Following is a PRELIMINARY study of occurrence of events in 4 regions used in Syzygy
studies. There are other equally useful methods to determine significance of these
data as occurring during Syzygy windows. Many of these methods show lower significance
than found here. Please examine this study and make any recommendation which
you feel would improve the usefulness of these statistics and/or better ways to
approach these data and questions.
Syzygy windows were provided from JOB through Roger Hunter. This study attempts
to find the statistical significance that more earthquakes than random occur during the
JOB syzygy windows.

Earthquake occurrences were obtained from the NGDC catalog including
NEIS, NCSN, SCSN, PNSN and other pertinent data.
After the results for each catalog were obtained using observed,
earthquakes a series of random simulations were performed on each
catalog. While the JOB windows were kept the same, the date of
each earthquake was randomized by adding a random number of
days to each date. The C- language rand() random number generator
was used. This additional time ranged from 0 to 220 days. To give
equivalent results the random catalog started in January 1973
instead of September 1973. Each catalog was randomized in 1000
simulations and the total number of hits tabulated. Table 1 shows
the results of this series of analyses:

The null hypothesis in each case is that there is no relation
between the number of occurring earthquakes and the JOB windows.
The time period consisted of 10015 total days of which 2044
(8X292) were in JOB windows (23.3%).

Table 1: Statistics of tests on seismicity in four JOB test areas

Group 1: Global earthquakes of Mw>=7, Sept 1973 - Dec 2000
Group 2: Earthquakes in Seattle area Sept 1973 - Dec 2000, 3.0<=Ml<=5.0
(within 2 degrees of 47.0N 122.0W)
Group 3: Earthquakes in San Jose area Sept 1973 - Dec 2000, 3.5<=Ml<=5.5
(within 2 degrees of 37.15N 121.75W)
Group 4: Earthquakes in Los Angeles area Sept 1973 - Dec 2000, 3.5<=Ml<=6.0
(within 2 degrees of 34.0N 118.0W)

DATA SIMULATIONS
Total Windowed %(T/W) Average STD %tile* Z-statistc Accept**
Group Events (T)Events (W) X100 Windowed Events(P) Null

1 416 125 30% 106.2 8.44 0.983 2.22 0.017
2 1292 411 31% 347.5 16.67 1.000 >3.00 <0.001
3 1165 462 39% 309.6 14.74 1.000 >3.00 <0.001
4 2194 649 29% 600.9 19.67 0.989 2.44 0.011

*1.00 in percentile indicates that NONE of the 1000 random simulations
had as many events within JOB windows as were found in the real data.

** In 17 simulations the total number events within windows in group
1 was higher than the observed number; in groups 2 and 3 none of the
simulations yielded more hits than were observed; in group 4 11
simulations had more events within windows than the observed data showed.

AFTERSHOCKS AND SWARMS:

In the three regions of the western United States, aftershocks
were a major portion of the catalog. There were few aftershocks
in group 1 - the events of Mw>=7.0, so this section does not consider
that data set.
To test what effect aftershock sequences had on the observed results,
the 3 or 4 largest aftershock sequences (or swarms) were removed from the
catalog. This was done by removing all events in the aftershock sequence for
the first month after the mainshock, but retaining the mainshock in
the catalog.
The months which were removed were:
Group 2: 3-18-1980 to 5-18-1980 (Mt. St. Helen's swarm)
2-14-1981 to 3-14-1981
8-21-1986 to 9-21-1986
Group 3: 5-2-1983 to 6-2-1983 (Coalinga aftershocks)
8-4-1985 to 9-4-1985 (Kettleman aftershocks)
10-18-1989 to 12-18-1989 (Loma Prieta aftershocks)
Group 4: 4-23-1992 to 5-23-1992 (Joshua Tree aftershocks)
6-28-1992 to 7-28-1992 (Landers aftershocks)
1-17-1994 to 2-17-1994 (Northridge aftershocks)
10-16-1999 to 11-16-1999 (Hector Mine aftershocks)

In each case the time extent of the catalog is now 9895 days instead
of the original 10015 days. The windowed period is now 23.6% of the
total time.

Table 2 shows the effect of removing the largest aftershock and
and clustering events from each catalog.

Group Original Minus aftershocks % of Cat. Windowed Percentage
# events # events HITS (Hits/Total)
AFSRM (ORIGINAL)
2 1292 474 36.6% 148 31% (31%)
3 1165 943 80.9% 302 32% (39%)
4 2194 1371 47.3% 318 23% (29%)

When the 4 months of aftershocks are removed from group 2 (Seattle)
about 2/3rds of the catalog is lost. The remaining 36.6%, however
has the same percentage of hits/total events as in the original
catalog, so removing aftershocks from this catalog appears to have
made little difference in the results. In group 3 (San Jose) removal
of aftershocks eliminates about 20 % of the catalog and the percentage
of events within JOB windows is reduced by 7% from 39% in the
original catalog to 32% in the catalog with aftershock sequences
removed. In group 4 (Los Angeles), removal of aftershock reduces
the catalog to about half it's original size. In this catalog
the percentage of events in JOB windows is reduced about 6 percent
from the original, and is about the same percentage as expected
in a random catalog (23%).

CONCLUSIONS:

In each of the four catalogs investigated, events occur with
statistical significance in which the null hypothesis can be
accepted with less than 2% confidence. In other words, our
simulations suggest that events are contained within JOB time
windows more often than they ought to by random chance in each
area. In groups 2 and 3 none of the 1000 simulations had as many
events in windowed times as the observed data.
Although simulations have not been down with catalogs where
large aftershock sequences have been removed, these preliminary
results suggest that aftershock removal (or declustering) makes
a significant difference in the results obtained.

In terms of the JOB hypothesis, however these differences may
not be significant. If syzygy does enhance seismicity as claimed,
then it should also enhance aftershock sequences and the removal
of these events may not be warranted.