Download Draft 2.5 - posted 15 June 2014 /2500k

Global View of Great Earthquakes and Large Volcanic Eruptions
Matched to Polar Drift and its Time Derivatives
by Douglas W. Zbikowski, Institute for Celestial Geodynamics
www.celestialgeodynamics.org
Draft 2.5 - posted 15 June 2014
Introduction
[1]
The rotational axis of Earth moves with respect to two reference frames—the celestial and terrestrial. Axial motion with respect to
the celestial frame has been traditionally divided into two parts, precession and nutation. Precession is a smooth motion of the axis
about the pole of the ecliptic that traces out two opposing cones in space with apexes at Earth's center and, presently, an angular
radius of 23.44°. This secular motion, with a 25,800-year cycle, is produced by differential gravitational (tidal) torquing on Earth's
aspherical, equatorial bulge by the Moon, Sun, and in much smaller amounts by solar system planets. Nutation is a small amplitude,
periodic 'nodding' of the axis along that conical path and is comprised of short-period components. The dominant component, with
the largest amplitude (9 arcseconds) and longest period, is associated with the 18.61-year lunar-nodal cycle. The total combined
movement of the rotational axis with respect to the celestial frame appears to be entirely astronomically forced.
[2]
Axial motion with respect to the terrestrial frame is motion referenced to the net surface of Earth. Net surface represents an
averaging of all crustal motions due to global tectonics, secular deformations (e.g. post-glacial rebound, orogenic upheavals), and
periodic deformations (e.g. Earth tides, atmospheric or oceanic loading). In 1991, the International Union for Geodesy and
Geophysics (IUGG) approved a reference system model, the International Terrestrial Reference System (ITRS), which defined
requirements for suitable reference frames. Requirements included, in part, an origin that is the geocenter of Earth's masses—
including oceans and the atmosphere—and a coordinate frame that has no residual global rotation with respect to horizontal
motions at Earth's surface.
[3]
Axial motion with respect to the terrestrial frame is usually divided into three categories, polar wobble, polar drift, and polar
wander. Polar wobble is the annual motion of the rotational pole on the net surface in a roughly circular figure that varies in size,
the diameter being about 12 m during 2001–2005. Polar wobble has two main components—the Chandler and annual wobbles.
The Chandler wobble is a free oscillation with a period of about 435 days, which is excited by a combination of atmospheric and
1
oceanic processes, with the dominant excitation mechanism being ocean‐bottom pressure fluctuations. The annual wobble is a
forced oscillation due to seasonal displacements of air and water masses. Polar drift is residual movement along the path of annual
mean poles and has averaged about 15 cm/yr since 1890. The speed and direction of polar drift can vary considerably in just a few
years. Polar wander is the large amplitude geographic motion of polar drift on the geologic timescale. Polar drift and polar wander
are reasoned to be caused mainly by slow redistributions of mass within or on Earth (especially suspect, currently, are post-glacial
rebound and polar ice loss). This premise is challenged, herein, by differentiating the drift path into its time-derivative curves, drift
speed and acceleration, which both show cyclical patterns thereby producing a basis in rotational dynamics for suspecting cyclical
forcing, hypothetically, with astronomical causes. The cyclical time derivatives of polar drift are also shown to correlate strongly
with global earthquakes and volcanic eruptions, thereby raising the possibility of forecasting such events.
[4]
Note:
1. Gross, R. S. (2000). The excitation of the Chandler wobble, Geophys. Res. Lett., 27(15), 2329–2332,
doi: 10.1029/2000GL011450.
Figure 1. A tsunami wave crashes over a sea wall and street in Miyako City, Iwate Prefecture, in northeastern Japan
shortly after a record M9.0 earthquake struck off the coast on March 11, 2011.
http://news.nationalgeographic.com/news/2011/03/pictures/110315-nuclear-reactor-japan-tsunami-earthquakeworld-photos-meltdown/
Figure 2
Drift Path of North Rotational Pole
[5]
2
Figure 2 shows the secular drift path of the north rotational pole for 1846–2011.05. Dr. Daniel Gambis, Director of EOP PC at the
Observatoire de Paris and Board Member of the International Earth Rotation and Reference Systems Service (IERS), supplied
sequential mean poles for every 0.30 year (109.58 days) in 1846–1890, every 0.15 year (54.79 days) in 1890–1900, and every 0.05
year (18.26 days) in 1900–2011.05. In computing the mean poles, Dr. Gambis filtered pole components to remove both wobble
terms, the Chandler and annual. Resolution of the roughly circular path of polar wobble is provided using modern astrometrical
methods—Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS). Using GPS, the motion of polar wobble is
3
now determined daily with a precision of +/- 0.2 milliarcsecond (0.6 cm on surface).
[6]
4
On this graph, one-tenth second (0".10) of geocentric arc equals 3.0818 meters on Earth's surface near the North Pole. Decades
are marked and labeled to show the nonuniform nature of drift speed. It is apparent that when drift direction is changing more
rapidly, the pole drifts more slowly. Although the century trend of the path is toward 80° W, path detail shows extended excursions
from that direction. The accuracy of the path prior to 1890 seems suspect in that those mean poles are found to be positioned more
irregularly than the rest and did not produce, with incremental calculation, consistent drift directions. The calculation of direction
should not have yielded such inconsistency solely from the relatively longer 0.30-year intervals. Hereinafter, mean poles prior to
1890 are not utilized.
[7]
The filtered path of secular polar drift, with mean poles calculated for periodically varying but regular intervals, will be utilized to
calculate both aspects of drift velocity—(1) velocity magnitude (speed) and its sequential time derivative, acceleration, and (2)
velocity direction. Drift-velocity aspects and their time derivatives will be shown to affect the timing, location, and intensity of
earthquakes and volcanic eruptions on the globe.
[8]
Notes:
2. On 21 March 2011, Dr. Daniel Gambis supplied a homogeneous solution of mean poles for 1846.00–2011.05, with pole components filtered
to remove the Chandler and annual terms. http://www.obspm.fr/
3. IERS http://www.iers.org/IERS/EN/Science/Techniques/gps.html retrieved 23 December 2011.
4. Using the derived polar radius, b = 6,356,752.3142 m, from Department of Defense World Geodetic System 1984, NSN 7643-01-402-0347,
23 Jun 2004 rev.
Figure 3
Global Great Quakes and Large Eruptions Matched to Drift Speed, Acceleration, and Jounce
[9]
Figure 3 shows speed and acceleration of drift of Earth's north rotational pole with respect to the net surface. The relative motion of
5
the rotational axis in this tip-over mode (TOM) of the spinning Earth physically requires proportionate angular migration of the
ellipsoid via equipotential adjustment of the figure. Figure adjustment generates commensurate crustal strain, the most being
created where: (1) the ellipsoid migrates fastest—on the meridian great circle that is aligned with drift direction, and (2) the
ellipsoidal surface slope is maximum—near 45° N and 45° S latitudes. In the time domain, abrupt changes in crustal strain/stress
may plausibly trigger quakes and volcanic eruptions. To investigate this possibility, such events are plotted on the acceleration trace
to check for event correlation with abrupt changes in the rate of acceleration—a likely generator of abrupt changes in strain/stress.
These events are simultaneous on the acceleration trace, but no other shared attribute is implied by superposition of their markers.
[10]
Markers on the LOESS-smoothed acceleration trace indicate the timing and categorical size of great earthquakes and large volcanic
6,7
eruptions.
Note that most quakes and eruptions occur when the acceleration rate-of-change is changing rapidly—the trace curves
markedly at full turning arcs—and the events of greatest energy usually occur at or near maximum or minimum turning points. Also,
event groupings of extreme energy appear to match acceleration turning points that occur immediately after or during periods of
unusually high drift speed. Correlations shown between seismic or volcanic triggering and time derivatives of drift may result
because the timescales of seismic or volcanic nucleation are fulfilled by the timescale of drift-driven strain/stress fluctuations.
Changing rate-of-change of acceleration (or the second time-derivative of acceleration) is called jounce and the cyclical TOM
acceleration and slow jounce may be astronomically forced.
[11]
The TOM acceleration appears regularly forced, hypothetically, by varying tidal torque that arises from the combination of orbital
variations within local celestial-mechanical cycles: the 18.61-year lunar-nodal cycle, the 8.85-year revolution of lunar perigee, and
Earth's annual solar orbit (supporting graphs not included). Notice that the total cyclic forcing regularly produces 59-year super
peaks in acceleration (e.g. 1892.5, 1952.5, 2010.1) and about 8 years later in speed (e.g. 1901, 1960, 2021?). Commensurabilities of
resonance may be: (18.61 yr x 3 = 55.83) and (8.85 yr x 7 = 61.95) with [(55.83 + 61.95)/2 = 58.89]. A spectral analysis should be
performed to test this hypothesis and a celestial-mechanical model completed to corroborate the result.
[12]
The TOM acceleration peak of 2010.1 exceeds all other acceleration peaks in the past 120 years by at least 20%. To support the
hypothesis of astronomical forcing, orbital aspects of the Earth, Sun, and Moon at this time or just before (non-rigid Earth) must
have been extremely favorable for applying tidal torques to Earth's equatorial bulge. Solar-tidal forces create optimum torque on
the bulge when Earth's axis tilts within a plane that is normal to the ecliptic and includes the Sun's center. This ideal orientation
8
occurs at winter or summer solstice, and winter solstice occurred about six weeks before 2010.1, on December 21, 2009 (2009.97).
Also, tidal torques are inversely proportional to the cube of the distance between two celestial bodies and perihelion occurred on
8
January 3, 2010 (2010.01). On Earth, solar and lunar tidal effects combine best at syzygy, when the three bodies are configured in a
straight line, which is the case during solar and lunar eclipses (solar eclipses are optimally effective). An annular solar eclipse
9
occurred on January 15, 2010 (2010.04). On average, lunar-tidal forces on Earth are about twice the strength of solar-tidal. Thus,
10
most importantly, a partial lunar eclipse occurred on December 31, 2009 (2010.00) and, remarkably, lunar perigee the next day,
11
January 1, 2010 (2010.00). Therefore, it seems likely that a coincidence of multiple torque-optimum, orbital aspects combined
within a period of about three weeks to create the preeminent acceleration peak of 2010.1.
[13]
While the last two drift-speed super peaks in 1901 (23 cm/yr) and 1960 (24.5 cm/yr) had significantly greater speed than interim
levels, the next super peak may actually be a mega peak in comparison. Our projections indicate that a drift speed of 52 cm/yr may
be reached by 2021. The rarity of the 32 cm/yr drift speed of 2011 is evidenced in its effect by the March 2011 Japanese quake of
M9.0 following a long history of many centuries of regional quakes never exceeding M8.5. However, to accurately translate drift
speed into global seismic energy is not presently possible, as the relationship mechanisms are not yet known and may be quite
nonlinear. Regardless of how accurately the size of global events can be projected, judging from the timing of some great events in
history, super peak regularity in drift speed may extend at least back to 1783 [1901 – (2 x 59) = 1783] with the infamous Laki fissure
eruption in Iceland that killed, possibly, millions globally.
[14]
Showing correlations between time derivatives of drift and global great quakes or large eruptions is intriguing, but is not, in itself, a
tool for usefully forecasting such events. The problem is that although strong associations hint at polar drift driving equipotential
adjustments (this mechanism is hereinafter called ellipsoidal demand), which generates crustal strain fluctuations that may trigger
quakes and eruptions, event locations are not indicated. For ellipsoidal demand to be proven useful for forecasting events, a
significant history of its time derivatives at a location of interest must be determinable and correlate well with the record of local
seismic and/or volcanic events.
[15]
Notes:
5. The 'TOM' used here is not the tilt-over mode of axial motion with respect to the celestial frame that results in precession and nutation, but
the tip-over mode of the planet's net surface with respect to the rotational axis.
6. Earthquake data, retrieved 24 July 2011:
Pre-1900
NOAA The Significant Earthquake Database, parameter search: magnitude ≥ M8.0, focal depth ≤ 230 km
(preference given to this database for geographic coordinates)
http://www.ngdc.noaa.gov/nndc/struts/form?t=101650&s=1&d=1
USGS Historic World Earthquakes, compiled list
http://earthquake.usgs.gov/earthquakes/world/historical.php
Post-1900
NOAA The Significant Earthquake Database, parameter search: magnitude ≥ M8.0, focal depth ≤ 230 km
(preference given to this database for geographic coordinates)
http://www.ngdc.noaa.gov/nndc/struts/form?t=101650&s=1&d=1
USGS Magnitude 8 and Greater Earthquakes Since 1900, compiled list
http://earthquake.usgs.gov/earthquakes/eqarchives/year/mag8/magnitude8_1900_date.php
7. Volcanic data from the Smithsonian Institution's Global Volcanism Program, retrieved 22 July 2011:
Volcano list (name, subregion, eruption date, eruption size) http://www.volcano.si.edu/world/largeeruptions.cfm?sortorder=asc
Link to coordinates (latitude, longitude, description) http://www.volcano.si.edu/world/list_volcanoes.htm
8. Planetary and Lunar Coordinates 2001–2020, HM Nautical Almanac Office, Willmann-Bell, Inc.; 2001, p. 99.
9. Ibid., p. 42.
10. Ibid., p. 41.
11. Ibid., p. 96.
Figure 4
Global Great Earthquakes and Large Eruptions Related to Drift Direction
[16]
Figure 4 relates the epicenters of great earthquakes and locations of large volcanic eruptions to the direction of polar drift for 1890–
2011.05. The line of drift direction is constructed incrementally from numerous polar drift directions that are calculated as tangents
2
sequentially from the data set of mean poles, which has been filtered to remove both wobble terms, the Chandler and annual.
[17]
For graphic simplicity, the energetic events and drift direction are plotted on only the Eastern Hemisphere, by designating the
eastern meridian of the meridian great circle (MGC) upon which they are located. To permit graphical continuity of the line of drift
direction, the 'Eastern Hemisphere' displayed extends from 40–220° E longitude. This method of projection takes advantage of the
hemispherical symmetry inherent in the global refiguring that is required by polar drift. The resulting angular migration of Earth's
ellipsoidal shape (and equatorial bulge) produces, essentially, a matched pair of antipodal waves traversing the surface—generally
with southward migration on the western hemisphere and northward migration on the eastern. Territory along the MGC that is
aligned with drift direction experiences the fastest migration of ellipsoidal profile. Therefore, along this MGC, equipotential forces
driving figure adjustment will generate the greatest crustal strain/stress fluctuations and may have the greatest potential to trigger
events. So, to accurately display the energy relationship between events and drift direction—the total event response from along
the entire drift-aligned MGC is recorded over time. And for clarity, all events may be projected onto one hemisphere that is selected
to best display drift direction.
[18]
Global earthquakes of category 8.8≤M≤9.5 appear to be strongly correlated to the MGC of drift direction. Five of these seven
quakes occurred 4.8–12.8 years after epicenter coincidence with the drift MGC, averaging 9.3 years afterward. The other two
occurred either 5.1 years after the 1901 peak or 4.2 years after the 1960 peak in drift speed, as shown in Figure 3. The first, a 1906.1
quake in Ecuador, occurred when the approaching drift MGC was 15° in longitudinal distance and the second, a 1964.2 quake in
Prince William Sound, Alaska, lagged a 14° longitudinal proximity with the drift MGC by 22 years. The category 8.4≤M≤8.7 with 25
quakes, appears less correlated to drift direction, with eleven quakes occurring within 5 years of epicenter coincidence to the drift
MGC. However, this category also appears correlated to peaks in drift speed with ten quakes within 5 years of the 1901 peak and
three quakes within 5 years of the 1960 peak. Category 8.0≤M≤8.3 with 115 quakes, has no clear correlations to drift direction or
speed and would require spatial-statistical analysis to evaluate. From the above, it appears that the greater a quake's magnitude,
the more sequentially probable it is that: (1) a coincidence of its epicenter with a drift direction MGC preceded quake release by 5–
12
13 years, or (2) the quake occurred within 5 years of the 1901 or 1960 peaks in drift speed, or (3) its epicenter is close in longitude
to the concurrent drift MGC.
[19]
Global volcanic eruptions of Volcanic Explosivity Index (VEI) category 5>VEI≥6 also appear to be correlated to the MGC of drift
direction. Three of these five eruptions occurred 6.6–12.0 years after site coincidence with the drift MGC, averaging 9.1 years
afterward. The fourth, a 1902.8 eruption in Guatemala, occurred 1.8 years after the 1901 peak in drift speed and when the
approaching drift MGC was 18.5° in longitudinal distance. The fifth, a 1912.4 eruption on the Alaska Peninsula, occurred 11.4 years
after the 1901 peak in drift speed and when the drift MGC was 71° in longitudinal distance. The category 4<VEI≤5 with ten
eruptions, appears mildly associated with drift direction and drift speed, with three eruptions occurring within 5 years of site
coincidence to the drift MGC and three eruptions within 5 years of the 1960 peak in drift speed. Category 3.9≤VEI≤4 with 82
eruptions, has no clear associations to drift direction or speed and would require spatial-statistical analysis to evaluate. Volcanic
eruptions involve mechanisms of fluid transport (e.g. rock melt and water), extreme thermal effects on materials (e.g. chemical,
phase, viscosity, and density changes), bulk material properties (e.g. strength and weight), and other parameters. Thus, eruptions
are controlled by many widely diverse parameters making eruption nucleation likely a more complicated phenomenon than
earthquake nucleation. However, triggering of the largest eruptions does appear to be affected by ellipsoidal demand, as evidenced
by the spatial association of eruptions to drift MGC and possibly drift speed.
[20]
A majority of the greatest quakes and largest eruptions appear to follow a coincidence between the event location and the drift
MGC, averaging (9.3 yr x 5 quakes + 9.1 yr x 3 eruptions)/8 events ≈ 9.2 years afterward. Of course, eight events is not a large
enough data set for a valid statistical analysis, making this correlation suggestive only. In the interpretation of Figure 3, a hypothesis
was advanced which, in part, proposed that varying tidal torque caused by the 18.61-year lunar-nodal cycle may be responsible for
some of the cyclical forcing of drift acceleration. It was also noted that "events of greatest energy usually occur at or near maximum
or minimum turning points [in drift acceleration]." Because turning points occur twice per cycle, the time between points
influenced, hypothetically, by the dominant torque of the lunar-nodal cycle might tend toward 18.61/2 ≈ 9.3 years. Proximity to this
mean should depend on precisely how the two lunar cycles—the nodal and revolution of perigee—factor together throughout time
to produce the tidal torque applied to Earth by the Moon. Thus, it seems supportive of the proposed hypothesis that triggering of
the majority of greatest quakes and largest eruptions averages about 9.2 years after event locations coincided with the drift MGC.
[21]
Notes:
2. On 21 March 2011, Dr. Daniel Gambis supplied a homogeneous solution of mean poles for 1846.00–2011.05, with pole components filtered
to remove the Chandler and annual terms. http://www.obspm.fr/
12. Californians may note that the corresponding location MGC for San Francisco is 57.57° E. The famous 1906 M7.8 earthquake (almost a
great quake) occurred 8.6 years after the drift MGC matched that longitude.
Discussion
Data Quality
[22]
This work utilizes data representing earthquakes worldwide during a period that the instrumentation recording quakes varied
considerably in both sensitivity and availability. At the turn of the century, seismographs were relatively crude devices and not welldistributed, globally. In the 1920s and early 1930s new models were introduced with much improved sensitivity and became
13
successful and more widely deployed. Because the quality of global seismic data depends both on the sensitivity of instruments
and their broad distribution in a global network from which to combine information, data quality greatly improved through the early
1900s. Thus, accuracy of the size and location of quakes worldwide may be considered more reliable after the early 1930s.
Causality
[23]
14
The cause and effect relationship between polar drift (or wander) and earthquakes has been discussed since the late 1800s.
We may, however, assume one thing as certain: The forces which displace continents are the same as those which produce great foldmountain ranges. Continental drift, faults and compressions, earthquakes, volcanicity, transgression cycles and polar wandering are
undoubtedly connected causally on a grand scale. Their common intensification in certain periods of the earth's history shows this to
be true. However, what is cause and what effect, only the future will unveil.
15
– Alfred Wegener
Figure 3 demonstrates a correlation between Earth's cyclical pattern of polar drift acceleration and great earthquakes worldwide.
The greatest quakes occur when drift jounce is near its greatest absolute value—near the turning points on the acceleration trace. If
the cyclical pattern of acceleration can be shown to be astronomically forced, it would seem difficult to reason how global quakes
could be both synchronous with the turning points of rotational acceleration and also antecedent. By what mechanism could
quakes that occur worldwide find the quasi-regular cyclicity? Although the preeminent acceleration peak of 2010.1 has, herein,
been associated with a coincidence of multiple torque-optimum, orbital aspects (Section [12]), thereby lending support for the
proposed hypothesis of astronomical forcing, unequivocal proof of such forcing may depend upon the result of a spectral analysis of
drift acceleration. However, time lags demonstrated in Figure 4, between the MGC of drift direction and the greatest seismic and
volcanic events also seem to indicate that polar drift, by some mechanism(s), drives these events. The greatest events after 1930
suggest an average lag of 9.2 years, as discussed (Section [20]). This delay both supports the cyclicity that imitates a lunar periodicity
known to be dominant in tidal torque and hints to ellipsoidal demand generating commensurate crustal strain/stress (see Section
[26]).
[24]
At this point, it seems most probable to the author that the arrow of dominant causality denotes polar drift driving seismic energy.
However, the complete reality is not that simple, because there is a feedback loop. When drift jerk (the first time-derivative of
acceleration) is calculated and graphed and the great quakes plotted on its quite irregular trace, one finds that some great quakes do
appear to perturb polar drift—not just polar wobble, as is commonly recognized. Moreover, it is well-known that quakes can trigger
quakes, by means of stress coupling.
Clustering
[25]
Another debate, which has waged for some time and may be alluded to in the Wegener quote, concerns episodic clustering of both
earthquakes and volcanic eruptions. Seismic gap theory seems to fit the slow, regular loading expected from the imperceptible
movements of plate tectonics. Yet, researchers have noticed a tendency for events to cluster in both time and space—exclusive of
16
aftershocks or stress-coupled quakes—occasionally overriding the quasi-periodicity that is generally expected. Polar drift driven,
tectonic mechanisms, exhibiting a cyclicity presumably derived from astronomical forcing, would explain a tendency for clustering.
Consistent with the idea of crustal energizing by ellipsoidal demand, event clustering in time should match periods of extreme, polar
drift jounce and clustering in space should match proximities to common MGCs. A recent example of both is the coincidence of the
disastrous 2010.03 Haitian M7.0 quake at 72.57 W long. and the 2010.16 Chilean M8.8 quake at 72.73 W long. Although 6,000 km
apart, the quakes were timed equally astride the 2010.1 preeminent acceleration peak and their longitudes closely matched.
Partial Factors
[26]
In Figures 3 and 4, correlations between the dynamics of polar drift and great quakes and large eruptions hint that mechanisms exist
that relate polar drift to crustal strain/stress. Polar drift velocity includes both drift speed and drift direction. In Figure 3, the
greatest drift speed and time derivatives appear required to trigger the largest energetic events. In Figure 4, the longitudinal
distance from the MGC of drift direction to a site also appears important to event triggering at that site. On the globe, the cosine of
that angular distance, multiplied by the speed of polar drift determines the speed at which the equipotential ellipsoid migrates at
that site. When this product is multiplied by the ellipsoid's local slope in the direction of migration, the result is the speed of
ellipsoidal demand at the site. Thus, Figures 3 and 4 hint at two factors (drift speed derivatives, proximity to drift MGC), which when
taken alone, correlate mostly to the greatest energetic events, but when appropriately factored together with the site slope, yield
the dynamics of ellipsoidal demand. In further work, energy resolution will be shown to improve vastly in the ratio of quake energy
to the dynamics of ellipsoidal demand, as compared to that found in the ratio of quake energy to the dynamics of polar drift.
Summary
[27]
Ellipsoidal demand, driven indirectly by cyclical forcing—hypothetically, astronomical—may be an important control for triggering
great earthquakes and large volcanic eruptions. However, plate dynamics, as driven by convective mechanisms generally accepted
in the theory of plate tectonics—slab pull, ridge push, and basal traction from lateral components of convection currents—must
surely be a major contributor to lithospheric loading. Such loading has been accumulating for many thousands of years, and the
usual levels of strain/stress in many regions may be sub-critical of energetic release by amounts small enough to allow an additional
effect that is fluctuating to control triggering. Scholz recognizes this sub-critical possibility, stating that “. . . a large part of Earth’s
17
lithosphere must be stressed [near] to failure, even in regions not undergoing active tectonic deformation.” Regardless of exactly
how the two strain-generating regimes work together, the relevant fields of Geophysics and Public Safety would be advanced by
investigating the contributions of ellipsoidal demand at many potentially hazardous locations around the world. An algorithm for
location analysis of ellipsoidal demand will be refined and selected studies will be posted on the website as they become available.
[28]
Notes:
13.
14.
15.
16.
17.
Howell, B. F. Jr. (1990). An Introduction to Seismological Research, Cambridge University Press, pp. 59-65.
Lambeck, K., (1980). The Earth's Variable Rotation, Cambridge University Press, p.220.
Wegener, Alfred (1928). The Origin of Continents and Oceans, translated from the 4th revised German edition, Dover, 1966, p. 179
Scholz, C. H. (2002). The Mechanics of Earthquakes and Faulting, 2nd ed., Cambridge University Press, p.356.
Ibid., p. 350.
Acknowledgments
[29]
I wish to thank Dr. Daniel Gambis, Director of EOP PC at the Observatoire de Paris and Board Member of the International Earth
Rotation and Reference Systems Service (IERS) for the pole data; Amelia A. McNamara, Ph.D. candidate in Statistics at UCLA, for
statistical programming and graphing; Dr. Debra J. Blake for non-technical editing; Daniel S. Helman, M.S. Geology, for comments;
Delores M. Zbikowski for funding; and the Minnesota Library Information Network (MnLINK) for providing interlibrary book loans.
Dedication
I dedicate this work to the memory of William A. Zbikowski, my father, who never tired of my little reports of progress.
Institute for Celestial Geodynamics
BY-ND-14Jun2014