section.6}{}} \bibstyle{plainnat} \bibdata{refs} \bibcite{Aplin2005}{{1}{2006}{{Aplin}}{{}}} @@ -218,16 +221,17 @@ \bibcite{HP1997}{{7}{1997}{{Hodrick and Prescott}}{{}}} \bibcite{Homola2023}{{8}{2022}{{Homola et~al.}}{{}}} \bibcite{Kanamori1977}{{9}{1977}{{Kanamori}}{{}}} -\bibcite{Kraskov2004}{{10}{2004}{{Kraskov et~al.}}{{Kraskov, St{\"o}gbauer, and Grassberger}}} -\bibcite{Odintsov2006}{{11}{2006}{{Odintsov et~al.}}{{Odintsov, Boyarchuk, Georgieva, Kirov, and Atanasov}}} -\bibcite{Potgieter2013}{{12}{2013}{{Potgieter}}{{}}} -\bibcite{Pulinets2004}{{13}{2004}{{Pulinets and Boyarchuk}}{{}}} -\bibcite{RahnUhlig2002}{{14}{2002}{{Ravn and Uhlig}}{{}}} -\bibcite{Schreiber2000}{{15}{2000}{{Schreiber and Schmitz}}{{}}} -\bibcite{SIDC2024}{{16}{2024}{{SILSO World Data Center}}{{}}} -\bibcite{Stoupel1990}{{17}{1990}{{Stoupel}}{{}}} -\bibcite{Tavares2011}{{18}{2011}{{Tavares and Azevedo}}{{}}} -\bibcite{Theiler1992}{{19}{1992}{{Theiler et~al.}}{{Theiler, Eubank, Longtin, Galdrikian, and Farmer}}} -\bibcite{Urata2018}{{20}{2018}{{Urata and Tanimoto}}{{}}} -\bibcite{USGS2024}{{21}{2024}{{USGS Earthquake Hazards Program}}{{}}} -\gdef \@abspage@last{35} +\bibcite{KassRaftery1995}{{10}{1995}{{Kass and Raftery}}{{}}} +\bibcite{Kraskov2004}{{11}{2004}{{Kraskov et~al.}}{{Kraskov, St{\"o}gbauer, and Grassberger}}} +\bibcite{Odintsov2006}{{12}{2006}{{Odintsov et~al.}}{{Odintsov, Boyarchuk, Georgieva, Kirov, and Atanasov}}} +\bibcite{Potgieter2013}{{13}{2013}{{Potgieter}}{{}}} +\bibcite{Pulinets2004}{{14}{2004}{{Pulinets and Boyarchuk}}{{}}} +\bibcite{RahnUhlig2002}{{15}{2002}{{Ravn and Uhlig}}{{}}} +\bibcite{Schreiber2000}{{16}{2000}{{Schreiber and Schmitz}}{{}}} +\bibcite{SIDC2024}{{17}{2024}{{SILSO World Data Center}}{{}}} +\bibcite{Stoupel1990}{{18}{1990}{{Stoupel}}{{}}} +\bibcite{Tavares2011}{{19}{2011}{{Tavares and Azevedo}}{{}}} +\bibcite{Theiler1992}{{20}{1992}{{Theiler et~al.}}{{Theiler, Eubank, Longtin, Galdrikian, and Farmer}}} +\bibcite{Urata2018}{{21}{2018}{{Urata and Tanimoto}}{{}}} +\bibcite{USGS2024}{{22}{2024}{{USGS Earthquake Hazards Program}}{{}}} +\gdef \@abspage@last{36} diff --git a/paper/main.bbl b/paper/main.bbl index 51a8d67..e7cc897 100644 --- a/paper/main.bbl +++ b/paper/main.bbl @@ -1,4 +1,4 @@ -\begin{thebibliography}{21} +\begin{thebibliography}{22} \providecommand{\natexlab}[1]{#1} \providecommand{\url}[1]{\texttt{#1}} \expandafter\ifx\csname urlstyle\endcsname\relax @@ -73,6 +73,13 @@ Hiroo Kanamori. 2981--2987, 1977. \newblock \doi{10.1029/JB082i020p02981}. +\bibitem[Kass and Raftery(1995)]{KassRaftery1995} +Robert~E. Kass and Adrian~E. Raftery. +\newblock Bayes factors. +\newblock \emph{Journal of the American Statistical Association}, 90\penalty0 + (430):\penalty0 773--795, 1995. +\newblock \doi{10.1080/01621459.1995.10476572}. + \bibitem[Kraskov et~al.(2004)Kraskov, St{\"o}gbauer, and Grassberger]{Kraskov2004} Alexander Kraskov, Harald St{\"o}gbauer, and Peter Grassberger. diff --git a/paper/main.blg b/paper/main.blg index b3f48c6..9e11366 100644 --- a/paper/main.blg +++ b/paper/main.blg @@ -3,44 +3,44 @@ Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 The top-level auxiliary file: main.aux The style file: plainnat.bst Database file #1: refs.bib -You've used 21 entries, +You've used 22 entries, 2773 wiz_defined-function locations, - 766 strings with 8739 characters, -and the built_in function-call counts, 9334 in all, are: -= -- 875 -> -- 471 -< -- 16 -+ -- 162 -- -- 141 -* -- 762 -:= -- 1451 -add.period$ -- 78 -call.type$ -- 21 -change.case$ -- 109 -chr.to.int$ -- 21 -cite$ -- 42 -duplicate$ -- 409 -empty$ -- 790 -format.name$ -- 179 -if$ -- 1941 + 775 strings with 8910 characters, +and the built_in function-call counts, 9804 in all, are: += -- 922 +> -- 492 +< -- 17 ++ -- 169 +- -- 147 +* -- 801 +:= -- 1522 +add.period$ -- 82 +call.type$ -- 22 +change.case$ -- 114 +chr.to.int$ -- 22 +cite$ -- 44 +duplicate$ -- 429 +empty$ -- 830 +format.name$ -- 188 +if$ -- 2040 int.to.chr$ -- 1 int.to.str$ -- 1 -missing$ -- 18 -newline$ -- 128 -num.names$ -- 84 -pop$ -- 186 +missing$ -- 19 +newline$ -- 134 +num.names$ -- 88 +pop$ -- 193 preamble$ -- 1 -purify$ -- 88 +purify$ -- 92 quote$ -- 0 -skip$ -- 318 +skip$ -- 334 stack$ -- 0 -substring$ -- 389 -swap$ -- 21 +substring$ -- 416 +swap$ -- 22 text.length$ -- 0 text.prefix$ -- 0 top$ -- 0 -type$ -- 231 +type$ -- 242 warning$ -- 0 -while$ -- 94 +while$ -- 99 width$ -- 0 -write$ -- 306 +write$ -- 321 diff --git a/paper/main.log b/paper/main.log index 8f97773..5369d59 100644 --- a/paper/main.log +++ b/paper/main.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2026.4.24) 24 APR 2026 20:21 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2026.4.24) 24 APR 2026 21:03 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -709,234 +709,242 @@ LaTeX Font Info: External font `lmex10' loaded for size [4] [5] [6] Package hyperref Warning: Token not allowed in a PDF string (Unicode): -(hyperref) removing `math shift' on input line 216. +(hyperref) removing `math shift' on input line 221. 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(pdftex.def) Requested size: 409.71692pt x 191.94183pt. - [29 <./figs//rolling_correlation_oos.png> <./figs//full_series_with_envelope_f -it.png>] [30] -Overfull \hbox (9.19893pt too wide) in paragraph at lines 1352--1357 + [30 <./figs//rolling_correlation_oos.png> <./figs//full_series_with_envelope_f +it.png>] [31] [32] +Overfull \hbox (9.19893pt too wide) in paragraph at lines 1442--1447 \T1/lmr/m/n/12 (-20) We have con-ducted a rig-or-ous, pre-registered repli-ca-t ion of the claimed cosmic-ray/earthquake [] -[31] [32] (./main.bbl [33] [34]) [35] (./main.aux) +[33] (./main.bbl [34] [35]) [36] (./main.aux) Package rerunfilecheck Info: File `main.out' has not changed. (rerunfilecheck) Checksum: 4C6DAC4BA1A6488C04C1CB417177CB2A;10188. ) Here is how much of TeX's memory you used: - 19468 strings out of 477975 - 366873 string characters out of 5839281 - 1874330 words of memory out of 5000000 - 38839 multiletter control sequences out of 15000+600000 - 628233 words of font info for 254 fonts, out of 8000000 for 9000 + 19476 strings out of 477975 + 367014 string characters out of 5839281 + 1872330 words of memory out of 5000000 + 38843 multiletter control sequences out of 15000+600000 + 628196 words of font info for 254 fonts, out of 8000000 for 9000 59 hyphenation exceptions out of 8191 - 75i,12n,76p,1001b,1071s stack positions out of 10000i,1000n,20000p,200000b,200000s + 75i,12n,76p,1001b,1095s stack positions out of 10000i,1000n,20000p,200000b,200000s {/usr/share/texmf/fonts/enc/dvips/lm/lm-ts1.enc}{/usr/share/texmf/fonts/enc/d vips/lm/lm-rm.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-ec.enc}{/usr/share/te xmf/fonts/enc/dvips/lm/lm-mathex.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-ma @@ -955,10 +963,10 @@ sr/share/texmf/fonts/type1/public/lm/lmtt10.pfb> -Output written on main.pdf (35 pages, 4580694 bytes). +Output written on main.pdf (36 pages, 4586307 bytes). PDF statistics: - 826 PDF objects out of 1000 (max. 8388607) - 698 compressed objects within 7 object streams - 177 named destinations out of 1000 (max. 500000) + 838 PDF objects out of 1000 (max. 8388607) + 707 compressed objects within 8 object streams + 181 named destinations out of 1000 (max. 500000) 65000 words of extra memory for PDF output out of 74296 (max. 10000000) diff --git a/paper/main.pdf b/paper/main.pdf index 6684f44..856ac10 100644 Binary files a/paper/main.pdf and b/paper/main.pdf differ diff --git a/paper/main.tex b/paper/main.tex index 8af8a0b..9446998 100644 --- a/paper/main.tex +++ b/paper/main.tex @@ -50,45 +50,41 @@ and Out-of-Sample Validation}} \begin{abstract} \noindent \citet{Homola2023} reported a statistically significant positive correlation -($r \approx 0.31$) between galactic cosmic-ray (CR) flux measured by neutron -monitors and global seismicity (M~$\geq$~4.5) at a time lag of $\tau = +15$~days, -suggesting that elevated CR flux precedes increased earthquake activity. -That earlier value used a physically invalid seismic metric (direct sum of moment -magnitudes $M_W$, which are logarithmic); the correct metric — summed radiated energy -$E = 10^{1.5 M_W + 4.8}$\,J per bin \citep{Kanamori1977} — yields $r(+15\,\text{d}) = 0.081$. -We present a systematic replication and extension of this claim using data from -44 Neutron Monitor Database (NMDB) stations, the USGS global earthquake catalogue, -and SILSO daily sunspot numbers spanning 1976--2025. +($r \approx 0.31$) between galactic cosmic-ray (CR) flux and global seismicity +at a lag of $\tau = +15$~days, suggesting that elevated CR flux precedes +increased earthquake occurrence. +That value relied on an inappropriate seismic metric (direct summation of +moment magnitudes, which are logarithmic); the correct energy-based metric +\citep{Kanamori1977} gives $r(+15\,\text{d}) = 0.081$. -Our analysis proceeds in four stages. -\textit{Stage~1} replicates the raw cross-correlation (with correct seismic energy metric: -$r(+15\,\text{d}) = 0.081$, peak $r = 0.139$ at $\tau = -525$~days) but demonstrates -that naive $p$-values are invalid because temporal autocorrelation and a shared -$\sim$11-year solar cycle inflate the apparent significance. -\textit{Stage~2} applies iterative amplitude-adjusted Fourier transform (IAAFT) -surrogate tests with $10^4$ realisations: after Hodrick--Prescott (HP) detrending -to remove the solar-cycle component, the peak correlation drops to -$r = 0.101$ and achieves formal significance ($p_\text{global} < 10^{-4}$, $>3.9\sigma$), -but $r(+15\,\text{d}) = 0.027$ --- well within the surrogate null distribution. -\textit{Stage~3} scans $34 \times 207 = 7{,}037$ station--grid-cell pairs for -geographic localisation; 455 pairs survive Benjamini--Hochberg correction -(expected false discoveries: 352), and the optimal lag $\tau^*$ shows no -dependence on great-circle distance ($\beta = -0.45$~days/1000~km, $p = 0.21$), -consistent with an isotropic CR signal rather than a local mechanism. -\textit{Stage~4} applies a pre-registered out-of-sample test on an independent -2020--2025 window ($T = 390$ five-day bins, $10^5$ phase-randomisation -surrogates on a Tesla M40 GPU): -$r(+15\,\text{d}) = 0.030$ (surrogate 95th percentile~$= 0.101$), -$p_\text{global} = 0.100$ --- consistent with noise. -Fitting a sinusoid to the 1976--2025 annual cross-correlation timeseries yields -a best-fit period of $P = 13.0$~years and a Bayes factor of $\text{BF} = 0.75$, -slightly favouring a constant (no modulation) over a sinusoidal relationship. +We systematically replicate and extend this analysis using the \emph{global +CR index} — the normalised neutron-monitor count rate (dimensionless, station +mean $\equiv 1$) averaged over 44 NMDB stations with $\geq 3$ reporting per +5-day bin — the USGS earthquake catalogue ($M \geq 4.5$; $n \approx 232{,}000$ +events, 1976--2025), and SILSO sunspot numbers. +Methods include IAAFT surrogate tests ($10^4$ realisations), Hodrick--Prescott +detrending, geographic localisation (7{,}037 station--cell pairs, +Benjamini--Hochberg correction), a pre-registered out-of-sample validation +(2020--2025, $10^5$ surrogates), and seven additional robustness checks +(block bootstrap, partial correlation, spectral coherence, mutual information, +missing-data sensitivity, bin-size sensitivity, and earthquake declustering). -We conclude that the CR--seismic correlation reported by \citet{Homola2023} is an -artefact of the shared solar-cycle modulation of both galactic CR flux and -global seismicity, and not evidence of a physical causal link. -All analysis code, pre-registration document, and results are publicly available at -\url{https://github.com/pingud98/cosmicraysandearthquakes}. +After solar-cycle detrending, $r(+15\,\text{d})$ falls to 0.027--0.037 across +three methods, all within IAAFT surrogate null distributions. +The pre-registered out-of-sample test yields $r(+15\,\text{d}) = 0.030$ and +$p_\text{global} = 0.100$. +Partial correlation on unfiltered data reduces $r(+15\,\text{d})$ by 63\% +after sunspot regression; mutual information at the claimed lag is +indistinguishable from zero ($p = 1.000$). +The geographic scan finds no propagation-delay signature +($\beta = -0.45$~d/1000~km, $p = 0.21$). + +We find no statistically robust evidence for a causal CR--seismic relationship +within the linear cross-correlation and surrogate-testing frameworks tested +here, after controlling for solar-cycle modulation. +The primary limitation is that the 2020--2025 validation window +(${\approx}5$~yr, no complete solar cycle) provides limited statistical power, +and nonlinear or threshold-based coupling mechanisms were not assessed. \end{abstract} \textbf{Keywords:} cosmic rays; seismicity; surrogate test; solar cycle; @@ -123,9 +119,11 @@ Three statistical pitfalls immediately suggest themselves: \item \textbf{Temporal autocorrelation.} Both CR flux and seismicity exhibit strong low-frequency structure (solar cycle, regional seismic cycles). - Treating successive 5-day bins as independent dramatically inflates - the degrees of freedom; a Bretherton effective-$N$ correction \citep{Bretherton1999} - is required. + Treating successive 5-day bins as independent is statistically invalid + under the violated serial-independence assumption: autocorrelation + inflates the nominal sample size from $T \approx 3{,}200$ bins to an + effective $N_\text{eff} \approx 600$--$2{,}900$ (see Table~\ref{tab:neff}), + requiring a Bretherton-style effective-$N$ correction \citep{Bretherton1999}. \item \textbf{Shared solar-cycle trend.} Galactic CR flux is modulated by the heliospheric magnetic field, which @@ -174,9 +172,14 @@ daily coverage over the in-sample window 1976--2019, and \textbf{35 stations} over the out-of-sample window 2020--2025. Each station's daily series was normalised by its long-run mean and resampled to non-overlapping 5-day bins. -A global CR index was formed as the mean across all stations with valid data in -each bin, requiring at least three stations; bins failing this criterion were -set to \texttt{NaN}. +A \emph{global CR index} $x_t$ (dimensionless; each station normalised so its +long-run mean $\equiv 1$) was formed as the arithmetic mean of valid station +values in each 5-day bin, requiring at least three reporting stations; bins +failing this criterion were set to \texttt{NaN}. +Values above unity indicate a CR-flux enhancement relative to the long-run +station mean; values below unity indicate suppression (e.g.\ Forbush decreases +during solar maximum). +This index is used as the primary predictor variable throughout all analyses. \subsection{Seismic Activity: USGS Earthquake Catalogue} \label{sec:usgs} @@ -197,9 +200,11 @@ $E_\text{bin} = \sum_i E_i$, and the metric is $\log_{10}(E_\text{bin})$ (empty bins set to NaN). This formulation correctly weights large earthquakes: an $M_W\,8.0$ event contributes $\sim$1000$\times$ more energy than an $M_W\,6.0$ event. -Directly summing $M_W$ values — as used in several earlier studies — is -physically invalid because $M_W$ is logarithmic; such sums do not correspond -to any additive physical quantity. +Directly summing $M_W$ values --- as used in several earlier studies --- +is physically inappropriate: $M_W$ is a logarithmic quantity, so such sums +have no additive physical interpretation and artificially amplify the +contribution of solar-cycle-driven catalogue completeness fluctuations to +the seismic time series. \subsection{Solar Activity: SIDC Sunspot Number} \label{sec:sidc} @@ -474,6 +479,40 @@ The pre-registered predictions, scored after unblinding, were: surrogate 95th percentile. \end{itemize} +\paragraph{Confirmatory versus exploratory analyses.} +Table~\ref{tab:prereg_scope} distinguishes analyses that were pre-specified +(confirmatory) from those added after data examination (exploratory). + +\begin{table}[htbp] + \centering + \caption{Analysis scope and pre-registration status. + Pre-specified parameters locked before data access: $\lambda = 4.54 \times 10^{10}$, + lag range $[-200, +200]$~bins, $M \geq 4.5$, min.\ 3 stations per bin, + 5-day bin size, IAAFT surrogate count $S = 10^4$.} + \label{tab:prereg_scope} + \begin{tabular}{lll} + \toprule + Analysis & Type & Pre-specified parameters \\ + \midrule + OOS cross-correlation at $\tau = +15$~d & Confirmatory & All \\ + OOS global $p$-value (P1--F1) & Confirmatory & All \\ + In-sample IAAFT surrogate test & Confirmatory & All \\ + HP detrending with $\lambda$ & Confirmatory & $\lambda$ locked \\ + Geographic BH scan & Confirmatory & $q = 0.05$, $10°$ grid \\ + \addlinespace + STL / sunspot-regression detrending & Exploratory & — \\ + Block-bootstrap surrogates (3a) & Exploratory & — \\ + Partial correlation analysis (3b) & Exploratory & — \\ + Spectral coherence + MI (3c) & Exploratory & — \\ + Missing-data sensitivity (3d) & Exploratory & — \\ + Bin-size sensitivity (3e) & Exploratory & — \\ + Earthquake declustering (3f) & Exploratory & — \\ + Sub-period / per-cycle analysis (3g) & Exploratory & — \\ + Sinusoidal modulation fit & Exploratory & — \\ + \bottomrule + \end{tabular} +\end{table} + \subsection{Combined Timeseries: Sinusoidal Envelope Fit} \label{sec:sinusoid} @@ -556,7 +595,7 @@ panel 3). We compute both Pearson $r$ (linear; Fisher $z$-transform 95\% CI) and Spearman $\rho$ (rank-based; appropriate for the heavy-tailed marginal -distributions of $E_t$ and CR flux). +distributions of $E_t$ and the global CR index). Bonferroni correction for $3\ \text{pairs} \times 3\ \text{windows} = 9$ tests is applied; star levels refer to the corrected $p$-values. Full results are given in Table~\ref{tab:rawcorr}. @@ -712,7 +751,7 @@ Figure~\ref{fig:homola} shows the full cross-correlation function of the raw (undetrended) CR index and seismic metric (log$_{10}$ summed energy, Eq.~\ref{eq:energy}) over 1976--2019 ($T = 3{,}215$ five-day bins, 44 stations). The dominant peak is at $\tau = -525$~days ($r = 0.139$), corresponding to a -half-solar-cycle lead of seismicity over CR flux. +half-solar-cycle lead of seismicity over the global CR index. At the claimed lag $\tau = +15$~days we find $r = 0.081$. Although naive significance is high (4.6$\sigma$ treating bins as i.i.d.), both series share the $\sim$11-year solar cycle, which drives the apparent signal. @@ -758,8 +797,11 @@ surrogate null distribution. \caption{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.} + The raw peak is improbably large under the null; the detrended peak + ($p < 10^{-4}$, $>3.9\sigma$) is nominally significant but sensitive to + the choice of $N_\text{eff}$ estimator (see Table~\ref{tab:neff}), + and occurs at a lag inconsistent with the claimed mechanism. + The correlation at the claimed $\tau=+15$~d is not significant.} \label{fig:stress} \end{figure} @@ -1167,10 +1209,13 @@ Figure~\ref{fig:geodistlag} shows the regression of the optimal lag $\tau^*(s,g) on great-circle distance $d(s,g)$. The slope is $\beta = -0.45$~days/1000\,km ($p = 0.21$, $R^2 = 0.0002$), indistinguishable from zero. -If CRs caused earthquakes via a propagating local disturbance, we would expect -a positive slope (distant pairs have longer propagation delays). -The null result is consistent with CR isotropy --- any apparent correlation -arises from a globally coherent (not distance-dependent) solar-cycle confound. +A local wave-propagation or diffusion mechanism would predict a positive slope +(distant pairs accumulate longer propagation delays); the observed null result +is inconsistent with such models. +However, it does not rule out instantaneous global coupling mechanisms +(e.g.\ modulation of the atmospheric electric field), which would produce +distance-independent lags, nor does it exclude the possibility that the +apparent correlation arises from a globally coherent solar-cycle confound. \begin{figure}[htbp] \centering @@ -1178,7 +1223,10 @@ arises from a globally coherent (not distance-dependent) solar-cycle confound. \caption{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.} + indistinguishable from zero. + A local propagation or diffusion mechanism predicts a positive slope; + the null result is inconsistent with such models but does not exclude + globally instantaneous coupling.} \label{fig:geodistlag} \end{figure} @@ -1261,8 +1309,9 @@ full 1976--2025 record, together with the best-fit sinusoidal envelope. \end{figure} The global surrogate test on the full 1976--2025 window yields $p = 0.010$ -($\sigma = 2.57$) at the dominant peak $\tau = -125$~days --- marginally -significant, but at a lag inconsistent with the claimed $+15$~day CR precursor. +($\sigma = 2.57$) at the dominant peak $\tau = -125$~days --- +nominally significant but sensitive to $N_\text{eff}$ estimation +and at a lag inconsistent with the claimed $+15$~day CR precursor. The sinusoidal fit (Equations~\ref{eq:modA}--\ref{eq:bf}) does \emph{not} prefer $\mathcal{M}_B$ over $\mathcal{M}_A$ with the corrected seismic metric: @@ -1274,10 +1323,14 @@ $\mathcal{M}_B$ over $\mathcal{M}_A$ with the corrected seismic metric: \end{itemize} A Bayes factor of 0.75 is less than 1.0, indicating that the constant (no -modulation) model is marginally preferred over the sinusoidal model. +modulation) model is weakly preferred over the sinusoidal model (following +the interpretation scale of \citet{KassRaftery1995}, $\text{BF} < 1$ favours +$\mathcal{M}_A$; note that this comparison is restricted to the two +hypotheses $\mathcal{M}_A$ and $\mathcal{M}_B$ and does not account for +model uncertainty outside this pair). With the correct seismic energy metric, the oscillatory rolling cross-correlation -previously attributed to solar-cycle modulation is no longer strongly supported; -the apparent modulation in the old results was partly an artefact of the invalid +previously attributed to solar-cycle modulation is no longer supported. +The apparent modulation in the old results was partly an artefact of the summed-$M_W$ metric, which amplified the solar-cycle confound. %%%% ═══════════════════════════════════════════════════════════════════════════ @@ -1288,22 +1341,37 @@ summed-$M_W$ metric, which amplified the solar-cycle confound. The raw $r \approx 0.31$ reported by \citet{Homola2023} at $\tau = +15$~days (reduced to $r = 0.081$ with the correct seismic energy metric) and the naive -$p \sim 10^{-72}$ are products of compounding statistical errors: -(i) using a physically invalid seismic metric (direct sum of logarithmic $M_W$ -values), which artificially inflated the solar-cycle variation in the seismic series, -(ii) treating autocorrelated time series as independent observations, -(iii) failing to account for the shared solar-cycle trend driving both CR flux and -seismicity, and (iv) not correcting for scanning over 401 lag values. +$p \sim 10^{-72}$ result from four compounding errors: +(i)~using a physically inappropriate seismic metric (direct summation of +logarithmic $M_W$ values), which artificially amplifies solar-cycle variation +in the seismic series; +(ii)~treating autocorrelated time series as independent observations --- +statistically invalid under the violated serial-independence assumption, since +autocorrelation inflates the nominal sample size by a factor of 3--5 +(Table~\ref{tab:neff}); +(iii)~failing to account for the shared $\sim$11-year solar-cycle trend driving +both CR flux and seismicity; and +(iv)~not correcting for scanning over 401 lag values. The solar cycle is the key confounder. During solar minimum, the heliospheric magnetic field weakens, allowing more -galactic CRs to reach Earth, simultaneously, global seismicity has been reported -to be slightly elevated during solar minimum phases \citep{Odintsov2006}. -The resulting shared $\sim$11-year oscillation in both series induces a -substantial raw cross-correlation with a lag structure determined by the -phase relationship between the two solar responses --- approximately $\pm$half-cycle -($\sim$5.5 years $\approx 2{,}000$ days), consistent with the dominant raw peak -at $\tau = -525$~days. +galactic CRs to reach Earth. +Independently, global seismicity has been reported to be slightly elevated +during solar minimum phases \citep{Odintsov2006}. +The resulting shared $\sim$11-year oscillation in both series generates a +substantial raw cross-correlation with a lag structure set by the phase +relationship of their respective solar responses --- approximately +$\pm$half-cycle ($\sim$5.5 years $\approx 2{,}000$ days), consistent with +the dominant raw peak at $\tau = -525$~days. + +It should be noted that the $\sim$10-year periodicity shared by CR flux and +seismicity need not originate exclusively from the Schwabe solar cycle. +Alternative sources of shared decadal variability include geomagnetic activity +cycles (themselves driven by solar activity but mediated by different physical +pathways) and long-term seismic clustering or quasi-periodic accumulation and +release of tectonic stress. +Any of these mechanisms could generate the observed coherence without implying +a direct CR--seismic link. \subsection{Physical Plausibility of the Claimed Mechanism} @@ -1315,9 +1383,11 @@ transfer meaningful mechanical energy to fault zones, which require shear-stress changes of order $\sim$0.01--1~MPa to trigger earthquakes. Proposed mechanisms via radon ionisation \citep{Pulinets2004} or nuclear transmutation require orders-of-magnitude larger CR fluxes than observed. -The null geographic result (Section~\ref{sec:res:geo}) further argues against -a local physical mechanism: any genuine coupling would produce a distance-dependent -lag between CR detector and seismic source, which is not observed. +The geographic scan (Section~\ref{sec:res:geo}) finds no propagation-delay +signature ($\beta = -0.45$~d/1000~km, $p = 0.21$), which is inconsistent +with simple wave-propagation or diffusion coupling models. +This result does not, however, exclude mechanisms that would act instantaneously +on a global scale, such as modulation of the atmospheric electric field. \subsection{Comparison with Prior Replication Attempts} @@ -1333,16 +1403,36 @@ out-of-sample validation. Several limitations should be acknowledged: \begin{enumerate} - \item The OOS window (2020--2025) encompasses Solar Cycle~25, a period of - rising solar activity after the deep minimum of Cycle~24. - The absence of a solar minimum in this window limits statistical power. - \item Seismicity is not stationary; major seismic sequences (e.g.\ Tonga 2022) - can inflate the seismic metric in individual bins. - \item The sinusoid fit assumes a constant solar-cycle period, whereas the actual - cycle length varies from 9 to 14 years. - \item Out-of-sample $p_\text{oos}$ from script~08 was not produced due to - insufficient NMDB historical data in the default path; the OOS result from - the dedicated script~07 ($10^5$ surrogates) is authoritative. + \item \textbf{Out-of-sample statistical power.} + The OOS window (2020--2025, $T = 390$ bins, $\approx 5$~yr) encompasses + only the rising phase of Solar Cycle~25 and contains no complete solar + minimum. + Because the primary hypothesis concerns a correlation that is modulated + by the solar cycle, a single incomplete cycle provides limited power to + discriminate a genuine sub-cycle signal from noise. + The OOS failure to replicate ($p_\text{global} = 0.100$) should therefore + be interpreted as \emph{consistent with} the null hypothesis rather than as + strong independent evidence against the claimed effect; it carries + substantially less weight than the 44-year in-sample analysis. + + \item \textbf{Seismicity non-stationarity.} + Seismicity is not stationary; major seismic sequences (e.g.\ Tonga 2022) + can dominate the seismic metric in individual bins, introducing transient + structure that is not related to CR flux. + + \item \textbf{Sinusoidal model rigidity.} + The sinusoidal modulation fit assumes a constant solar-cycle period, + whereas the actual Schwabe cycle length varies from 9 to 14 years. + A more flexible model (e.g.\ a time-warped sinusoid) might alter the BF + comparison. + + \item \textbf{Untested mechanisms.} + This analysis tests for linear cross-correlation between the global CR + index and a globally-aggregated seismic energy metric. + Threshold effects (e.g.\ CR triggering only above a critical fault stress), + nonlinear coupling, frequency-selective interaction, or extreme-event + coupling are not addressed and cannot be excluded on the basis of these + results. \end{enumerate} %%%% ═══════════════════════════════════════════════════════════════════════════ @@ -1357,20 +1447,21 @@ Our principal findings are: \begin{enumerate} \item The raw cross-correlation $r(+15\,\text{d}) = 0.081$ (corrected seismic - energy metric) is modest and misleading; it is driven by a shared - $\sim$10-year solar-cycle modulation of both CR flux and global seismicity, - not by a physical CR$\to$seismic mechanism. + energy metric) is modest; it is consistent with a shared $\sim$10-year + solar-cycle modulation of both CR flux and global seismicity rather than + a direct CR$\to$seismic mechanism. The larger value ($r \approx 0.31$) reported by \citet{Homola2023} results - from the physically invalid practice of directly summing logarithmic $M_W$ - values rather than the underlying energies. + from the physically inappropriate practice of directly summing logarithmic + $M_W$ values rather than the underlying energies. \item After solar-cycle detrending, $r(+15\,\text{d})$ falls to $0.027$ (HP), $0.030$ (STL), or $0.037$ (sunspot regression) --- all within the surrogate null distribution and consistent with zero. - \item No geographic localisation is detected: the optimal lag between CR station - and seismic cell shows no distance dependence ($\beta = -0.45$~d/1000~km, - $p = 0.21$), inconsistent with a local propagation mechanism. + \item No propagation-delay signature is detected: the optimal lag between CR + station and seismic cell shows no distance dependence ($\beta = -0.45$~d/1000~km, + $p = 0.21$), inconsistent with local wave-propagation or diffusion models, + though globally instantaneous coupling mechanisms remain untested. \item A pre-registered out-of-sample test on 2020--2025 yields $r(+15\,\text{d}) = 0.030$ and $p_\text{global} = 0.100$, entirely @@ -1405,8 +1496,12 @@ Our principal findings are: \end{itemize} \end{enumerate} -We conclude that there is no statistically credible evidence for a physical -causal link between galactic cosmic-ray flux and global seismicity. +We find no statistically robust evidence for a causal relationship between +galactic cosmic-ray flux and global seismicity within the tested statistical +frameworks, after controlling for solar-cycle modulation. +Threshold effects, nonlinear triggering, and extreme-event coupling --- +mechanisms not assessed in the present analysis --- cannot be excluded on +the basis of these results alone. %%%% ═══════════════════════════════════════════════════════════════════════════ \section*{Data Availability} diff --git a/paper/main.toc b/paper/main.toc index c29430c..0f3d5a0 100644 --- a/paper/main.toc +++ b/paper/main.toc @@ -2,55 +2,56 @@ \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 {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{7}{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 {subsection}{\numberline {3.3}Surrogate Significance Tests}{8}{subsection.3.3}% +\contentsline {subsubsection}{\numberline {3.3.1}Phase Randomisation}{8}{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 {subsubsection}{\numberline {3.3.5}GPU Acceleration}{9}{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 {3.5}Partial Correlation Analysis}{10}{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 {paragraph}{Confirmatory versus exploratory analyses.}{11}{section*.4}% \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 {4.1.1}CR index: station distribution}{13}{subsubsection.4.1.1}% +\contentsline {subsubsection}{\numberline {4.1.2}Seismic energy metric}{13}{subsubsection.4.1.2}% +\contentsline {subsubsection}{\numberline {4.1.3}Sunspot number}{13}{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}% +\contentsline {paragraph}{CR vs.\ seismicity.}{13}{section*.6}% +\contentsline {paragraph}{CR vs.\ sunspot number.}{14}{section*.7}% +\contentsline {paragraph}{Sunspot vs.\ seismicity.}{14}{section*.8}% +\contentsline {subsubsection}{\numberline {4.1.5}Interpretation: a confounding triangle}{14}{subsubsection.4.1.5}% +\contentsline {subsection}{\numberline {4.2}In-Sample Replication (1976--2019)}{17}{subsection.4.2}% +\contentsline {subsection}{\numberline {4.3}IAAFT Surrogate Test}{18}{subsection.4.3}% +\contentsline {subsection}{\numberline {4.4}Effect of Solar-Cycle Detrending}{19}{subsection.4.4}% +\contentsline {subsection}{\numberline {4.5}Detrending Robustness}{19}{subsection.4.5}% +\contentsline {subsection}{\numberline {4.6}Comparison of $N_\text {eff}$ Estimators}{19}{subsection.4.6}% +\contentsline {subsection}{\numberline {4.7}Magnitude Threshold Sensitivity}{21}{subsection.4.7}% +\contentsline {subsection}{\numberline {4.8}Block-Bootstrap Surrogate Comparison}{21}{subsection.4.8}% +\contentsline {subsection}{\numberline {4.9}Partial Correlation: Controlling for Sunspot Number}{22}{subsection.4.9}% +\contentsline {subsection}{\numberline {4.10}Spectral Coherence and Mutual Information}{22}{subsection.4.10}% +\contentsline {paragraph}{Coherence.}{22}{section*.22}% +\contentsline {paragraph}{Mutual information.}{23}{section*.23}% +\contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{23}{subsection.4.11}% +\contentsline {subsection}{\numberline {4.12}Bin-Size Sensitivity}{25}{subsection.4.12}% +\contentsline {subsection}{\numberline {4.13}Earthquake Declustering (Gardner--Knopoff)}{25}{subsection.4.13}% +\contentsline {subsection}{\numberline {4.14}Sub-Period Analysis by Solar Cycle}{26}{subsection.4.14}% +\contentsline {subsection}{\numberline {4.15}Geographic Localisation}{26}{subsection.4.15}% +\contentsline {subsection}{\numberline {4.16}Pre-Registered Out-of-Sample Validation (2020--2025)}{29}{subsection.4.16}% +\contentsline {subsection}{\numberline {4.17}Combined 1976--2025 Analysis: Sinusoidal Modulation}{30}{subsection.4.17}% +\contentsline {section}{\numberline {5}Discussion}{31}{section.5}% +\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{31}{subsection.5.1}% +\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{32}{subsection.5.2}% +\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{32}{subsection.5.3}% +\contentsline {subsection}{\numberline {5.4}Limitations}{32}{subsection.5.4}% +\contentsline {section}{\numberline {6}Conclusions}{33}{section.6}% diff --git a/paper/refs.bib b/paper/refs.bib index df51430..e8f23a3 100644 --- a/paper/refs.bib +++ b/paper/refs.bib @@ -185,6 +185,17 @@ howpublished = {\url{https://www.nmdb.eu}}, } +@article{KassRaftery1995, + author = {Kass, Robert E. and Raftery, Adrian E.}, + title = {Bayes Factors}, + journal = {Journal of the American Statistical Association}, + year = {1995}, + volume = {90}, + number = {430}, + pages = {773--795}, + doi = {10.1080/01621459.1995.10476572}, +} + @article{Kraskov2004, author = {Kraskov, Alexander and St{\"o}gbauer, Harald and Grassberger, Peter}, title = {Estimating mutual information},