IEEE Geoscience and Remote Sensing Magazine - December 2016 - 52

BACKGROUND
An early attempt to correlate earthquake occurrence with
moon location is the analysis by Knott [1] who, in 1897, examined 15 sets of earthquake data from Japan and related
the time of the earthquakes to the time of the moon's meridian passage at the quake locations, i.e., when the moon
had been overhead, to determine the values of MEAs (where
1 h of time represents 15° of angle in the earth's rotation).
He then normalized the occurrence data across a day and
Fourier-analyzed it to obtain
a model in the form of harmonic coefficients. His results
A pRONOUNCeD AND
showed a tendency toward
CONSISteNt teNDeNCY wAS
twice-daily occurrences at
fOUND fOR eARthqUAKeS
times roughly 6 h after and
tO CLUSteR AROUND CeR6 h before the moon's passage
over the earthquake location,
tAIN vALUeS Of MOON-tOwith the times varying by a
eARthqUAKe ANGLe IN
few hours among the locaALL Of the MAGNItUDe
tions. Knott did not parse the
RANGeS StUDIeD.
data by earthquake magnitude, but he did contrast regions with mainly smaller
quakes against regions with larger quakes, and he noted, in
particular, that odd behavior in some harmonic coefficients
provided "a warning of the danger of lumping together statistics of different countries or different seismic areas" in studies
of earthquake behavior. This was the situation he encountered in the last of his data sets, which comprised the other
15 sets combined.
Knott's analysis was criticized shortly afterward by
Schuster [2], who agreed with Knott's approach but argued
that the harmonic results for the all-quake set did not deviate significantly from those of random occurrences, despite
the fact that Knott's results for specific locations showed
correlative behavior. This reinforced Knott's warning about
"lumping together" earthquake data while not diminishing
his location-specific findings.
The potential benefit of considering the moon's effects
through the combined parameter of the MEA is suggested
by the results of recent studies that conclude that neither
the moon phase nor gravity alone correlate well with earthquake occurrence, as exemplified in [3] and [4]. In [4], the
authors noted the suggestion of a delay between the times
of high tidal stresses and the occurrence of an earthquake.
Correlation between tidal stresses and tectonic events was
noted in [5], and, although the MEA parameter is not discussed directly there, its material suggests offsets between
the times of peak stresses and the earthquake events that
imply some combined effect.
The most detailed analysis of MEAs following Knott's
was performed by Stetson in 1937 [6] for earthquakes in
the Pacific and South America. Stetson found, as did Knott,
"a distinct tendency for major seismic disturbances to
follow preferential positions of the moon" at the time of
the quake. Instead of a Fourier analysis, Stetson matched
52

earthquake clustering behavior to a reference two-cycle sinusoid function, and he determined that significant clustering occurred at angles of roughly 90° west (to the left on
the earth as seen from the moon and 6 h before the quake's
location passed the moon) and 100° east of the earth-moon
axis. Stetson noted, in particular, that the greatest numbers
of quakes did not occur at the sublunar point where the
moon's gravitational force is strongest.
By matching the data to a sinusoid, however, Stetson assumed that the behavior of the data was basically sinusoidal.
Apparent modeling errors would result if, in fact, the intrinsic
properties of the data did not possess sinusoidal variability.
This reflects a limitation on frequency domain models if the
earthquake occurrences do not behave with regular periodicity in a given location or possess the same periodic behavior in different regions or even among repeated quakes in
the same region. The harmonic coefficients or phase angles
would need to be recalculated for each region.
Neither of the reference analyses involving explicit
MEAs [1], [6] treated quake magnitude as a parameter, and
so they did not explore whether larger and smaller quakes
have different relations to the moon position. Finding such
a variation with magnitude would suggest varying earthquake mechanisms.
The present analysis seeks to determine the intrinsic
relationship between earthquake and moon position in
the time domain. The approach taken here, which was
initially arrived at independently of Knott's and Stetson's
approach through consideration of the "pull angle" of the
moon at the location of the quake, extends previous work
by cross correlating MEA data with a smooth matching
function to reduce data scatter and more clearly reveal
the underlying behavior in the MEAs associated with the
earthquakes. In addition to dividing the data into discrete
magnitude ranges, this approach foregoes modeling that
would require the definition of coefficients that would
depend in unknown ways on properties of location and
geology. Based on the trends found in the analysis results,
however, a physical basis for the observed data characteristics is proposed.
ANALYSIS
The geometric characterization of the earth-moon-quake
relationships used in this analysis is illustrated in Figure 1.
The independent variable in the analysis is the angle difference in coordinates of the earth between the position of the
moon and the position of an earthquake.
This study examined a set of U.S. Geological Survey
(USGS) earthquake data [7] for the Southern California
region comprising 229 earthquake events occurring between 1769 and 2004 and ranging in magnitude from
5.2 to 8.25. The earthquake data specified date, time, location, and magnitude.
The analysis approach taken here made provision for
an effect of quake magnitude on the correlation results,
anticipating differing mechanisms underlying large and
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