\documentclass[twoside]{article}
\usepackage[silent,pdf,hyper]{elxshort}
\usepackage{color}
\usepackage{hyperref}
\journalid{ES}{19}{1}{19}
\citnumber{}{5}
\paperid{2019ES000650}
\papertype{RAR}
\cpright{}{2019}
\lefthead{M. Kovalyov}
\righthead{On the correlation  of seismic activity to  syzygies.}
\received{11}{October}{2018}
\accepted{12}{November}{2018}
\published{14}{February}{2019}
\definecolor{brown}{RGB}{157,23,4}

\authaddr{Mikhail Kovalyov, Professor Emeritus, University of Alberta, Edmonton, Alberta, Canada. (mkovalyo[at] ualberta.ca)}

\begin{document}

\title{On the correlation  of seismic activity to  syzygies.}

\author{1}{Kovalyov}{Mikhail}{}{1}{}{}

\affil{1}{Professor Emeritus}{University of Alberta}{}{Canada}

\keywd{earthquakes}
\keywd{volcanic eruptions}
\keywd{syzygies}

\abstract{There must be hundreds of papers dedicated to the studies of the relationship between lunar phases and seismic activity on Earth;  half of them claim to prove that lunar phases affect seismic activity on Earth, while the other half disprove the same.  It is shown here that the lunar phases indeed affect seismic activity on Earth,  the correlation between them is especially easily seen in  magnitude $\geqslant8.2$ earthquakes and VEI $\geqslant5$ volcanic eruption, but  only seasonally.  The seasons of correlation last centuries and  are intimately connected to the behavior of the Earth's magnetic field.  The correlation between the lunar phases and seismic activity may be also easily observed in the seismic activity away from well-formed  tectonic lines, e. g. the earthquakes along the East African Rift and high-magnitude deep earthquakes.}

\section{Introduction}

A simple online search for  the correlation  of powerful seismic events  with  syzygies yields literally  an enormous number of research papers going back to, at least, the 19th century, [\itc{Klotz,} \reflink{klot14}{1914}];    some prove  the existence of such a relationship  while the others disprove it.

Rejections of the very existence of such correlation  are
plentiful both in the scientific literature  and online, with any correlations attributed to mere coincidence.   The existence of correlation between seismic activity and lunar motion is   a  seismic stand-off between those who believe that seismic activity can be predicted and those who do not. The former are best represented by the    International Institute of Earthquake Prediction Theory  founded by Vladimir Keilis-Borok, whose algorithm for earthquake prediction   has been used to successfully  predict  the outcomes of numerous elections.  The latter are represented by   western institutions, who, after remarkably unsuccessful attempts to predict earthquakes in 1970s, have switched to a complete denial of any seismic predictions.  The latter  argue that the increase in the   tidal pull near syzygies is too  small to have any effect. However, quite a few physical phenomena exhibit drastic responses to rather tiny changes in parameters.  One example is provided by $\text{CO}_2$ which can be liquefied at $\approx 304.25$\,K at a pressure of $\approx 73$ atm, but not at a slightly higher temperature, even under pressures as high as 3\,000 atm;  of course, that is because $\approx 304.25$\,K, $\approx 72.9$ atm is $\text{CO}_2\text{'s}$ critical point. If the Earth is in a critical state in some sense, it may be sensitive to relatively small changes in the forces exhorted on it.



Can we detect the effect of syzygies? Our research shows that it is indeed possible to detect  tidal  influence on Earth's seismic activity,  yet it   is often  obscured by other factors.  In this paper we discuss the seismic activity  showing  correlation with lunar  syzygies, specifically   1)  magnitude $\geqslant 8.2$ earthquakes, 2) VEI $\geqslant 5$ volcanic eruptions, 3) earthquakes in Africa, 4) earthquakes originating below  400  km,  5) the year 2012 phenomenon.

\section{Data Sources Used}

The seismic data seems to be reliable from 1978 onwards; the first disagreements between major  catalogs of seismic data appear  as recently as  1977, e. g. USGS and NOAA
catalogs (\href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}) disagree~on the magnitude of   the 1977/8/19 earthquake, the earthquake is   given magnitude 8.3 by USGS and magnitude 8.0 by NOAA.  With a considerable leap of faith we may assume that   the seismic data from 1900 onwards is   sufficiently reliable to draw conclusions. The pre-1900 seismic data cannot be considered   reliable and  may be used to draw only the most general conclusions.

Author has compiled a data base of seismic activity versus lunar phases from open sources; the data is arranged in ten tables [\itc{Kovalyov,} \reflink{kova19}{2019}] published in
\href{http://esdb.gcras.ru/}{Earth Science Data Base}, created and managed by \href{http://gcras.ru/}{GCRAS}.

The sources of data for each table are provided in the note to the table.

\section{Data Analysis}


  The main ingredients of the patterns associated with the lunar motion are the synodic and anomalistic months.
A  {\it synodic month} is  the time between two exactly the same adjacent phases of the Moon, e.g. two adjacent Full Moons, two adjacent New Moons, etc.; an {\it anomalistic  month} is  the time between two adjacent perigees. The exact values of   synodic and anomalistic months vary, but  the {\it average  synodic  month} is $\approx 29.530587981$   days   and the {\it average  anomalistic month}   is $\approx 27.554551$ days. Since  14 average synodic months  $\approx 413.428$ days and  15 average anomalistic months $\approx 413.318$ days are almost the same,   the    lunar  motion is almost cyclicly  repeating itself approximately every 413--414  days.  Thus we may define a  {\it full lunar cycle} to be a period of   $\approx 413$  consecutive   days which begins and ends with the same lunar phase and  contains 14 New Moons, 14 Full Moons, and 15 perigees.

The  {\it closest perigee} and {\it 2nd closest perigee} of a full lunar cycle   come within less than 11 hours of New/Full Moon,  and
are typically separated from each other by 6--8 synodic months, (\href{https://www.fourmilab.ch/earthview/pacalc.html}{https://www. fourmilab.ch/earthview/pacalc.html}
 e.g.  the closest perigee and Full Moon were less than 2 hours apart on 2015/9/28, the 2nd closest perigee and New Moon were less than 8 hours apart on\linebreak 2015/2/19. Less often, the 2nd closest perigee may be merely a month away from  the closest perigee, e. g. in  1963 the  perigees on 1963/11/2 and 1963/11/30 were at, correspondingly,   356\,958 km  and   356\,954 km  with, correspondingly     10 hours 30 minutes and 10 hours 47 minutes   separating the perigees from Full Moon; the third closest perigee of  356\,972 km  was on 1963/4/23  with only two hours away from New Moon.
 Seismic activity is   influenced  not only by mere proximity to a  syzygy, but also by different aspects of the syzygy, e. g. the distance between  Moon and Earth,   proximity to perigee/apogee,   proximity to perihelion, etc.
In this paper, for simplicity's sake, we divide  syzygies into only three types: 1) {\it  regular syzygy} is a syzygy more than 12 hours away from   the nearest perigee; 2) {\it syzygy-closest/2nd closest perigee}   is a syzygy within 11 hours of  a closest/2nd closest  perigee; 3) {\it twin pair}    is a syzygy within 11 hours of  a closest/2nd closest  perigee coupled   with    an adjacent syzygy with very similar parameters, e.g.   1963/11/2 and 1963/11/30 and  define $\mathcal{H}_\nu $ to be the time either within 30+$\nu$ days of a syzygy-closest/2nd closest perigee, or   within 30 + $\nu$ days of a twin pair, here 1 day = 24 hours.

An  example of a twin pair  is   provided by the already mentioned    1963/11/30 Full Moon  separated from the closest perigee of  356\,954 km by 10 hours 47 minutes and    1963/11/2 Full Moon  separated from the 2nd closest perigee of  356\,958 km  by 10 hours 30 minutes; they were preceded by   the  1963/4/23 New Moon  separated from the 3rd-closest perigee of  356\,972 km  by merely two hours.  For our purpose, the three events are practically  indistinguishable, all three should be treated as syzygy-closest/2nd closest perigees; it is easier, however, to  view the  two syzygy-perigees  of 1963/11/30 and 1963/11/2 as a single event of a  twin pair.
\enlargethispage{.85pc}

We say that an event is in  $\mathcal H_\nu,$  if it is either within $0.5+\nu$ days  of a regular syzygy or within   30 + $\nu$ days of a syzygy-closest/2nd closestperigee or a twin pair;;  $\mathcal H_\nu\subset\mathcal H_{\nu+1}.$
To estimate the percentage of days in  $\mathcal{H}_\nu,$  consider
the period of   1004 average synodic months   $\approx 1004 \times 29.530587981 \approx  81 \text{ years }$ $ 63.46033 \text{ days}$ or 1076 average anomalistic months   $\approx
1076 \times 27.554551 \approx  81 \text{ years } 63.446488 \text{ days,} $ with a year taken
to be 365.25 days.  The difference  between 81 years 63.46033 days and 81 years 63.44688
days is $\approx$0.01345 days or slightly more than half an hour so for any practical
purposes we may consider the two periods to be equal to 81 years 63.5 days or 29\,648.7 days and contain 2008 syzygies.  The period will contain  $\dfrac{1004}{14}\times 2=144$ full lunar cycles, almost each cycle has  two syzygy-closest/2nd closest perigees, but some cycles may have  a
syzygy-closest/2nd closest perigee and a twin pair of syzygies which consists of two syzygy-perigees separated by a synodic month, e.g.  2002/2/27 and 2002/3/28.   As a sample of such a period we may
take   1921/1/1--2002/2/4, it contains 2008 syzygies comprising 1851 regular syzygies, 133 syzygy-closest/2nd closest perigees, 12 twin pairs of syzygy-perigees.  The number of days  of 1921/1/1--2002/2/4 in $\mathcal H_\nu$ is given by the formula
$1851\;(0.5+2\nu)+133\;(60+2\nu) +12\;(89.5+2\nu)= 9979.5+3992\nu.$  Thus the days in $\mathcal H_\nu$ make $\dfrac{9\,979.5+3\,992\;\nu}{29\,648.7}$ portion of 1921/1/1--2002/2/4; we take it as a reference formula for all periods of time:

\[\approx \dfrac{9\,979.5+3\,992\;\nu}{29\,648.7}\approx  \begin{cases}
 74.1\%, \text{ if } \nu=3\\
60.6\%, \text{ if } \nu=2 \\
 47.1\%, \text{ if } \nu=1 \\
33.7\%, \text{ if } \nu=0
 \end{cases}= \]
 \[ =74.1\%/60.6\%/47.1\%/33.7\% \eqno{\rm(1)}\]

\noindent  If a sufficiently large group of events  has  $p_3\%/p_2\%/\linebreak p_1\%/p_0\%$ in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0,$ then the ratios $
\pmb \kappa_3=\dfrac{p_3}{74.1}, \pmb \kappa_2=\dfrac{p_2}{60.6},$ $ \pmb \kappa_1=\dfrac{p_1}{47.1}, \pmb \kappa_0=\dfrac{p_0}{33.7}$  are indicative of the syzygies' influence on the events.

For the sake of brevity, we shall use M for "magnitude".

\section{M $\pmb {\geqslant 8.2}$ earthquakes  in  1550--2017}

\href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}    shows   M $\geqslant8.2$ earthquakes in 1938--2017. It was compiled by merging  data from USGS and NOAA; fore/aftershocks are not listed.

 Of the 36 earthquakes in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}     listed by USGS
 as M $\geqslant8.2,$  34/29/23/18, or 94.4\%/80.6\%/63.9\%/\linebreak 50\%, are in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0;$   the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{94.4}{74.1}\approx 1.27, \pmb \kappa_2=\dfrac{80.6}{60.6}\approx 1.33, \pmb \kappa_1=\dfrac{63.9}{47.1}\approx 1.36,$ $ \pmb \kappa_0=\dfrac{50.}{33.7}\approx1.48$ increase  as $\nu$ decreases.
Only two earthquakes from USGS
did not make it to  $\mathcal{H}_3,$ both rather special.
 The 2006/11/15 earthquake, followed by an M=8.1 2007/1/13 aftershock,   started the eleven-month season 2006/11/15--2007/9/29  with the most M $\geqslant 8.0 $ earthquakes, five in total;  for comparison there were 69 M $\geqslant 8.0$ earthquakes in 1938--2017 averaging $\approx 0.79$ earthquakes per an eleven-month period.
  The 1977/8/19   earthquake  started the 1977/8/20--1985/3/3  $\text{M}\geqslant 8.0$ earthquake drought, the longest period in
  1900--2017 without a M $\geqslant 8.0$ earthquake.
Of the 39 earthquakes  in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}  listed by NOAA
as M $\geqslant8.2,$ 38/33/27/20, or 97.4\%/84.6\%/69.2\%/51.3\%, are in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0;$  the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{94.4}{74.1}\approx 1.27, \pmb \kappa_2=\dfrac{84.6}{60.6}\approx 1.4, \pmb \kappa_1=\dfrac{69.2}{47.1}\approx 1.47,$ $ \pmb \kappa_0= \dfrac{51.3}{33.7}\approx1.52$ increase  as $\nu$ decreases. Since the 1977/8/19   earthquake is listed by NOAA as having M $<8.2,$  only
  the  2006/11/15  earthquake   is left out of  $\mathcal{H}_3.$ The 2006/11/15 earthquake   preceded  the 2006/12/5 X9.0 solar flare, [\itc{Kovalyov,} \reflink{kova19}{2019}, Table 1];
  whether that is a pure coincidence or there is a connection between  the earthquake and solar flare is not clear.  In 1957--1965  M $\geqslant8.2$ earthquakes struck practically every year, all but one in $\mathcal{H}_0;$ the years coincided with the  19th primary solar cycle of 1955--1965, the most powerful primary solar cycle since the record-keeping began  in 1700.

\vspace*{.25pc}

\href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table02.pdf}{Table 2}     shows   M $\geqslant8.2$ earthquakes in 1900--1933. It was compiled exactly the same way  as \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}.      Of the 12 earthquakes from USGS  5/3/2/2,\,or 41.7\%/25\%/16.7\%/16.7\%, are in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0;$
   the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{41.7}{74.1}\approx 0.56, \pmb \kappa_2=\dfrac{25}{60.6}\approx 0.41, \pmb \kappa_1=\dfrac{16.7}{47.1}\approx 0.35, \pmb \kappa_0=\dfrac{16.7}{33.7}\approx0.5;$ the portion outside of $\mathcal{H}_3$ got $\dfrac{1-41.7}{1-74.1}$\linebreak  $\approx 2.25$ times its fair share of earthquakes.
  Of the 27 earthquakes from NOAA,   15/12/8/6,\,or 55.6\%/\linebreak 44.4\%/29.6\%/22.2\%, are in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0,$  the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{55.6}{74.1}\approx 0.75, \pmb \kappa_2=\dfrac{44.4}{60.6}\approx 0.73, \pmb \kappa_1=\dfrac{29.6}{47.1}\approx 0.63, \pmb \kappa_0=\dfrac{22.2}{33.7}\approx0.66;$  the portion outside of $\mathcal{H}_3$ got\linebreak  $\dfrac{1-55.6}{1-74.1}\approx 1.71$ times its fair share of earthquakes.   Instead of being attracted to syzygies, the earthquakes were repelled from syzygies; we may call such behavior  {\it anti-correlation}.  Both catalogs lead to $\pmb \kappa_3 \geqslant \pmb \kappa_2 \geqslant \pmb \kappa_1 \leqslant \pmb \kappa_0.$   The thirteen earthquakes in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table02.pdf}{Table 2}    that did not make it to $\mathcal{H}_3$  may be divided in clusters:  three  in 1901/8/9--1903/6/2; three in  1905/7/9--1906/1/31; three in 1917/5/1--1918/8/15; and two in  1922/11/11--1924/4/14.



\begin{figure*}[t]                 %  Fig. 1
\figurewidth{35pc}
\setimage{}{}{41pc}{}{2019es000650-f01}
\crosscaption{Modelled path of the magnetic poles; yellow squares indicate observed locations,  \url{https://maps.ngdc.noaa.gov/viewers/historical_declination/}.   The gUFM model was used for  1590--1890, the  IGRF model was used for  1900--2020, a smooth transition was imposed for 1890--1900 to connect the models.
The modelled path often significantly deviates from the observed locations, and thus should be viewed only as a
rough approximation  of the real path. The 1859 turn in the path coincided with the Carrington solar storm of 1859/9/1-2;
the 1730 turn in the path coincided with the Boston solar storm of 1730/10/22.  The paths of both poles made significant turns in 1753--1755.}
\end{figure*}

   There is no reliable data about the  pre-1900 earthquakes,  the magnitude, coordinates of the epicenter, or even date  of pre-1900 earthquakes  often vary widely between catalogs. The reason for that is that the pre-1900 earthquake data is compiled based on historical descriptions, often very vague and subjective; the interpretations of these descriptions are also very subjective. The first glance at pre-1900 M $\geqslant8.2$ earthquakes is provided by \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table03.pdf}{Table~3}
 comprising the most-gossiped-about 1550--1899  M $\geqslant8.2$ earthquakes compiled from two   articles  in Wikipedia;
 the sheer number  of non-scientists involved in Wikipedia  seems to guarantee a  certain degree of objectivity.
\href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table03.pdf}{Table 3}  indicates that the anti-correlation of  M $\geqslant 8.2$ earthquakes    with syzygies  shown in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table02.pdf}{Table 2}     extends all the way back to
  1835,   reaching  its peak in  1905--1918 when  the number of earthquakes in $ \mathcal{H}_3$ was merely 3 out of 7, or 42.9\% much less than predicted by (1). The   1919--1933 years seem  to be the transition period between the 1898--1918 core of anti-correlation and the correlation season of 1938--present.  The 1835--1897  years seem to be the transition period between the 1898--1918 core of anti-correlation and the correlation season of 1550--1834.

\vspace*{-.5ex}

  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table04.pdf}{Table 4}, showing  M $\geqslant8.2$ earthquakes from NOAA and GHEA,
allows us to zoom in on the 1550--1833 years.   The New Madrid earthquakes have been  since downgraded to  lower magnitudes and the  1761/3/30, 1716/2/11, 1586/7/10,    1584/\linebreak 3/17 earthquakes seem to be aftershocks of preceding earthquakes; hence  they are  moved to the bottom of the table.   The  1818/11/8, 1793/2/17, 1787/3/28, 1725/2/1,   1647/5/14 earthquakes did not make it to $\mathcal{H}_3$ but were close. Over all, \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table04.pdf}{Table 4} confirms the correlation of M $\geqslant8.2$ earthquakes with syzygies in
    1550--1761. The 1793/2/17, 1792/8/22,  1784/5/13 earthquakes cluster together; they struck in or right  after the 1781--1789  season of intensive geomagnetic storms and may have been caused by them, [\itc{Vaquero and Trigo,} \reflink{vaqu05}{2005}]; it is also possible the beginning of the transition period of 1835--1897  should  be extended from 1835 to 1755--1762.      Of the 24 earthquakes in 1555--1755,     22/1815/12, or 91.7\%/75\%/63\%/50\% are in
  $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0,$  the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{55.6}{74.1}\approx 1.24, \pmb \kappa_2=\dfrac{44.4}{60.6}\approx 1.24,   \pmb \kappa_1=\dfrac{29.6}{47.1}\approx 1.34,   \pmb \kappa_0=\dfrac{22.2}{33.7}\approx1.48$ increase as $\nu$ deceases.     The 1755--1762 years separating the 1555--1755 and  1762--1835 periods are chronologically close to 1753--1755  when the magnetic poles' paths changed their directions as shown in \figref{1}.\vspace*{-.5\baselineskip}


\section{The  year 2012 phenomenon}\vspace*{-.5\baselineskip}

   A strong connection to syzygy-closest perigees  was   exhibited by the strongest earthquakes of the full lunar  cycle  in 2009/7/21--2018/7/13  when
 the strongest earthquake  of the full lunar cycle struck  within 33 days of Full Moon-closest perigee in  six out of eight full lunar cycles, as shown in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table05.pdf}{Table 5}.     The correlation is,  most likely,   due to Full Moon coming within less than 66 minutes  of the closest perigee of the full lunar cycle  for five years in a row: on   2011/3/19,  2012/5/6, 2013/6/23, 2014/8/10,  2015/9/28  Full Moon  and the closest perigee were correspondingly 59,  2,  23,  27, and  65 minutes apart; such an event is very rare and might be the reason why the ancient Maya  used 2012 as a time stamp to mark the end of one time cycle and the beginning of   another, hence we refer to the event as {\it the year 2012 phenomenon}.
  The previous sequence of  Full Moon-closest/2nd closest perigees of less than an hour between Full Moon and perigee was on  1809/5/29,  1810/7/16, 1811/9/2, 1812/10/20, followed by Full Moon-closest perigees  of  356\,496 km on 1813/12/7  and of  56\,647 km on 1815/1/25; it was followed by the  1815/4/10   VEI=7 eruption of Tambora.    Would there be a powerful eruption in a year or two?

  The full lunar cycles started and ended on the day of New Moon-2nd closest perigee in 2009/7/21-2012/12/12, in 2014/1/30-2018/8/10, the full lunar cycles started and ended one synodic after
 New Moon-2nd closest perigee; that may have contributed to the breakdown in the pattern causing the strongest earthquake to strike on 2014/4/1 rather than within 33 days of the 2014/8/10 Full Moon-closest perigee.

 The years 2010--2014 produced   five  M $\geqslant 8.2$  earthquakes, averaging  one per year; for comparison,  in 1900--2009 there were only 39 M $\geqslant 8.2$ earthquakes averaging less than   0.36 earthquakes   per year.  Of the thirteen M $\geqslant8.6$ earthquakes in 1900--2017, three, or 23\%. struck in 2010\,-\,2012.
In the   2017/5/26--2018/7/13 full lunar cycle, the second strongest earthquake was 21 days after Full Moon-closest perigee, the strongest earthquake of the lunar cycle struck  within two days of 2017/9/6  Full Moon  and 2017/9/7 X9.3 solar flare.


In the 2008/6/3--2009/7/21 full lunar cycle, the strongest earthquake was of  M=7.8 and it  struck on  2009/7/15,  6 days before the 2009/7/21 syzygy-perigee; it was preceded by a M=7.7 earthquake on 2009/7/5, 16 days before the 2009/7/21 syzygy-perigee. Another M=7.7 earthquake struck on \newline 2009/1/3,  22 days after the   2008/12/12 Full Moon-closest perigee.   In the 2007/4/17--2008/6/3 full lunar cycle, the strongest earthquake was of M=8.4 and it struck on 2007/9/12,   44 days before the 2007/10/26  Full Moon-closest perigee.  So the pattern was building up two full lunar cycles prior to 2009/7/21--2018/7/13. We may expect
the pattern to  wither after 2018/7/13  but  it still should be  felt in the  2018/7/13--2019/8/30 full lunar cycle suggesting  a powerful earthquake of M $\geqslant7.7$ close to  the 2019/2/19 Full Moon-closest perigee.



\section{M $\pmb {\geqslant 6.6}$ earthquakes in Africa}\vspace*{-.5ex}

  The East African
Rift Line is  only a forming tectonic line, the earthquakes along it cannot be attributed to the motion of continental plates and may be expected  to be more influenced by syzygies than earthquakes elsewhere.    Africa's 1900--2017  earthquakes listed by USGS
as  M $\geqslant 6.6$  are shown  in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table06.pdf}{Table 6}.  Of the total of 18 earthquakes,     15/15/11/10, or  83.3\%/83.3\%/61.1\%/55.6\%,  were in $\mathcal H_3/\mathcal H_2/\mathcal H_1\mathcal H_0,$  the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{83.3}{74.1}\approx 1.12, \pmb \kappa_2=\dfrac{83.3}{60.6}\approx 1.37, \pmb \kappa_1=\dfrac{61.1}{47.1}\approx 1.3, \pmb \kappa_0=\dfrac{55.6}{33.7}\approx1.65$ may be said to "almost increase" as $\nu$ decreases. Of the ten   earthquakes along the East African
Rift Line, shown in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table06.pdf}{Table 6} in bold,  8/8/6/6, or 80\%/80\%/60\%/60\%,  were in $\mathcal H_3/\mathcal H_2/\mathcal H_1\mathcal H_0;$   the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{80.}{74.1}\approx 1.08, \pmb \kappa_2=\dfrac{80.}{60.6}\approx 1.32, \pmb \kappa_1=\dfrac{60.}{47.1}\approx 1.27, \pmb \kappa_0=\dfrac{60}{33.7}\approx1.78$ may be said to "almost increase" as $\nu$ decreases.  The  1990/7/9 earthquake  was 107 minutes short of $\mathcal H_1$, had it struck 107 minutes earlier, both ratios would have been increasing as  $\nu$ decreases.  Three more earthquakes listed as M $\geqslant 6.6$  by NOAA
are shown  at the bottom of \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table06.pdf}{Table 6}.



 \section{Powerful earthquakes at great depths}

   Most earthquakes   strike in or near the crust  and/or upper mantle with the focal depth in the range of  0--400 km; yet some have  focal depth up to  700 km, striking  in the  transition zone separating the upper mantle from the lower mantle.  The high temperature and pressure in the transition zone    should make them more susceptible to  tidal forces.

 \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table07.pdf}{Table 7}      shows  M $\geqslant7.4$ earthquakes of the focal depth $\geqslant 400$ km
    according to USGS and NOAA in 1900--2018/8/1.  Of the 22 earthquakes  from USGS,  18/16/12/7, or
   81.8\%/72.7\%/ 54.5\%/31.8\%  are in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0;$ of the 28 earthquakes from NOAA     23/19/14/9, or    82.1\%/67.9\%/ 50\%/32.1\%,
    are in $\mathcal{H}_3/\mathcal{H}_2/\mathcal{H}_1/\mathcal{H}_0;$ both distributions are somewhat similar to (1).
    A bit more careful examination of  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table07.pdf}{Table 7}  shows that    all earthquakes that did not make it to $\mathcal{H}_3,$ almost did so. Three earthquakes 1963/8/15, 1958/7/26,  1957/9/28 that did not make it to $\mathcal{H}_3$ were at the time of the most powerful primary solar cycle.\vspace*{-.5\baselineskip}

\section{VEI $\pmb {\geqslant 5}$ volcanic eruptions in 1600--2017}
\vspace*{-.5\baselineskip}

   Unlike earthquakes, most powerful volcanic eruption leave long-lasting traces letting us  determine their VEI and dates.    Although the dates and VEI  of powerful eruptions can  be determined sufficiently  well, it is hard to determine when the seismic activity associated with  such eruptions actually started as  powerful eruptions are often preceded by earthquakes and less powerful eruptions; with that in mind,   \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table08.pdf}{Table 8}     shows   all  VEI $\geqslant5$ eruptions in 1600--2017, with the date and time selected or estimated  to be those of the strongest blast, unless otherwise stated.

  The number of eruptions in $\mathcal H_3/\mathcal H_2/\mathcal H_1/\mathcal H_0$ in 1600--1815 was 14/12/10/8  or  82.4\%/70.6\%/58.8\%/\linebreak 47.1\% of the total of 17;   the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{82.4}{74.1}\approx 1.11, \pmb \kappa_2=\dfrac{70.6}{60.6}\approx 1.165, \pmb \kappa_1=\dfrac{58.8}{47.1}\approx 1.25, \pmb \kappa_0=\dfrac{47.1}{33.7}\approx1.4 $  increase  as    $\nu$ decreases.

  The number of eruptions in $\mathcal H_3/\mathcal H_2/\mathcal H_1/\mathcal H_0$ in 1913--2017 was  8/7/5/4  or 72.7\%/63.6\%/45.5\%/  36.4\% of the total of 11; which is  almost identical to (1) and the the ratios  of these percentages to (1)   $\pmb \kappa_3=\dfrac{72.7}{74.1}\approx 0.98, \pmb \kappa_2=\dfrac{63.6}{60.6}\approx 1.05, \pmb \kappa_1=\dfrac{45.5}{47.1}\approx 0.97, \pmb \kappa_0=\dfrac{36.4}{33.7}\approx1.08 $ are all close to one.
Yet the three eruptions that did not make it to $\mathcal H_3$ were close, so $\pmb \kappa_3\approx  \pmb \kappa_2\approx   \pmb \kappa_1 \approx  1 $  might be   due to lack of refinement of the method employed in this paper rather than due to
  lack of correlation.   The 1963/3/17 eruption  of Agung occurred right in the midst of the 1957/3/9--1965/1/2/24 period which had nine M $\geqslant8.2$ earthquakes, most likely caused by the 19th primary solar cycle, the most powerful primary solar cycle known since the record-keeping started in 1700.

 \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table09.pdf}{Table 9}     shows that each VEI $\geqslant 6$ eruption was preceded by additional  celestial events which either increased the tidal pull, or applied the tidal pull periodically several times, or added electromagnetic force to the tidal force; these events are not taken into account by $\mathcal H_\nu\text{'s.}$

   During the anti-correlation season of 1822--1912, 8 out of 9 volcanic eruptions, or 88.9\% were outside  of $\mathcal H_3;$ that is $\dfrac {88.9}{100-74.1}\approx 3.4$ times more than what a random distribution of eruptions would have produced.

All but one known M $\geqslant8.2$ earthquakes in 1687--1755  and all but two known VEI $\geqslant5$ volcanic eruptions in  1707--1815 occurred  within 30 days of a syzygy-closest/2nd closest perigee; all of them occurred within 3.5 days of a regular syzygy or within 33.5 days of a syzygy-perigee.



\section{Antipodal symmetry of earthquakes and eruptions}

Since the tidal forces produced by the Moon,   and amplified near   syzygies,  are   almost antipodally symmetric, we may expect   the regions of powerful seismic activity to show antipodal symmetry, i.e.      the most powerful seismic activity may be expected to be   accompanied by considerable seismic activity near  the antipodal location.    \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table10.pdf}{Table 10}   shows that this is indeed the case.  Not only the  M $\geqslant 8.6$ earthquakes
 correlate with syzygies  but so do their almost antipodal matches.

\begin{figure*}[t]                 %  Fig. 2
\figurewidth{35pc}
\setimage{}{}{41pc}{}{2019es000650-f02}
\crosscaption{Seismic activity  on the map of antipodes in Mercator projection.  The land antipodal to water is shown in light sandy color,
water antipodal to land  is shown in light purple,    land antipodal to land is shown in pink, water antipodal to water is shown in blue.
Magnitude $\geqslant 8.2$ earthquakes in 1900--2017, according to,  are shown by circles. Known VEI $\geqslant 5$ eruptions and five
known  Antarctic eruptions in 1892--2018 are shown by the  symbols of volcanoes.}
\end{figure*}


Magnitude $\geqslant8.2$ earthquakes  in 1900--2017, according to USGS,
are shown in \figref{2}   by circles.  They may be divided into groups based on location:  1)  in or close to South America or its antipode,  marked purple; 2) over  or near the shallow floor of the Scotia Sea,   shown in  an inset,  or its antipode, marked brown; 3) over or close to  the shallow floor of Zealandia, shown in an  inset, or its antipode, marked green; 4) along the Kuril-Japan and Aleutian trenches or close to Alaska, marked yellow.

\begin{sloppypar}
NOAA Catalogue
assigns magnitude $\geqslant8.2$ to additional earthquakes: 1969/8/11, 1959/5/4, 1948/1/24, 1943/4/6,  1942/8/24, 1941/11/25, 1939/1/25, 1924/4/14, 1919/1/1, 1918/9/7, 1917/6/26, 1908/12/12, 1907/4/15, 1906/12/12, 1906/1/21, 1905/1/22, 1904/8/27, 1904/6/25, 1903/6/2,   1901/8/9 in Japan, 1901/8/9 Loyalty Island, 1900/10/29    and  1900/10/9;   each one of them fits into either of the categories marked purple, green, brown or yellow.
\end{sloppypar}

\begin{figure*}[t]                 %  Fig. 3
\figurewidth{35pc}
\setimage{}{}{41pc}{}{2019es000650-f03}
\crosscaption{Yearly mean sunspot number (black) up to 1749 and monthly 13-month
smoothed sunspot number (blue) in 1749--2017,  \url{http://www.sidc.be/silso/yearlyssnplot}.
The   maxima of the primary solar cycles  rise and fall in somewhat cyclical manner known as the {\it secondary solar cycles}.}
\end{figure*}


\def\bottomfraction{.9}
\begin{figure}[b]                 %  Fig. 4
\figurewidth{35pc}\vspace*{-\baselineskip}
\setimage{10.5pc}{}{41pc}{}{2019es000650-f04}
 \crosscaption{M$\geqslant8.2$ earthquakes and VEI$\geqslant$5 volcanic eruptions versus  cosmic ray intensity (CRI) in 1958--2016.
 Daily average of  CRI   is shown in purple. M$\geqslant8.2$ earthquakes are marked by solid  vertical lines, red lines
 indicate  earthquakes near considerable drop-downs in CRI,  green lines indicate earthquakes near insignificant drop-down, blue
 lines indicate earthquakes far away from any drop-downs.   VEI$\geqslant 5$ volcanic eruptions are marked by dotted vertical lines,
 all of them are  near drop-downs in CRI. The recurring drop-downs in 1973/5/17--1991/6/15  are marked by asterisks. (After \href{http://cr0.izmiran.ru/mosc/ }{http://cr0.izmiran.ru/mosc/ })}
\end{figure}




 VEI $\geqslant5$ volcanic eruptions in 1600--2017 are shown   in \figref{2}  by symbols of volcanoes.    The majority struck  on or near land or shallow water antipodal to land or shallow water or along the  Kuril-Japan and Aleutian trenches or in  Alaska; the only exception is the 1980/5/18 eruption of St. Helens.    The only five   surface  Antarctic volcanoes, known to erupt in 1892--2018,  are near the land antipodal to land.

  Most of powerful seismic activity occurs in or close to South and Central America or its antipodes and along the  Kuril-Japan and Aleutian trenches and close to Alaska. The earthquakes in continental Asia and the volcanic eruptions in Iceland, Italy and the Atlantic are not  in the Pacific Ring of Fire but their antipodes are.\vspace*{-.5\baselineskip}

 \section{The correlation pattern and the Earth's magnetic field}\vspace*{-.5\baselineskip}

The anti-correlation of earthquakes to syzygies  in 1835--1933 in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}, \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table02.pdf}{Table 2},   \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table03.pdf}{Table 3},    and  anti-correlation of volcanic eruptions  to syzygies  in
1822--1912  in \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table08.pdf}{Table 8}     are chronologically close to the chaotic part   the magnetic  North pole's path  in 1826--1910 seen in   \figref{1};  the three intervals are also close to a secondary solar cycle $\approx$ 1800--1910   in \figref{3}; the longer period 1784--1933  of  anti-correlation of
earthquakes to syzygies suggested by  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table04.pdf}{Table 4}     is also  close to  the secondary solar cycle 1800--1930. That  suggests a  connection between secondary solar cycles and seismic activity, but with so little data available any attempts to draw a conclusion would be premature.


  Several more aspects of the magnetic North Pole seem to mirror seismic activity:
1)   the 1647/5/14 earthquake   and 1631/12/16 eruption  occurred close to  the 1632  sharp turn  in the path  of the magnetic North pole at the beginning of the Maunder minimum;
  2)  the 1977/8/19 earthquake  in  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table01.pdf}{Table 1}      and  the worsening of correlation of volcanic eruptions to syzygies  in 1956--1980 in
  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table08.pdf}{Table 8}      were chronologically close to  the    change in  the direction of    motion of the magnetic North pole  around 1955--1975 shown in the inset; 3)    the  1684--1755  angle in the path  of the North magnetic pole   coincides with a period of   extremely good correlation   in    \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table03.pdf}{Table 3} and  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table08.pdf}{Table 8}.

\enlargethispage{-28\baselineskip}

\figref{4}       shows  M $\geqslant8.2$ earthquakes and VEI $\geqslant5$ volcanic eruptions in 1958--2016 versus cosmic ray intensity (CRI).  All the eruptions and most of the earthquakes occurred  close to drop-downs in CRI; one may be tempted to conclude that the drop-downs contributed to the powerful seismic events. However, the most pronounced drop-downs in CRI  recurred in 1973/5/17--1991/6/15     approximately every 600 days,  yet only    two M $\geqslant8.2$ earthquakes and only two VEI $\geqslant5$ volcanic eruptions occurred at that time.  The drop-downs in CRI are usually caused by   solar flares,
yet some drop-downs follow earthquakes rather than precede them suggesting that there might be a third agent affecting both the earthquakes   and the solar activity leading to  the solar flares.  That certain terrestrial activities seem to precede solar activities was also pointed out in [\itc{Hathaway and Wilson,} \reflink{hath06}{2006}].


  Drop-downs in CRI may also be due to changes in the geomagnetic field.
  The existence of correlation between powerful seismic activity and drastic changes in the geomagnetic field  is supported by other observations, e.g.  1) the eruption of Pinatubo, the most powerful eruption of the past 60 years coincided with a drastic increase in solar flare, [\itc{Kovalyov,} \reflink{kova19}{2019}, Table 8],
  which certainly affected the Earth's magnetic field; 2)  2004/12/27 powerful $\gamma-$ray burst practically coincided with the 2004/12/26 M=9.1 earthquake; 3) powerful solar flares in March-April of 1950 preceded the 1950/5/22 M=9.5 earthquake;  4) the only two earthquakes in  \href{http://esdb.wdcb.ru/doi/2019/RJES-data-650/table05.pdf}{Table 5}  that did not strike within 31 days of perigee-syzygy, struck 1--3 days after considerable solar flares.


  Is there  a deep-rooted relationship between the seismic and geomagnetic activities? The geophysicists of today do  not believe so and attribute any correlation between the geomagnetic and seismic activities to a  mere coincidence.  But if the most powerful seismic events draw their power from the liquid core, then the seismic activity should be affected by both the tidal and electromagnetic forces for the liquid core is affected by both.\vspace*{-.5\baselineskip}

 \section{Discussion}\vspace*{-.5\baselineskip}

The weather forecast involves work with numerous factors affecting the weather,  the seismic forecast should also be based on numerous factors. Yet a number of researchers persistently fixate on syzygies alone in their attempts to show lack of correlation of seismic activity with syzygies.  Different aspects of earthquakes  depend  on whether the  earthquakes are intraplate or interplate, shallow or deep, in ocean or on land; they are affected by cosmic rays, solar flares and coronal mass ejections, as well as lunar syzygies.  Sometimes the influence of syzygies becomes dominant  making correlation of seismic activity with syzygies more clear.

The syzygies themselves are not the same and affect seismic activity differently, depending on the distance from Earth, time to the nearest perigee, the subsolar and sublunar points, and much more. A very rudimentary and simplistic attempt to account for these differences is the separation of syzygies into   regular syzygies and syzygy-closest/2nd closest perigees employed in this paper.
Failure to differentiate between regular syzygies and syzygy-closest/2nd closest perigees   leads to  the seismic events within $30+\nu$ days of syzygy-closest/2nd closest perigees, spread out more or less uniformly over
different lunar phases, overshadowing any correlation between regular syzygies and seismic events. The   tools used in this paper might be the first, albeit rudimentary, tools to study the effect of tidal forces on seismic activity.
To develop   better tools, one needs to  study   patterns of seismicity;  yet with only 50 years of totally reliable seismic data and another 50 years of relatively reliable seismic data available, only few  patterns of seismic activity are  easily detectable.

The seismic activity appears to be  sensitive to both the tidal forces  exhorted by Moon and Sun and the electromagnetic forces exhorted by solar flares and cosmic rays. There is only one part of Earth  sensitive to both, and that is the liquid core, suggesting that, at least some, powerful earthquakes draw their power from the liquid core.  Recent work [\itc{Gardonio et al.,} \reflink{gard18}{2018}] suggests that, at least some, earthquakes  may be caused by pulses of deep fluids. We believe the fluid is coming from the liquid core.

\acknowledgments{The author would like to thank Selena and Nickolas  Kovalyov who helped with  the preparation and verification of the tables  and data analysis. The author would like to thank  the organizations and individuals who produced   the data and software  used in the paper. The author would  also like to thank the  reviewers and  editors for helpful suggestions. Especial thanks go to Dr. Vitaly Nechitailenko who thoroughly checked and corrected the manuscript and formatted the manuscript and patiently  guided  the author through the preparation of the manuscript for publication.}



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\vspace*{.37pc}

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\end{document}
