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Earth's Wobble
 (AKA Chandler Wobble or Chandler's Wobble)
 

Introduction   |   Table of Graphs & Charts  |  Key Findings


IERS Graphs X & Y Plots of Wobble Motion  |  Spiral Track Charts  |  Wobble Tracker Charts
True Polar Wander | Cosmic Correlations


 

Abstract  |  Major Findings  |  Table of Contents  |  Introduction  |  Background


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Abstract:


 

Table Of Contents

 


Summary of Major Findings


Introduction


Background Information & Knowledge/Data Sources:

 

Spin Energy In The Earth's Mass

John Carnicom provides an interesting computation of the spin energy in the mass of the Earth:  1E+29 Joules
He also analyzes how much energy would be converted if the rotation of the Earth:

lost one second of time per day: 5.943E+24 Joules

one second per year: 1.6E+22 Joules

one second per 45 day period: 1.3E+23 Joules

Carnicom succinctly observes that "This exists as a tremendous amount of energy in a transformational state."  

For details, see http://www.carnicom.com/time3.htm

Energy Occurrences In Phenomenon
keywords energy consumption release creation in natural phenomenon and human things

http://www.phy.syr.edu/courses/modules/ENERGY/ENERGY_POLICY/tables.html

 

 

 

 

 

 

 

 

The Drift, Anomalies, & Correlations
of
 Earth's Shifting Wobble
from
1846-2007


Abstract


Table Of Graphs & Charts

A.  IERS Graphs

The Storyboard begins with five graphs which are posted at the iers.org website (International Earth Rotation Service).  The Storyboard for these graphs provide the basic orientation to the concepts of polar motion and the wobble and an understanding of all the terms.

1.  True Polar Wander (Average Drift of Location)1900-1996
     &Typical Wobble Spiral Motion (
provided by IERS circa 1999)
 

2.  IERS X & Y Plots of Wobble Motion
 

3.  Xplot of Wobble Motion 2005-2007
 

4.  Yplot of Wobble Motion 2005-2007
 

5.  Analytic X Plot of Wobble Motion 1900-2000

B.  X & Y Plots of Wobble Motion

X Plot of Wobble Motion 1846-2006
area plot in landscape orientation

 

X Plot of Wobble Motion 1846-2006 - Line Graph

line plot in landscape orientation

 

X Plot of Wobble Motion 1846-2006 - Giant
giant area plot in landscape orientation

 

X Plot of Wobble Motion 1890-2006 - Giant
giant area plot in landscape orientation

 

X Plot of Wobble Motion 1846-2006 Expanded
expanded line plot in landscape orientation

 

X Plot of Wobble Motion 1846-2006 Giant
giant line plot in landscape orientation

 

Y Plot of Wobble Motion 1846-2006

line plot in landscape orientation

 

Y Plot of Wobble Motion 1846-2006 Giant
giant area plot in landscape orientation

 

X Plot of Wobble Motion 1962-2007 Gigando
giant area plot in landscape orientation

 

Y Plot of Wobble Motion 1846-2006 Giant

giant line plot in landscape orientation

 

X Plot of Wobble Motion 1992-2007
line plot in portrait orientation

 

X Plot of Wobble Motion 1992-2007 Expanded
line plot in landscape orientation

 

X Plot of Wobble Motion 1999-2007

line plot in landscape orientation

 

X Plot of Wobble Motion 1992-2007

line plot in landscape orientation

 

X Plot of Wobble Motion 1962-2007 Expanded
expanded line plot in landscape orientation

 

X & Y Combined Plot of Wobble Motion 1890-2006 Giant
(with annual average sunspot count)

expanded line plot in landscape orientation

 

X & Y Combined Plot of Wobble Motion 1962-2006 Giant

(with monthly average sunspot count)

expanded line plot in landscape orientation

 

Analysis Of The Cartoid Moment Which Ends/Begins Each Seven Year Wobble Cycle
This giant line plot in landscape orientation by MWM probably reveals the moments of absolute stability in the Spin Axis every seven years which may be the best positions for plotting the true, absolute drift in the location of the Poles.

 

See Also Solar Activity Correlation Graphs or El Nino Correlation Graphs Below (D) & (E)

Most of the Solar Activity  and El Nino Correlation Graphs are special purpose adaptations of the X & Y Plots.

C.  Wobble Track Plots

Wobble Track Plot of the Anomaly Of 2005/2006

Actually it wasn't as anomalous as it looked.  It was a "cartoid moment" and there have been several of them during the past 100 years.  What IS anomalous about this event in 2006 was the long time of the "hanging moment", over two months.  Nothing else has came nearly as close.

D.  Solar Activity Correlation Graphs

1890-2006:  Sunspots & The Wobble X Axis;
Correlation of Annual Average Sunspot Activity With Earth's Wobble On The X Axis  - giant line plot in landscape orientation by MWM

 

1890-2006:  Sunspots On Both The X & Y Axis Of Earth's Wobble;
Correlation of Annual Average Sunspot Activity (ISSN) With Earth's Wobble On Both Axis - giant line plot in landscape orientation by MWM

1962-2006:  Sunspots & The Wobble X Axis;

Correlation of Monthly Average Sunspot Activity (ISSN) With Earth's Wobble On The X Axis  - giant line plot in landscape orientation by MWM


1962-2006:  Sunspots & The Wobble Y Axis;
Correlation of Monthly Average Sunspot Activity (ISSN) With Earth's Wobble On The Y Axis  - giant line plot in landscape orientation by MWM
 

1962-2006:  Sunspots On Both The X & Y Axis Of Earth's Wobble;
Correlation of Monthly Average Sunspot Activity (ISSN) With Earth's Wobble On Both Axis - giant line plot in landscape orientation by MWM

E.  El Nino Correlation Graphs

1.  El Nino & The Wobble X Plot 1890-2006
        expanded version    giant version

 

2.  El Nino & The Wobble Y Plot 1890-2006
     (this is a giant-sized horizontal graph.
 

3.  El Nino & The 7 Year  Wobble Cycle 1962-2005

 

F.  Spiral Wobble Charts

1.  Spiral Chart of Wobble Motion 1861-2006
                                        expanded version
 

2.  Spiral Chart of Wobble Motion 1861-1945
                                        expanded version
 

3.  Spiral Chart of Wobble Motion 1898-1963
                                        expanded version
 

4.  Spiral Chart of Wobble Motion 1890-1970
                                        expanded version
 

5.  Spiral Chart of Wobble Motion 1898-2006
                                        expanded version
 

6.  Spiral Chart of Wobble Motion 1910-2006

                                        expanded version

 

G.  True Polar Wander Graphs (drift of average location of the Spin Axis)

 

Just how do you calculate the true pole of the Spin Axis and its rate drift as it slowly changes location through the decades? Here are four methods.

 

The first is the method used by IERS geophysicists.  It is a statistical average.  Essentially, it is a mathematical fantasy of an "approximate" true location of the Spin Axis and its progressive drift.  It is not such a bad one, but it leaves a lot to be desired.  It essentially cuts us off what is really happening in the wobble and makes us oblvious to its connection to other factors.

 

The second method the author devised to look at the progressive march of each wobble spiral and cycle taken in its largest wobble.  When the Wobble is at its MAX phase of spiral size, the track is the most perfectly circular and regular.  A statistical "average" computed on this circle might have the least deviance factors but all the variations in the drift of the wobble from MAX to MAX could be defined. It is an interesting approach and in fact it demonstrates without doubt that "averages" hide a lot of phenomenon.  But this approach suffers greatly from the fact that the wobble cycle is somewhat unstable and can be highly variable. The approach flamed out on the chaos which seems to rule.  The drift of the wobble, and its variable rate, can both be clearly be seen, but between (1) and (2) we have apples and oranges.  What to do?. Also what to do about the changing size of the wobble.

 

The third method the author devised under the simple theorem that the wobble must be the most stable during the MIN phase.  The Earth is wobbling the least at this time, hence must be closest to its point of real mass balance, the real "mass" pole of the Spin Axis, minus all external complications which shift the balance.  Not a bad observation.  In fact a plot of the X MIN locations (averages computed during the smallest spiral tracks) is far superior to the first two.  The track is clearly linear with some episodic hunting episodes, the rate is variable, defining and proving what the XY plots and circular charts clearly reveal (the shift in the overall seven year wobble spirals sometimes vary from cycle to cycle), and, best of all worlds, the average rate of drift computed from this approach agrees closely with the average of the annually averaged locations.  Accordingly, then, these appear to be useful numbers.

 

For the overall drift, even better is the fourth method. It is based on a profoundly simple but apparantly un-noticed or at least un-remarked upon fact.  The track of the Wobble occassionally can be seen to exhibit "cartoid moments", which is a mathematical term to describe when an inward moving spiral line terminates and a new spiral line spontaneously generates to expand outward in what can be seen as the opposite direction.  The cartoid moment in the spiral form is essentially the point when the yin turns into yang. The clearest expression of this is the cartoid which appeared in the Perihelion moment of 2006.  Essentially the wobble ceased and the Spin Axis hung in one location for nearly two months, a remarkable, never before duplicated moment. Clearly a point which marks one cycle from another. Minute examination of the Xplot, season by season, month by month, of the wobble since 1890, identified a few other clear cartoid moments.  In general the majority of MIN phases do not show a distinguishable cartoid, or at least not one this author was willing to work with, but mathematicians may be able to define many more moments than I have.  This chart plots the easily defined cartoids, the first one in 1907, the last in early 2006.  From these matrix definitions, the drift of the wobble can be easily plotted, the distances computed into centimeters, and the average plotted.  Only six points were used, but they draw a line which in a stunning "coincidence" confirms Hofpner's average annual drift of the wobble and pretty much his general angle of the drift ..... The weakness of this approach is that you cannot define variations in the rate of drift from wobble cycle to wobble cycle, only in ad=hoc groups of them, and you lose you ability to see the "hunting episodes" which appear in the other tracks.  The fact that these six cartoid moments define a century's worth of average drift in the "statistical average location of the Spin Axis suggests clearly that these cartoid moments do in fact represent the true location of the Spin Aix when its mass is in true spin balance.

1.  True Polar Wander 1962-1998

     computed from average annual coordinates

 

2.  True Polar Wander 1846-2003

     computed from Wobble MAX phase

 

3.  True Polar Wander 1894-2005
    
computed from Wobble MIN phase

 

4.  True Polar Cartoid Wobble Wander 1894-2006
     computed from "cartoid moments" in the Wobble MIN phase

 

5.  True Polar Cartoid Wobble Wander 1894-2006 With 1961

     computed with an additional "cartoid moment" in the Wobble MIN phase

 

H.  Correlations With Earthquakes

coming soon

I.  Correlations With Volcanism

coming soon

J.  Correlations With Global Warming

1.  Nine Geophysical Trends (Graph 200)

2.  Chemtrails - The Source Of "Earth Dimmng" & Global Cooling?
     this is a PDF file of a brochure with graphic content

K.  Graphs Which Display The "Bad IERS Series"

Introduction

Here (below) is the table of contents (active links) to a large collection of charts and graphs which depict the wobbling motions of the Earth.  The graphs depict many subtle changes in the location of the Spin Axis (the poles) from year to year as well as what appear to be long term trends which are progressively shifting the location of the Earth's wobbling Spin Axis down towards North America.

These charts and graphs are of interest for two primary reasons.  First, they are mounted into a storyboard which explains the Earth's wobble and how scientists are studying it.  The basic concepts and terms are explained and the language is kept highly specific to enable a general audience to follow along. Accordingly, the Storyboard is a suitable introductory resource for students and schools at any level and for any media seeking a quick study of this topic. Professional scientists may also find these charts a convenient reference source.

Secondly, the graphs and charts demonstrate strong correlations between the trends in the wobbling motions of the Earth and other geophysical phenomena such as El Nino, La Nina, volcanism, earthquakes, and Global Warming. The El Nino phenomenon is so closely correlated, for instance, with the Seven Year Wobble Cycle that it must be produced by tectonic activity (volcanism) on the ocean floors. Of even greater import, the trend in Global Warming parallels very closely with the acceleration of world volcanism and earthquake activity and all three of these trends parallel with an era of drift in the location of the North Spin Axis which began in about 1916.

These correlations permit a radical shift in the paradigms of Global Warming and Plate Tectonics and open the way for an integrated Earth Science which is as far beyond today's science as plate tectonics was beyond the geology of the first half of the 20th century.  This Storyboard presents a few of the key concepts and connections which will open up this new Earth Science.

The collection of graphs is organized into this Storyboard only in HTML format.  It is not available in PDF.  Because of the nature of some of the graphs, only this format is suitable.  The graphs and charts are all GIF files and come in four basic physical sizes: (1) portrait for display in a 6x9 book, (2) landscape for a 6x9 book, (3) expanded size for full screen display in a web browser, (4) giant size for horizontal scrolling through a century of years.

The data for the charts was sourced from a variety of Iway (Internet) databases. A few of the charts were composed by others for the International Earth Rotation Service (iers.org).  These of course can be downloaded from that site as well as directly off this Storyboard.  The majority of charts were composed by MW Mandeville and these are available for download and re-use on other sites and in other media under "fair use" principles of attribution and linkage.

All the wobble and polar motion charts were constructed from a rather hefty Excel spreadsheet which contains the IERS database of polar motion since 1846. This spreadsheet, created by MW Mandeville, is entitled "WobblePlots_1846-now.xls". All the charts are "native" within the spreadsheet.  It will be available during 2007 for download through a subscription to the Earth Changes Bulletin or Phoenix Quest website or on a CDROM.  If you wish to use this file and cannot locate a link for it, use email to inquire about the availability of this file.

The original purpose for the graphs and charts was to create a display of certain correlations and concepts for  two books: "The Return of the Phoenix" and "The Nine Trends  Changing The Earth". Fulfilling that purpose required expanding the scope of the graphs to encompass more aspects of the wobble and how it interacts with other geophysical dynamics.  The Storyboard finally became  necessary to help the author organize his thinking and keep track of a large number of  facts.  The result is an integrated story about Earth's wobble and its behaviors during the past 160 years in a form which document the author's findings and observations and conveniently allows for professional peer review and scientific discussion .  Thus the Storyboard makes information available in a systematic way to other students and scientists who are in a position of knowledge and understanding to add to the scope and power of the findings.  Hopefully others will refine or modify Mandeville's observations with better ones.

At the moment the Storyboard in still under construction. More and more refinement will be added during March. Most of the text will appear in other forms, such as in "The Return of the Phoenix" (which is being revised to incorporate the most up-to-date data from a few of these charts) or in "The Nine Trends", which will publish many of the charts, or in an automated Power-point presentation for general audiences which quickly overviews the trends and how they work .

The graphs composed by MW Mandeville are also copyright by him.  These are provided through this Storyboard in convenient format and size to encourage their wide use by other students, writers, scientists, and media. "Fair Use" doctrine with attribution and links to this site is encouraged. However, reproduction of major portions of the storyboard or large numbers of the graphs and charts, or large blocks of the text will be interpreted as unfair use.

The graphs now  living in this Gallery provide an extensive briefing of the history of polar motion and the changes in the Earth's Wobble (the Chandler Wobble) since 1846, when recording of the exact location of the Spin Axis began.

Many of these charts were originally composed in the period 1999-2001 and some of them have lived on the Iway since then.  All of these earlier graphs should be eliminated and replaced by these updated versions.  This replacement is required by changes in the underlying databases. Many corrections, additions, and updates have been made in many of the online databases, most especially in the Earthquake Catalogs and in the IERS database of polar positions for any given date.  Though the differences are mostly quite subtle and only rarely can be detected in the graphs, it is a good idea to eliminate the obsolete versions.  It is extremely embarrassing being observed using obsolete, incorrect information.

One cautionary note on the IERS data which underlies all of the polar motion charts.  The graphs on based on data series which were updated during the period 2001-2005.  These graphs, however, DO NOT reflect changes made in the historical database during 2006/2007 by the IERS network. When Mandeville activated updates for the charts to incorporate the revised data series after 2006, certain ragged anomalies appeared in the charts.  Examination of the anomalies appear to suggest that they are "mathematical artifacts", not real anomalies in polar motion. Accordingly, Mandeville is convinced that the last round of "adjustments" (as of January 15, 2007) have resulted in a database which contains relatively small but occassional strange errors, principally in the first half of Century 20. Accordingly, the numbers used for all polar positions prior to 2005 are based on numbers downloaded prior to 2005. All numbers for dates since 2005 reflect the IERS database as of January 2007.

Charts which reveal the anomalies in the "bad series" may be found in the Table of Graphs, below. 

 

 

Key Observations & Findings About How The Drifting Of The Wobble Causes Changes In The Earth

The standard take on polar motion, polar drift, and Earth's Wobble in the reference books is one dimensional and needs consciousness expansion.

The standard take is essentially based on statistical averages manipulated by mathematicians who are seeking to locate the exact location of the wobble at any moment in time. They are now every good at this.  But the use of annual average positions of the Spin Axis (the center of the Wobble)  creates "a statistical fiction" and abstruse mathematical ways of talking about the wobble which do not do anyone else much good.  Important changes and dynamics in the Wobble and the geophysics of the Earth are hidden by this fiction and the obscure ways in which it is presented..

Among the hidden dynamics are profoundly  important  variations in the 7 Year Wobble Cycles.  For instance, when 100 year averages are abandoned and plots of polar motion are made to study the actual shifts in the Wobble Cycles through the 18 historical wobble cycles which are easy to define since 1890, it is easy to observe substantial variations in the rate of drift, in the direction of drift, as well as "hunting" incidences which reveal mass imbalance in the spinning globe, and other anomalies.  These are primary "facts" about the dynamics of the Earth which are more or less ignored, except in this Storyboard.

Here are a few of the most important observations about the Wobble which can be made from the graphs in this Storyboard.

The average rate of drift in the "average" absolute location of the Spin Axis (which is equivalent to the average center of the Wobble) has been measured to be 12.6 centimeters per year since 1900 along Longitude West 80 by Hofstader.  See Chart xxx. 

This average measurement "hides" the fundamental possibility that this drift in the location of the Wobble may be only about 90 years old.  Examination of the charts of polar motion clearly demonstrates that no drift in the wobble of the Spin Axis (True Polar Wander) was apparent from 1846 until nearly 1916.  No matter how you plot the location numbers, or compute them, drift prior to 1916 bobbed and meandered with a net change of nearly "0".

Since then drift of the Wobble has gone through several phases (or perhaps better described as short-lived eras) during which the average rate of drift varied significantly.  The rate of drift may have accelerated to as high as xxx, though more typically it fell  in the range of xxxx to xxx.  Some of this acceleration paralleled a substantial acceleration of tectonic change. 

Thus it would appear that the average measurement "hides" short eras of acceleration and change in the drift which may have directly produced significant tectonic activity.

During the period of about 1925 to 1945, the  bobbing meander in the average location of the wobble during the prior century began to become far more directional, i.e., change along a definite Longitude. This varied significantly and caused various researchers to report directions which varied from about Long. West 60 to about West 90. The directionality  has increasingly tended to become more and more parallel with Longitude West 90, and this can be seen most esp. since....xxx.   Hofstader's century average of Longitude West 80  is a good one, but this average may be hiding  a strong tendency during the past 50 years to shift down Longitude West 90.

For those with orbital and plasma minds, this is a highly significant fact. This shift is very closely tracking  with the Longitude of the Magnetic North Pole (on Longitude West ~114, Latitude North ~83).  During the past 80 years, for unknown reasons, the Magnetic North Pole has begun accelerating its rate of drift (now 40 km per year) towards the North Spin Axis on the same side of the Earth, indeed within the same quadrant of the Earth.  Given the physics of motion and balance on so vast a scale, it is unlikely that these behaviors are unrelated.  Something connects them, the question of course is, what?

In the era 1925-1945,

In the era 1935-1955

In the era 1955 ----

Since approx. 1990, the rate of drift has slowed...

The Solar Connections

The El Nino Connection

The Divergence & The Tectonic Trends

Global Warming

To make these analyses, it is highly convenient to identify each of the  7 Year Wobble Cycles with a specific number.  This makes for easier communication of comparisons between the wobble cycles (which vary a lot).  It also helps in discussion of correlations with other phenomenon.  The easiest method for numbering the Wobble Cycles is to identify and number the largest spiral wobble tracks.  These re-occur nearly every seven years and are easily distinquished.  Since 1890, 18 Wobble cycles can be counted.  Prior to 1890, the data is too sparse to graph out the Wobble in a way which is smooth enough to consistently distinguish the largest spirals, thus these are not numbered and the series starts in 1890. Sophisticated filtering and re-projection mathematics would be required to define these Wobble Cycles but it hard to determine if this would be worth the trouble..

The Wobble happens to have been in its MAX phase during 1890, which thus becomes Wobble Cycle #1.  Currently we are shifting into Wobble Cycle #19.  We are currently in the first of six spiral tracks which will define Wobble Cycle #19.

 

Old Stuff

The Drift & Anomalies of Earth's Shifting Wobble from 1846 to 2007

 

by Michael Wells Mandeville

 

In this multi-dimensional, multi-perspective view of the historical track of the Spin Axis, some three dozen graphs and charts demonstrate  that Chandler's Wobble is progressively shifting the location of the spin axis and the shape of the earth to produce increased tectonic activity, El Nino, and Global Warming at an accelerating rate since 1916.

 

 

Introduction To The Earth’s Wobble:

 

The physical Earth is in constant motion relative to its orbital Spin Axis.   This gives rise to many consequences which are not yet understood even by scientists.  These consequences range from continental drift, volcanism, and ceaseless earthquakes, to global climate cycles ranging from El Nino to long term shifts which can range from a few hundred to tens of thousands of years in duration.

 

This motion of the Earth is usually described as the motion of the pole or spin axis. Most of this motion is a slight wobbling motion in the Earth’s spin.  This wobble, which is similar to the wobble one can see on a child’s top which is slightly off-center, is named the Chandler Wobble (or Chandler’s Wobble) after the name of the 19th century scientist who first “discovered” it. As the Earth spins each day, the focal point of the spin (the focal point is the pole or Spin Axis) creeps slowly around in a circle   It takes about 14 months for the Spin Axis to creep back to the same longitude on the circle. 

 

The story gets more complex than this because the radius of the creep varies on a seven year cycle. For approximately three and a half years, the circle slowly expands to a radius of about 50 feet, after which it slowly contracts to a radius of about 20 feet. To make the story even more complex, the amount of expansion and contraction also varies from cycle to cycle, usually by a small amount but occasionally by a relatively large percentage.  This makes each seven year wobble cycle virtually unique.  Studies have been made of these variations and a few scientists think that some long term cycles are present in these variations of the motions of the pole.  Unfortunately, however, human world databases are not yet long enough on the time line to be able to be certain of very much about any long range cycles. 

 

There is another layer to the complexity of polar motion and this layer is the most important for understanding both the geological and climate changes of the Earth.   The focal point of the wobble, day by day, year by year, is ceaselessly shifting or drifting to a new location.   A few scientists have used a variety of means to define, measure, and analyze this drift. .  Known as True Polar Wander, the current rate of drift (average for Century 20) has been defined by xxxx  xxxx as xxxx.  down approximately Long. W. 90.  Other calculations of the drift  have been made by other scientists and their results are similar to xxxx..

 

It is convenient for geophysicists to discuss the Earth’s wobble as motion in the poles or spin axis relative to a fixed grid (Longitude and Latitude) on the crust of the Earth. But this way of talking creates an illusion, one which is similar to saying that the Sun rises in the morning.  The Sun of course does no rising, it is the Earth’s rotation which creates the illusion of the Sun rising.  Similarly, the Spin Axis moves scarcely at all, almost all of the motion and drift of the Spin Axis is an illusion created by the movement of the physical Earth.

 

A better way to state the fundamentals of motion is that the Earth’s crust is in constant slow motion as it wobbles around a focal point of spin.  The Earth’s mass shifts its orientation relative to the Spin Axis constantly, on a daily basis even, through many daily, annual, and other cycles.  Although these shifts seem to be small amounts, they have large effects on navigation and location finders, thus the exact location of the Spin Axis on the Earth’s crust is carefully calculated on a daily basis by an international consortium of geophysicists.

 

The focal point of spin, which we call the Spin Axis, moves almost not at all, maintaining a fixed orientation to the North Star, Polaris.  It is said, of course, that the Spin Axis shifts its orientation to Polaris very slowly in a long 25,000 cycle.  But we can ignore this long slow cycle which is called the Precession.   It simply is not connected with the wobble cycles in the Earth’s daily rotation.  Or, other wise stated, the amount of energy transference between the two frames of reference must be exceedingly smaller than our brain lobes care to worry about.

 

Measuring The Motion Of The Crust (so-called Polar Motion)

 

Take a quick scan of the graphs below in order to get an image of in mind of what this discussion is about  Then return here to get the grounding you need to understand the numbers which underlie the graphs.

 

The location and motion of the poles  has been measured since 1846.  Unfortunately the Y coordinate of the North Pole was lost for a few years during the 1850’s.  The X without the Y on a graph is pretty worthless,  so it is not possible to provide a consistent view back to 1845.  It is best to begin with 1861.  This nominally gives us a database of  some 145 years (circa 2007) about the wobble. 

 

 

The earliest series (for 1845-1889) define the postion of the Norht pole at 10 times during the year, roughly at five week intervals.  The second series is for the period 1890 through to 1962, which uses 20 points during the year to define the location of the pole.  The third series is for the period 1962 onwards and it uses daily measurements, 365 per year to define the position of the pole.

 

 

Prior to 1890, only ten measurements were made per year.  This is far too scanty a sampling for circular graphs.  It also makes the XY plots of this period inconsistent with later periods, which are based on 20 measurements per year or daily measurements.  With ten points, a circular plot of the wobble is impossible unless mathematical “fiction” is introduced to extrapolate many additional points to make a circular plot look like a circular plot.  Since a lot can happen in a 30 day segment of the Earth’s Wobble, as will be seen in the graphs and charts which follow, extrapolation is not really a good idea if one is trying to correlate the wobble with other natural phenomenon.  It is like driving blind into a snowstorm.   

 

Though the data prior to 1890 is not very good, since then the measurements have gotten better and better. From 1890 to 1961, a sampling of 20 locations per year is in the data base and these are complete.  They make reasonable tracks of the changing location of the Spin Axis except when there are rapid shifts and anomalies in the motions of the crust.  During these times, and these show up several times, the track on the circular graphs becomes somewhat jerky and perplexing.

 

Since 1962, real daily measurements (not extrapolations) are available.  The circular plots improve greatly in quality and usefulness, jerky lines become profoundly meaningful rather than just unknown noise over the signal. This database provides the means to minutely study how the motions of the crust correlate with other phenomenon of the Earth. 

 

All of this information is available online through the International Earth Rotation Service (www.iers.org) which is headquartered in Belgium.  Keep in mind that the historical databases, unless otherwise stated, have been statistically “smoothed”.  This means that a running average, based on a certain number of preceding measurements and evolved equations, has been used to “filter” out daily fluctuations.  This is generally a good idea and it does not appear to lose important information.  The Spin Axis, or more correctly stated, the Earth, literally does a daily loop de loop, which can stretch out for a few days, within the 14 month spiraling track of the wobble.  The daily loop de loop is noise generated by the Earth’s major storms and tidal surges, and certain other environmental conditions, all of which have minute effects on the exact mass balance of the Earth and its resulting angle of spin.

 

How are the measurements made?  Bu using the timing and angles of the stars as they appear on the horizon or other parts of the sky in various parts of the Earth, scientists have been able to faithfully plot the orientation of the Earth as it wobbles slightly from year to year.  By knowing exactly how the Earth is oriented towards certain stars and the Sun, Earth scientists can determine exactly where the true spin axis poles (North and South) are located. Earth scientists measure the orientation of the Earth and calculated the locations of the poles every day.  The figures which they generate, which are known as the X and Y coordinates of the “geophysical pole”, are used to currect highly sensitive navigational equipment and scientific devices which record astrophysical information.

 

 

 

 

Necessaryly, the cicular plots for the first series is jerky

 

The second series is better, except when the motion of the pole becomes irregular, then the plots seem jerky but some of the jerkiness is exaggerated by the small number of defining oints.  The extreme jerky irreguarily you see in the circular plots for the early years is thus highly exaggerated and the true motion of the pole was considerably smoother and more circular.  This problem is elimiknated of course in the daily series from 1962 onwards.

 

 

Chart 500

Polar Motion 1861-1962

 

Provides a composite of a century of polar motion.

The total track of the pole is shown for the century, each color represents a 6.5 year spiral of the Min and Max in the motion of the crust in Chandler’s Wobble.  except that the first thirty year period is shown in black

The detail is so thick, many of the spirals seem so irregular, and the tracks are so overwritten by others that it is very difficult to understand the dyamics of motion.

 

Nonetheless,

by comparing the 1958-1962 spiral (shown in white)

with the 1861-1890 spiral

shown in black, some movement of the 6.5 year colored spirals can be seen. Through a century of motion, it is fairly clear that the average location of the pole (which is the center or eye of each 6.5 year colored spiral) has shifted towards the left (towards the Great Lakes) and slightly down (towards England).  Exactly how much is impossible to determine from this chart.

 

Chart 501

Polar Motion 1861-1962

 

Provides a simplified, less confusing way of showing a century of polar motion.

The total track of the pole is shown in four colors, each color represents a long era of time rather than 6.5 years, the first period is in white, the next period is in black, the third is in green, and the latest period in in red.  If one looks into the center or eye of the red spiraling circles, one can see what is approximately the average position of the pole for xxxeidt years.  Though obscured, one can fairly easily visualize the approximate center of the white spiral circles.  From these two points one can estimate readily that the total drift of the average location of the pole seems to be in fairly straight line down towards the left hand side of the chart.  The total distance is about .15 arcseconds, which is just slightly more than 15 feet or about 4.5 meters.  Or, the yearly average is about 1.8 inches (very close to 3.06 centimeters dead on).

 

Chart 502

Can we find out more about the dynamics of polar motion by examining the individual spirals in greater detail?  As a matter of fact we can, we can make the most important discovery about Chandler’s Wobble since it was noticed that the Wobble is influenced by all of the mass variables of the earth, including the motions of the atmosphere (fluctuating with the weather) and the behavior of the ocean tides.  We make this discovery by plotting each spiral in separately and slowly building up the composite to look for any changes in motion.

 

In Chart 502 we can see in Black the spiral plot of the location of the pole during 1903-1909.   Drawn from 20 points per year, it appears far more circular and regular than the jerky appearing plots for the periods of 1861-1890.  We can also see that the average location of the pole does not appear to have moved by much, if at all.  It would  take a mathematician with fancy formulaes to accurately define the infinitesmal drift and as we can see it is probably not worth it, partly because the data is too sparse.

 

Hold on to this factoid. We have 50 years of measured polar motion and, though great variation in the 6.5 years cycles of Chandler’s Wobble are quite obvious, there IS NO DISCERNIBLE DRIFT IN THE LOCAITON OF THE AVERAGE POSITION OF THE POLE.

Chart 503

Look what happens when we add in the 1909-1919 spiral.  We can immediately sense some apparent drift in the eye of the wobble.

 

Chart 504

 

We see even more apparent drift when we add in the 1919-1923 spiral.

 

Chart 505  1903-1923

 

Dead reckon centers on the computer screen or on a print-out

for the black spiral 1903-1909 and for the blue spiral (1916-1923), the distance between them is about .07 arcsceonds.  If we assume the rate of drift is constant from 1909 through to 1923, the rate of motion is approximatley 6.1 inches per year ( almost 15.5 centimeters/year).  Serious mathematics can no doubt refine this crude number into something more precise and doubtless the number will be in the same range of increase.

 

After 50 years of no discernible drift, now suddenly we have 6 inches per year for 14 years.

 

a blue spiral form is diminished in size

 

Chart 506 1903-1931

Does the motion continue?  When we add the wobble spiral for 1923-1931 into the composite to create Chart 506 we get another surprise or two. The wobble is unseasonably longer than the average 6.5-7 year X Wave spiral cycle of Chandler’s Wobble.  And the wobble is even more crunched down in size and seems to trace a bowl of spagetti.   And there is no apparent drift of the “eye” of the wobble.  Annual drift seems to have disappeared again.

Chart 507 1931-1939

The bowl of spagetti begins to turn back into a spiral, even though the size remains very small

(of the white spiral) The “eye” might be even drifting but it is not very certain.

Chart 508 1939-1945

 

The red spiral motion for this period is still trancated but the “eye” of this spiral in the wobble definitely appears to have move in the same direction as the previous drift of the eye.

By now the eye seems to have moved a total of about .06 arcseonds since 1923 (the dark blue spiral is nearly dead on the geographic north pole position of x=0,y=0

 

but now the orange spiral eye of is about y=.06, y=.02

 

Chart 509 1945-1958

Suddenly in about 1945 the wobble spiral expands outward and and become becomes as large as it had previsouly been prior ot 1923.  As shown by the yellow and light blue colors, this enlarged pattern holds through 1958.  Since all parts of the spiral are now enlarged, even the “eye’, it is now more difficult to estimate the center of the “eye” by using one’s eyeball.  There may be a continuation of a slight amount of drift.

 

Chart 510 1958—1962 

 

new node analysis starts here, reesitmate the time lengths for previous

 

Between the eye of 1920 and the eye of 1935, there is ony about .01 arcsecond of movement, if that much.

 

or,  0.81 inches per year, or 1.24 centimeter/year

 

Suddenly, as the yellow plot shows, the motion of the pole has become quite jerky and the eye of this spiral seems to have shifted quite suddenly by a relatively large amount.   Using simple screen measurement, the eye of the yellow plot has shifted approximately .14 arcseconds since the eye of the 1931-1939 spiral.  Since the eyes were literally in 1935 and 1960 respectively, we have a 25 year shift of .14 arcseconds at a rate of 6.8 inches per year (17.29 centimeters).

 

 

 

Interestingly enough, Cayce predicted in the mid 1930’s that we would notice a gradual increase in the rate of tectonic change after 1958.  Since most of the apparent motion between 1935 and 1960 seems to have occurred after 1955, we find once again a strong correlation in the Earth Sciences which validates Cayce’s earth changes predictions. 

 

It gets even more interesting as we pursue the tracks of the Phoenix in the daily series from 1962 to 2001.

 

 

The Drift & Anomalies of Earth's Shifting Wobble from 1846 to 2007

 

by Michael Wells Mandeville

 

In this multi-dimensional, multi-perspective view of the historical track of the Spin Axis, some three dozen graphs and charts demonstrate  that Chandler's Wobble is progressively shifting the location of the spin axis and the shape of the earth to produce increased tectonic activity, El Nino, and Global Warming at an accelerating rate since 1916.

 

 

Introduction To The Earth’s Wobble:

 

The physical Earth is in constant motion relative to its orbital Spin Axis.   This gives rise to many consequences which are not yet understood even by scientists.  These consequences range from continental drift, volcanism, and ceaseless earthquakes, to global climate cycles ranging from El Nino to long term shifts which can range from a few hundred to tens of thousands of years in duration.

 

This motion of the Earth is usually described as the motion of the pole or spin axis. Most of this motion is a slight wobbling motion in the Earth’s spin.  This wobble, which is similar to the wobble one can see on a child’s top which is slightly off-center, is named the Chandler Wobble (or Chandler’s Wobble) after the name of the 19th century scientist who first “discovered” it. As the Earth spins each day, the focal point of the spin (the focal point is the pole or Spin Axis) creeps slowly around in a circle   It takes about 14 months for the Spin Axis to creep back to the same longitude on the circle. 

 

The story gets more complex than this because the radius of the creep varies on a seven year cycle. For approximately three and a half years, the circle slowly expands to a radius of about 50 feet, after which it slowly contracts to a radius of about 20 feet. To make the story even more complex, the amount of expansion and contraction also varies from cycle to cycle, usually by a small amount but occasionally by a relatively large percentage.  This makes each seven year wobble cycle virtually unique.  Studies have been made of these variations and a few scientists think that some long term cycles are present in these variations of the motions of the pole.  Unfortunately, however, human world databases are not yet long enough on the time line to be able to be certain of very much about any long range cycles. 

 

There is another layer to the complexity of polar motion and this layer is the most important for understanding both the geological and climate changes of the Earth.   The focal point of the wobble, day by day, year by year, is ceaselessly shifting or drifting to a new location.   A few scientists have used a variety of means to define, measure, and analyze this drift. .  Known as True Polar Wander, the current rate of drift (average for Century 20) has been defined by xxxx  xxxx as xxxx.  down approximately Long. W. 80.  (towards the Great Lakes).  Other calculations of the drift  have been made by other scientists and their results are similar to xxxx..

 

It is convenient for geophysicists to discuss the Earth’s wobble as motion in the poles or spin axis relative to a fixed grid (Longitude and Latitude) on the crust of the Earth. But this way of talking creates an illusion, one which is similar to saying that the Sun rises in the morning.  The Sun of course does no rising, it is the Earth’s rotation which creates the illusion of the Sun rising.  Similarly, the Spin Axis moves scarcely at all, almost all of the motion and drift of the Spin Axis is an illusion created by the movement of the physical Earth.

 

A better way to state the fundamentals of motion is that the Earth’s crust is in constant slow motion as it wobbles around a focal point of spin.  The Earth’s mass shifts its orientation relative to the Spin Axis constantly, on a daily basis even, through many daily, annual, and other cycles.  Although these shifts seem to be small amounts, they have large effects on navigation and location finders, thus the exact location of the Spin Axis on the Earth’s crust is carefully calculated on a daily basis by an international consortium of geophysicists.

 

Some people believe that the entire Earth wobbles around and over the spin axis.  But geophysical evidence which has accumulated during the past 20 years directly suggests that it is just the crust of the Earth which wobbles by floating over the hot liquid mantle of the Earth's deep interior. This is an immense important and powerful finding. If this is true, we can explain the basic motions of Earth’s tectonic plates as a product of Earth’s wobble.  Based on this we can pretty much explain rifting and subduction phenomenon, as well as most of the morphology of the surface of the Earth, as a product of orbital mechanics.

 

The focal point of spin, which we call the Spin Axis, moves almost not at all, maintaining a fixed orientation to the North Star, Polaris.  It is said, of course, that the Spin Axis shifts its orientation to Polaris very slowly in a long 25,000 cycle.  But we can ignore this long slow cycle which is called the Precession.   It simply is not connected with the wobble cycles in the Earth’s daily rotation.  Or, other wise stated, the amount of energy transference between the two frames of reference must be exceedingly smaller than our brain lobes care to worry about.

 

Measuring The Motion Of The Crust (so-called Polar Motion)

 

Take a quick scan of the graphs below in order to get an image in mind of what this discussion is about  Then return here to get the overview grounding you need to understand the numbers which underlie the graphs and why the graphs were constructed the way they are.

 

The location and motion of the poles  has been measured since 1846.  Unfortunately the Y coordinate of the North Pole was lost for a few years during the 1850’s.  The X without the Y on a circular graph is pretty worthless,  so it is not possible to provide a consistent view of the wobble back to 1845.  It is best to begin with 1861.  This nominally gives us a database of  some 145 years (to 2007) about the wobble. 

 

A further difficulty arises in trying to see the wobble.  Prior to 1890 (for 1845-1889), only ten measurements were made per year, roughly at five week intervals.  This is far too scanty a sampling for circular graphs and it does not make for smooth X or Y graphs either..  It also makes the X and Y plots of this period inconsistent with later periods, which are based on 20 measurements per year or daily measurements.  With only ten points, a circular plot of the wobble is impossible unless mathematical “fiction” is introduced to extrapolate many additional points to make a circular plot look like a circular plot.  Since a lot can happen in a 30 day segment of the Earth’s Wobble, as will be seen in the graphs and charts which follow, extrapolation is not really a good idea if one is trying to correlate the wobble with other natural phenomenon.  It is like driving blind into a snowstorm.   

 

Though the data prior to 1890 is not very good, since then the measurements have gotten better and better. From 1890 to 1961, a sampling of 20 locations per year is in the data base and these are complete.  They make reasonable tracks of the changing location of the Spin Axis except when there are rapid shifts and anomalies in the motions of the crust.  During these times, and these show up several times, the track on the circular graphs becomes somewhat jerky and perplexing.

 

Since 1962, real daily measurements (not extrapolations) are available.  The circular plots improve greatly in quality and usefulness, jerky lines become profoundly meaningful rather than just unknown noise over the signal. This database provides the means to minutely study how the motions of the crust correlate with other phenomenon of the Earth. 

 

All of this information is available online through the International Earth Rotation Service (www.iers.org) which is headquartered in Belgium.  Keep in mind that the historical databases, unless otherwise stated, have been statistically “smoothed”.  This means that a running average, based on a certain number of preceding measurements and evolved equations, has been used to “filter” out daily fluctuations.  This is generally a good idea and it does not appear to lose important information.  The Spin Axis, or more correctly stated, the Earth, literally does a daily loop de loop, which can stretch out for a few days, within the 14 month spiraling track of the wobble.  The daily loop de loop is noise generated by the Earth’s major storms and tidal surges, and certain other environmental conditions, all of which have minute effects on the exact mass balance of the Earth and its resulting angle of spin.

 

How are the measurements made?  By using the timing and angles of the stars as they appear on the horizon or other parts of the sky in various parts of the Earth, scientists have been able to faithfully plot the orientation of the Earth as it wobbles slightly from year to year.  By knowing exactly how the Earth is oriented towards certain stars and the Sun, Earth scientists can determine exactly where the true spin axis poles (North and South) are located. Earth scientists measure the orientation of the Earth and calculated the locations of the poles every day.  The figures which they generate, which are known as the X and Y coordinates of the “geophysical pole”, are used to currect highly sensitive navigational equipment and scientific devices which record astrophysical information.  Full technical documentation on how this is done can be found at iers.org.

 

 

What Can Be Seen In The Story Board

 

  1. By analyzing and comparing the various plots which are presented in the Story Board below, we can establish that: Prior to 1916, little or no detectable dirft in the average location of the Spin Axis.  This is a profoundly important observation.

     
  2. The period between 1861 to 1916  may define normal polar drift, or at least the normal polar drift of the past few hundred years, namely that it is/was virtually non-existent.  The corollary to this is that normal polar drift is probably immeasurably slow from decade to decade, century to century, and millennia to millennia, much slower than geophysicists are currently projecting.

     
  3. The length of the 14 month basic Wobble Cycle (The Chandler Term), the size of the Wobble (the Chandler Amplitude), the length and size of the seven year Wobble Cycle,  and the angle of drift  of the Wobble focal point (Spin Axis) varies constantly but not radically.  Through all the variations, the center of the Wobble has slowly drifted towards the Great Lakes since about 1923. About Longitude West 80 at an average spead.

     
  4. The tracks of the past 100 years shows anything but a constant rate of polar drift, ranging from almost no change at all to a rate of a meter or more per year, and then back to practically zero. Similarly, the angle of the drift has shifted between 90 to 45.  Currently the angle of drift is very close to Long. West 90.  From this it is very obvious that using mathematics to define long term averages creates “a fiction” which  is not useful for those attempting to correlate the changes in the wobble with other natural events.    It is more important to see the shifts from decade to decade.

     
  5. Thus it is certain from the existing facts that Humans have insufficient data on board to do much projecting about the drift of the average location of the pole prior to 1861.

     
  6. Calculations of the average drift of the pole during the past 100 years are probably reasonable but they should not be projected either backward or forward in time.  Given the observable fluctuations in the rate and direction of the shifting location of the Spin Axis during the past century, studies of the path and rates of the “paleo” pole during previous geological eras and epochs probably are not worthwhile.  Too much real world variation destroys the ability to make simplistic conclusions.  Many of the studies offer interesting speculations but provide no real knowledge nor basis of generalization.
     
  7. The modern epoch of geological activity began in 1916 with the beginning of a progressive drift of the spiral forms of Chandler's wobble.  The average rate of drift  has been about 6 inches per year since then.

     
  8. Between 1916 to 1930 polar motion became increasingly squirrely, resulting   in a tightening of the spiral into smaller circles which then degenerated into chaotic motion during the mid 1930's as the wobble went through a phase shift (as reported by Yumi during the 1960's).

     
  9. From 1939 polar motion  and wobble drift became progressively normal while moving at about 6 inches per year.

     
  10. In the period 1958 to 1964, the rate of drift of the wobble increased threefold   for several years while the the numbers of large earthquakes (2.5 mag plus) and the annual worldwide activity days of volcanoes began to increase in a long trend line.  This increase in tectonic activity culminated during the period 1995-1998 at rates which are about four times larger than the first half of the 20th century and this activity remains currently at close to this all time historical high.

     
  11. After 1964, the rate of drift has returned to 6 inches per year at times, increased again, then decreased again in irregular periods even while the wobble has slowly expanded in size.  These changes probably have sustained and expanded the increasing rates of tectonic activity in the Earth's crust.  As the exact location of the spin axis moves, the entire Earth must shape-shift slightly in reaction, which causes earthquakes and the pressure force which pushes lava up and out the world's volcanoes.

     
  12. The spiral wobble reached maximum size in 1996 and looked normal until 1998 when it hit a bump which caused a dent (which can be seen in the bottom) of the wobble for unknown reasons.  Since then the wobble has tightened up into an unusually small circular size and seems to be undergoing another 1930's style radical downsizing and phase-shifting.

     
  13. Since December 1998, the drift of the wobble also appears to have accelerated to at least twice the rate of the historical average between 1916 and 1996 but that is a tough call to make on an exact basis.  The method I have used, bisecting multiple times the entire 6.5 year spirals to find the average diameters and centers,   doesn't work on the current spiral which is not yet complete enough to give a result which is truly comparable with previous wobble cycles.  This difficulty is further compounded because the current spiral circle for 2001 is much smaller than it should be.  The 6.5 cycle should be close to Maxing out late next year or in 2003 and at its current rate of expansion, the maximum size of the 2003 wobble track simply isn't going to come close to its 1996 size.

     
  14. Mathematicians and astrophysicists might be able to take this line of analysis further and derive better numbers.  But even with better numbers, they might find things entirely unpredictable since, by comparison with other cycles, it looks like the next ten years of polar motion could look virtually like chaotic movement in a spaghetti bowl pattern  similar to the era of  the 20's and 30's when the modern era of progressive drift began after a shift in the phase of the spiral wave pattern in the wobble.

     
  15. Is the wobble showing further instability prior to setting off another era of increasing tectonic activity?  Or is the wobble shifting back to its pattern prior to the 1930's?

     
  16. For additional information see:  Vortex Tectonics

 

Technical Details About The Numbers, Units, and Charts

 

Algebraic Signs:

The IERS database and charts use a logic for algebraic signs which is the reverse of what is commonly used in mathematics and on spreadsheets.  The Minus Numbers are on the top and to the right, the opposite of most other charts in common use. The charts displayed here use the IERS logic to keep the story consistent with other geophysicists.

Units of Arcseconds:

The charts are shown in arcseconds of degrees.  They are labeled Longitude degrees in the charts, but technically it is probably more correct to use the term Latitude.  The distinction is meaningless at the poles, but technically there is a mathematical difference which actually adds up at the equatorial zone to several miles.  The term Latitude was not used in the charts to avoid introducing an additional term of reference.  Many of the charts use a grid structure equal to 0.1 per line.  A 0.1 arcsecond is equal to 3.087 meters or 10.127 feet.

The tiny grid lines mark either .01 or .02 Arcsecond;
.01 arcseconds = 12.1524 feet or 30.87 centimeters

 

Necessaryly, the cicular plots for the first series is jerky

 

The second series is better, except when the motion of the pole becomes irregular, then the plots seem jerky but some of the jerkiness is exaggerated by the small number of defining oints.  The extreme jerky irreguarily you see in the circular plots for the early years is thus highly exaggerated and the true motion of the pole was considerably smoother and more circular.  This problem is elimiknated of course in the daily series from 1962 onwards.

 

 

X Plot of Earth Wobble 1846-2001

X Plot Earth Wobble 1861-2001

 

 

 

Summary Overview 1861 to 2001 - Chart 500

The chart shows the plot of the location of the North Pole (spin axis of the Earth, not the magnetic pole) as it wobbles in the 14 month circles and 6.5 year spirals knows as Chandler's Wobble.   Each spiral cycle since 1890 is displayed in a unique color and of course most of the spirals tend to blot out each other. Consequently, not much can be seen about the early cycles.  Even so, we can glean two facts from this chart: (1)  Some of the earlier spirals seem somewhat  jerky and non-symmetrical compared to the more regular spirals of the recent past. (2) There is a definite movement of Chandler's Wobble (and thus the average position of the spin axis) since 1861 to the left of the chart along the Y axis in the direction of the Great Lakes.  For more information, we will have to look into the individual spirals.  Take note that this chart shows the center of the red spiral (the latest Wobble cycle) on about the X = .3 as line.

For this and all other Excel charts, the largest spiral circle in the 6.5 cycle is the X Max and the smallest circle in the 6.5 cycle is the X Min. Since the X Min points in the spiral are always the most unstable and show the greatest variations, the X Max was chosen to mark the beginning of each cycle.   The motion of the Earth during the X Max is always the most "regular" and symmetrical.  Accordingly, the X Max movement every 6.5 years should be most like the previous spiral motions during the X Max 6.5 years prior.  If changes are occuring, they will be most clearly seen by comparing the outer edges (X Max) of the spirals.   For the most part, each X Max is shown in a different color.

As will be seen, it turns out that most of the drift of Chandler's Wobble (the permanent "shifting of the poles")   tends to occur during the X Max period.  The pole appears to shift by making the X Max motion longer and deeper, then it never returns enough to move around the same "eye" of the preceeding years.  Literally, a new "eye" seems to be created in the space of a few months of the Earth's most extreme wobble motion.

Naturally, like all things celestial, there is some variation in the 6.5 year cycle.  It can last up to three to four months longer.

The choice of the X value (the measurement of the location of the pole relative to Greenwich Meridian) is arbitrary, the Y value (location of the pole relative to Long. West 90)  could have been used.   But since all of the vortex tectonic correlations have been made with the motion of the location of the spin axis up and down the X or Greenwich Meridian, these circular plots were also defined by using the X Max point to mark the beginning and end of each spiral cycle.

Overview 1861 to 1964 - Chart 501

Chart 501: Plot of Chandler’s Wobble from 1861-1964

Even if we wack off the past forty years of polar motion plots, very little additional information can be discerned.   We still see a definite migration of the location of the pole betweeen 1861 and 1964 in the same basic pattern. Note that the center of the most recent spiral in this chart (1958-1964) appears to be on about the X = 0.15 line.

That would seem to imply, very roughly, a drift in the location of something like 0.15 as in about 61 years (from 1958 to 2001), which is, very approximately, 0.002459 as/yr or about 3 inches/year or 7.6 cm/yr.

Polar Tracks 1861 to 1916 - Chart 502

 Chart 502: Plot of Chandler’s Wobble from 1861-1916

More information about the path of the pole can be seen by just examining the first 56 years of measurements, which finally became consistent enough to use in a database in 1861. (Sporadic measurements began in 1845).

We can see what appears to be a lot of chaotic jerkiness in the 1861-1890 plot. These plots are based on using 10 polar positions per year, which simply is not enough to produce a reasonably smooth curve.   The actual motion of the pole was not nearly as spastic as shown.  The only thing which seems reasonably clear is that there is not much motion in any particular direction.  The plot is enough of a "ball" to that no net drift can be readily seen. 

We can discern the facts more clearly after 1890. These spiral plots are based on records of 20 polar positions per year and become real tracks rather than spastic jerks. By comparing the1861-1890 period with the plots for 1890-1903 and 1903-1909 (in black and green) we can see that there is no or very little apparent movement in the pole. The spirals all overlap each other fairly tightly

A slight sense of movement down to the left bottom corner seems possible.  But if calipers and rulers are used to bisect these spirals to define the average circle and center, net motion during this period seems negligible.

In the 1909-1916 plot we notice an expansion of the spiral, it is larger that the 1903-1916 spiral with perhaps a slight drift towards the left bottom corner of the graph

The outer circle of 1903 parallels well the outer circle of 1909, so not much motion is apparent there. The eyes of the two spirals seem to be slightly apart. This may be motion of the average location of the pole but it may be an illusion caused by the irregularites.  The only major change appears to be that the 1909 spiral expanded in size.

Accordingly, It would appear that there is over the course of 56 years almost no change in the average location of the pole.

This finding is a fundamental fact which directly supports the vortex tectonics theorem. Imperceptible drift may be the normal condtion of the spin axis through most of the ages.  If so, we have fully accounted for the anomalous fourfold increase in tectonic plate motion, earthquakes, and volcanic activity during the last half of the 20th century.  It is directly related to an increasing tempo of drift in the location of Chandler's Wobble which is apparant in the last half of the 20th century.

This is virtually the final proof that the vortex rules. But wait, the evidence builds.

Polar Tracks 1861 to 1923 - Chart 503

Chart 503: Plot of Chandler’s Wobble from 1861-1923

With the addition of the 1916-1923 spiral we see a decided change.  Suddenly the spiral form is smaller than it was for at least the two prior ones.  It significantly smaller and became more irregular.  If there is a shift in locus, appears to be towards the bottom of the chart and slightly towards the right

The locus or center of the spiral seems to have defnitely shifted towards the bottom left corner of the graph.  This can be measured on the graph by using four bisects of each spiral from their outer edges to establish their centers.  By this method, it is possible that there was .05 as drift between 1903 and 1916.  However, these spirals are a litlte too irregular to put much stock on this number.

One can also simply analyze the relative positions of their outer edges.  By this means there is no apparent drift between the 1903 spiral and the 1909 spiral.  But it is possible that there was a shift of .02 as in 13 years from the 1903 spiral to the 1916 spiral.

Polar Tracks 1903 to 1931 - Chart 505

Chart 505: Plot of Chandler’s Wobble from 1903-1931

What a change we see when we add the 1923-1931 spiral!  Now the movement begins during the 1923-1931 X Wave along with great instability in the track of the spiral. The spiral waveform has degenerated into a bowl of spagetti. If there is a shift in locus, the shift is towards the left bottom corner but the 1923 spiral seems too difficult to average out to determine a number for the drift.

Notice that the locus or center appears to be almost exactly the same as the Geographic North Pole, x=0 and y=0.

For argument, suppose then that the center of the wobble has shifted some 0.075 arc seconds in the space of some 15 years, from 1916 to 1931

Polar Tracks 1903 to 1939 - Chart 506

 Chart 506: Plot of Chandler’s Wobble from 1903-1939

The 1931-1939 spiral is still very small  and is still somewhat chaotic but less so than the 1923 spiral.   There is more of a sense of drift in the locus towards the left bottom corner but it is too difficult to compute.  We wil have to wait for more regular spirals.

The X Min, during about 1935/36, shows the strange crazy 8 which created the phase shift in Chandler's Wobble reported by Yumi et al to the IERS conventions and journals. As a result the spiral "appears" longer than the 6.5 year average.  This crazy eight and phase shift confirmed Edgar Cayce's clairvoyant prediction about the change in the equilibrium of the earth causing a change in the Earth's orientation (a micro pole shift) during 1936.   As we can see in the tracks of the pole, it was coming on since about 1916 at the earliest.

Accordingly, 1916 may mark the best date for the end of polar stability which reigned during previous centuries and the time of the  onset of the accelerating shift in the poles which is still gathering speed a century later.

Polar Tracks 1903 to 1945 - Chart 507

Chart 507: Plot of Chandler’s Wobble from 1903-1945

The 1939 spiral is still erratic but far less so than the 1923-1931 period. The spiral seems to expand slightly and stabilize.  Ddespite stabilization, the locus is still very difficult to determine.   But it does allows us to see that the sense of slow drift which we have gathered since the 1916 spiral is becoming more definite.

Notice that the entire spiral remains tight, very small like the 1916-1921 spiral. It seems obvious that the spiral has shifted at an accelerated rate.  Since 1931 (at about 0,0 coordinates) the locus has probably shifted some .075 as.

Polar Tracks 1903 to 1958 - Chart 508

Chart 508 Plot of Chandler’s Wobble from 1903-1958

Another radical shift!   The 1945-1952 spiral suddenly expands radically to make Chandler's Wobble larger than is has been since recording began.  The drift of the locus of the spiral is now qute apparent. There is an apparent drift of some.04 as from 1945 to 1958, a period of 13 years.

Polar Tracks 1903 to 1964 - Chart 509

Chart 509 plot of Chandler’s Wobble from 1903-1964

The 1958-1964 spiral suddenly becomes chaotic and jerky.  My my, where have we heard this 1958 number before? The locus of the inner spiral has shifted suddenly to the left by a large amount. Apparent drift is .085 as from 1958 to 1964.

Polar Tracks 1903 to 1977 - Chart 510

Chart 510: Plot of Chandler’s Wobble from 1909-1977

Chandler's Wobble stabilized after 1964 but is still some what chaotic through 1977.  Clearly, the wobble began a steady progessive drift along Long West 90 slightly to the bottom corner.   Most of the shift came in the 1976/1977 period.

Using the outer edges of the X Max to measure the progression, there is .025 as drift FROM 1964 to 1971. Between 71 and 77 there was a drift of .045 as.

Since the spirals have become so much more regular, it is now easy to establish with some confidence that the over-all drift by 1977 was .295 as since 1916.

Polar Tracks 1909 to 1990 - Chart 511

Chart 511: Plot of Chandler’s Wobble from 1909-1990

Now suddenly again there is an expansion of the wobble in the 1977-1983 spiral.  There is a decided drift towards the bottom left corner of about .02 as from 1977 to 1983. The net motion between 1983 to 1990 is hard to determine.

Polar Tracks 1909 to 2001 - Chart 512

Chart 512: Plot of Chandler’s Wobble from 1909-2001

The 1996 spirl is drawn from Dec 13, 1996, several months early to show the shift of the outer edge of the current spiral more clearly against the previous spirals. Between 1990 and 1996, the aparrant drift is about .025 as. In 1996  a decided shift appears with the X Max (outer edge of the red in 1996 of about .025 as since the X Max in 1990. This is a fairly rapid new escalation in the rate of drift.

There appears for all the world what appears to be a dent in the the bottom of the inner red spiral, which is literally December of 1998. Since this dent in 1998, the spiral has become abnormal and is undergoing another major change. It appears to shrinking again, as it has done at least twice just before becoming chaotic or highly irregular, and the radical offset of the center of the spiral may suggest an acceleration in the rate of drift to some .02 as PER YEAR, some ten times the general average.

 

3.  Table Of Polar Track Data

click here

4.  The "Eras" in Chandler's Wobble Plotted By The Wobble Tracker

Wobtrac 1:  1962-1972

 Wobtrac 2:  1973-1984

 Wobtrac 3:  1984

Wobtrac 4:  1985-1995

Wobtrac 5:  1996-2001

 

4. The Amazing Correlations Of The Position and Motions Of The Pole With Volcanic and Earthquake Activity.

Cayce claimed in the early 1930's  that "cosmic forces" in the solar sysem created earthquake and volcanic activity.  Such statements seemed far-fetched to the earth scientists of his day.  But after surveying the geophysics of what might be involved, Mandeville concluded that the likely suspects were the Sun and the Moon since these were known to produce Chandler's Wobble.  Chandler's Wobble is a constant bobbing of the Earth as it spirals around in a small circle which takes 14 months to complete.  The circling motion varies between about 3 meters and 15 meters in a spiral which takes 6.5 years on the average.

To measure the effect of the Sun and the Moon on earthquake activity, Mandeville first plotted the position of the pole along the X Axis (Greenwich Meridian) as the Earth wobbled through its 6.5 year cycle. This created a 6.5 year waveform (called the X Wave in the Primary Axis Cycle).  This waveform was then integrated with charts of annual earthquake and volcanic activity in various regions of the world. Nearly everywhere, Mandeville found obvious correlations between the position and motion of the pole with increases and decreases in earthquake and volcanic activity.   These correlations are sufficiently consistent to conclude that it is the stresses in the Earth's crust which are directly induced by Chandler’s wobble which creates earthquakes and volcanic activity. 

Mandeville also found that the cosmic factors of the EMS (Earth-Moon-Sun) system are creating new changes in the location and motion of the spin axis which are sufficient to force a major new trend in the shape shifting of the Earth’s crust, most especially in the tropical zones.  This shape shifting is pulsed in the frequency of the 6.5 year X Wave (spiral waveform of Chandler's Wobble) and it has directly induced a huge increase (possibly a fourfold increase)  in the release of the Earth’s interior heat into the bottoms of the oceans during the past 50 years, most especially in the Pacific.  In otherwords, the 6.5 year spiral X Wave is causing El Nino while the progressively accelerating drift or shift in the location of the pole is inducing the release of a steadily increasing amount of heat with each El Nino.  This progressive shift is increasing the severity of each cycle while accumulating as the trend which has come to be known as global warming.

Unlike all other theories of Earth dynamics and global change, these truths are non-theoretical, are completely free of fancy mathematical sophistry, are strictly observation driven, and can always be found to be consistant with all of the data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chart 500

Polar Motion 1861-1962

 

Provides a composite of a century of polar motion.

The total track of the pole is shown for the century, each color represents a 6.5 year spiral of the Min and Max in the motion of the crust in Chandler’s Wobble.  except that the first thirty year period is shown in black

The detail is so thick, many of the spirals seem so irregular, and the tracks are so overwritten by others that it is very difficult to understand the dyamics of motion.

 

Nonetheless,

by comparing the 1958-1962 spiral (shown in white)

with the 1861-1890 spiral

shown in black, some movement of the 6.5 year colored spirals can be seen. Through a century of motion, it is fairly clear that the average location of the pole (which is the center or eye of each 6.5 year colored spiral) has shifted towards the left (towards the Great Lakes) and slightly down (towards England).  Exactly how much is impossible to determine from this chart.

 

Chart 501

Polar Motion 1861-1962

 

Provides a simplified, less confusing way of showing a century of polar motion.

The total track of the pole is shown in four colors, each color represents a long era of time rather than 6.5 years, the first period is in white, the next period is in black, the third is in green, and the latest period in in red.  If one looks into the center or eye of the red spiraling circles, one can see what is approximately the average position of the pole for xxxeidt years.  Though obscured, one can fairly easily visualize the approximate center of the white spiral circles.  From these two points one can estimate readily that the total drift of the average location of the pole seems to be in fairly straight line down towards the left hand side of the chart.  The total distance is about .15 arcseconds, which is just slightly more than 15 feet or about 4.5 meters.  Or, the yearly average is about 1.8 inches (very close to 3.06 centimeters dead on).

 

Chart 502

Can we find out more about the dynamics of polar motion by examining the individual spirals in greater detail?  As a matter of fact we can, we can make the most important discovery about Chandler’s Wobble since it was noticed that the Wobble is influenced by all of the mass variables of the earth, including the motions of the atmosphere (fluctuating with the weather) and the behavior of the ocean tides.  We make this discovery by plotting each spiral in separately and slowly building up the composite to look for any changes in motion.

 

In Chart 502 we can see in Black the spiral plot of the location of the pole during 1903-1909.   Drawn from 20 points per year, it appears far more circular and regular than the jerky appearing plots for the periods of 1861-1890.  We can also see that the average location of the pole does not appear to have moved by much, if at all.  It would  take a mathematician with fancy formulaes to accurately define the infinitesmal drift and as we can see it is probably not worth it, partly because the data is too sparse.

 

Hold on to this factoid. We have 50 years of measured polar motion and, though great variation in the 6.5 years cycles of Chandler’s Wobble are quite obvious, there IS NO DISCERNIBLE DRIFT IN THE LOCAITON OF THE AVERAGE POSITION OF THE POLE.

Chart 503

Look what happens when we add in the 1909-1919 spiral.  We can immediately sense some apparent drift in the eye of the wobble.

 

Chart 504

 

We see even more apparent drift when we add in the 1919-1923 spiral.

 

Chart 505  1903-1923

 

Dead reckon centers on the computer screen or on a print-out

for the black spiral 1903-1909 and for the blue spiral (1916-1923), the distance between them is about .07 arcsceonds.  If we assume the rate of drift is constant from 1909 through to 1923, the rate of motion is approximatley 6.1 inches per year ( almost 15.5 centimeters/year).  Serious mathematics can no doubt refine this crude number into something more precise and doubtless the number will be in the same range of increase.

 

After 50 years of no discernible drift, now suddenly we have 6 inches per year for 14 years.

 

a blue spiral form is diminished in size

 

Chart 506 1903-1931

Does the motion continue?  When we add the wobble spiral for 1923-1931 into the composite to create Chart 506 we get another surprise or two. The wobble is unseasonably longer than the average 6.5-7 year X Wave spiral cycle of Chandler’s Wobble.  And the wobble is even more crunched down in size and seems to trace a bowl of spagetti.   And there is no apparent drift of the “eye” of the wobble.  Annual drift seems to have disappeared again.

Chart 507 1931-1939

The bowl of spagetti begins to turn back into a spiral, even though the size remains very small

(of the white spiral) The “eye” might be even drifting but it is not very certain.

Chart 508 1939-1945

 

The red spiral motion for this period is still trancated but the “eye” of this spiral in the wobble definitely appears to have move in the same direction as the previous drift of the eye.

By now the eye seems to have moved a total of about .06 arcseonds since 1923 (the dark blue spiral is nearly dead on the geographic north pole position of x=0,y=0

 

but now the orange spiral eye of is about y=.06, y=.02

 

Chart 509 1945-1958

Suddenly in about 1945 the wobble spiral expands outward and and become becomes as large as it had previsouly been prior ot 1923.  As shown by the yellow and light blue colors, this enlarged pattern holds through 1958.  Since all parts of the spiral are now enlarged, even the “eye’, it is now more difficult to estimate the center of the “eye” by using one’s eyeball.  There may be a continuation of a slight amount of drift.

 

Chart 510 1958—1962 

 

new node analysis starts here, reesitmate the time lengths for previous

 

Between the eye of 1920 and the eye of 1935, there is ony about .01 arcsecond of movement, if that much.

 

or,  0.81 inches per year, or 1.24 centimeter/year

 

Suddenly, as the yellow plot shows, the motion of the pole has become quite jerky and the eye of this spiral seems to have shifted quite suddenly by a relatively large amount.   Using simple screen measurement, the eye of the yellow plot has shifted approximately .14 arcseconds since the eye of the 1931-1939 spiral.  Since the eyes were literally in 1935 and 1960 respectively, we have a 25 year shift of .14 arcseconds at a rate of 6.8 inches per year (17.29 centimeters).

 

 

 

Interestingly enough, Cayce predicted in the mid 1930’s that we would notice a gradual increase in the rate of tectonic change after 1958.  Since most of the apparent motion between 1935 and 1960 seems to have occurred after 1955, we find once again a strong correlation in the Earth Sciences which validates Cayce’s earth changes predictions. 

 

It gets even more interesting as we pursue the tracks of the Phoenix in the daily series from 1962 to 2001.

 

 

 

 

 

 

 

IERS Graphs & Charts
These are standard graphs which are posted at the iers.org website (International Earth Rotation Service)

The IERS website is evolving and changing and occasionally new graphs appear there.
Thus these graphs as of 2007 are housed at the same site as this Storyboard to insure stability of the links in this presentation with the correct graphs.  The IERS file names and the Storyboard file names are defined with each graph.

A1.  True Polar Wander (Average Drift of Location)  1900-1996 & Typical Wobble Spiral Motion
       (
provided by IERS circa 1999)
 

A2.  IERS X & Y Plots of Wobble Motion
 

A3.  Xplot of Wobble Motion 2005-2007
 

A4.  Yplot of Wobble Motion 2005-2007
 

A5.  Analytic X Plot of Wobble Motion 1900-2000

 

 

 

 

 

A1 - True Polar Wander 1900-1996
Chandler's Wobble with typical wobble spiral (partial)
wobble_tpw_iers_1900-1997.gif

The Chandler Wobble, Classically Shown
Earth's Wobble Spiral Motion 1994-1997 (dotted lines)
Drift of the Average Mean Location Of The Axis 1900-1996 (solid line)
Original image provided by iers.org; the large numbers and some year dates have been added by MW Mandeville.

As the Earth spins around each day to create day and night, it revolves on an imaginary axis  or pole which is known most widely as the North and South Pole.  More correctly, it should be called the Spin Axis.

In a sense, the Earth is like a giant child's "top" which can be spun quickly around and around on a table top.  Eventually the spinning of the toy "top" begins to slow down and bob around into a wobble.  Just so, the Earth spins with a slight bobbing motion. Each bob or circle of the wobble is some 14 months long.  Each "bob" completes one "wobble" circle (actually it is a spiral) when it returns the location of the Spin Axis to the same Longitude is occupied 14 months earlier.

American astronomer Seth Carlo Chandler in 1891.

move in an irregular circle of 3 to 15 metres in diameter,

 

Many people describe this wobbling activity as a form of "polar motion".  It is in fact convenient to describe the changing location of the Spin Axis as "polar motion" or as movement of the poles.  But this "movement" is an illusion, similar to the illusion of the Sun rising each morning. The Sun does not rise, the Earth rotates.  Similarly the poles or Spin Axis do not move (at least not much), it is the Earth which moves or bobs around the Spin Axis as it constantly shifts its mass in a vain effort to find a better balance. For a variety of reasons, it cannot and thus never does find a point of balance.   Accordingly the wobble continues.

 

 

Actually, is it probably mainly the outer shell of the Earth which wobbles.  Evidence during the past 70 years has slowly accumulated which points to the crust of the Earth rotating independently of the inner mantle and core.  During the last eight years, Depth sounding waves seem to show that the inner mantle (below 800-900 kilometers in depth) moves slightly more rapidly, enough to complete one additional rotation every 400 years or so.

What causes the Wobble?  For a variety of reasons, the mass of the Earth is not perfectly round nor evenly distributed, nor is the solar system perfectly symmetrical.  These imperfections in symmetry cause the gravity of the Moon and Sun to "drag" unevenly on the Earth from hour to hour, day to day, and month to month   This is the primary  cause for the slight wobbling in the Earth's Spin but it is not the only one. The Solar Wind, the circulation of the atmosphere, and the currents of the ocean also have what is known as a "seaonal" impact in adding or subtracting energy to or from the wobble.

As it wobbles slightly, the Spin Axis actually changes its location relative to the surface of the Earth. Or, in other words, the entire outer shell of the Earth shifts over and around the focal point of the Spin Axis.  This we could call this polar motion, but it is best defined as simply the wobbling of the Earth.

Polar motion is probably best described as the change and migration of the orientation of the Spin Axis relative to the stars, such as Polaris.  See the side panel to the right for a summary description of Polar Motion in the Great Platonic Year.  In this type of motion, there is no change in the physcial location of the Spin Axis relative to the surface of the Earth.

The wobbling of the Earth causes a ceasless shifting of the location of the Spin Axis relative to the ground.  The Spin Axis "appears" to circle around and around an imaginary "average" location every 14 months. In Graph A1 (in the panel to the right) the dotted lines show the Spin Axis moving around this average location. This wobble circle is called "The Chandler Wobble", or some times it is called "Chandler's Wobble.

Even more important than the unevenness of the mass of the Earth are the constant orbital variations of the Moon and Sun as they revolve around the Sun. Most of the variations are small. But each month the Lunar gravity changes in magnitude by as much as 15% as the Moon draws closer to the Earth (Perigee) or draws further away from the Earth (Apogee). These changes in gravity add (for the New Moon) or subtract (during the Full Moon) the gravity of the Sun. These changes create a ceaseless monthly  rhythmic change in the amount of gravity which pulls on the spinning surface of the Earth.

The changes in gravity induce continuous changes in the shape, size, and duration of the wobbling of the Earth. In addition to the monthly rhythms of the Moon, there are other cosmic rhythms and some of these can be observed in the rhythm of the Wobble. The most important of these rhythms include a seasonal fluctuation (semi-annual) in the Wobble, the Wobble circle of 14 months, and a cycle of 7.1 years which rhythmically changes the size and energy of the Wobble.

The large dotted circles in Graph A1 show part of the spiral track of of a typical 7 Year Wobble Cycle. It begins in 1995 (find the date on chart) and ends in 1998 (just below the starting date). This displays about 40% of a typical 7 year wobble cycle.

If one looks at the bottom of the spiraling circles, we can define the "Chandler Term", or length of the spiral in time. The Spin Axis moves to the right in a counter-clockwise rotation. It typically takes about 14 months (435 days) to return to the bottom of the circle.

One profoundly important chararcteristic of the wobble is its 7 Year Cycle. During this cycle the size of the wobble circles constantly shrink down to a very small circle (MIN phase) or constantly expand back out to the approximate size of the wobble tracks shown on Graph A1.

A typical 7 Year Wobble Cycle brings the spiral much tighter into the center of the circles formed by the two outer spirals which are shown in this example. These happen in this example graph to be the Wobble in its maximum size (the MAX phase).  Missing completely is the Wobble in its minimum size (the MIN phase).

A complete 7 Year Wobble Cycle will show the spiral shrink during the MIN phase to about one sixth the size of outer spirals in the MAX phase. In a complete cycle, one can trace the spiral moving down to MIN and then back up to MAX. This will be seen in many Spiral Charts in other sections of this Storyboard.

Typically, at MIN, the wobble spiral is about xxxx. At MAX, the size is about xxxx. This change in size is called the Chandler Amplitude.

Arcseconds scale = 0.01 =
divided into fifths of 0.01 = 0.002 for the smallest grid

Graph A1 demonstrates two other highly important things. First and most importantly for all navigation, especially the modern form of using Satellite location finders, Graph A1 demonstrates how the location of the Spin Axis, the real North Pole, varies from the Geo-coordinates which are used by maps. The Geo-Reference system, so-called by geophysicists, was fixed at the beginning of Century 20 to show the "North Pole" at a certain point on the Earth's surface.

Map-makers still draw their maps using this same Geo-Reference point.  But this point is no longer accurate enough for electronic location finders. A daily "offset" must be computed to exactly locate the "real" North Pole relative to the stars, and hence the "real" location of any point on the Earth.

The computation of the correction factor is computed in Belgium, using a "celestial frame of reference".  They calibrate the orientation of the Spin Axis to the fixed stars with the latest location of the Axis relative to Green Meridian and a Longitude at 90 degrees.  The correction "offset" is distributed worldwide through the Iway. This is the purpose of the International Earth Rotation Service. The IERS also keeps track of the real time of day, which constantly varies with the varying rotation speed of the Earth.

In Graph A1, one can see that IERS geophysicists use graphs differently than most people are used to seeing. They reverse the algebra so that the signs are the reverse of what is usually shown on graphs. The negative numbers are on top and to the right. The positive numbers are on the bottom and the left.

They define the "X Axis" as Greenwich Meridian and the Y Axis as Longitude West 90. The Greenwich Meridian, of course is Longitude "0" and runs through east England. Longitude West 90 bisects North America and runs close by Chicago.


long term drift of the Spin Axis during all or most of the 20th century


Literally, the location of the center of the Wobble NEVER returns exactly to its previously center of balance, it slowly creeps it is progressively moving
Graph based on "smoothing" out the seven year variation. so the average annual position is computed into a running average of several years.


1900 to 1997
a purely fictional line
a few zigzags, which can all be "averaged" out to two numbers which define the long range trend
rate of drift 12 etc centimeters per year
angle of drift approx Long. West 80
obscures a lot, as will be seen, better to see a real plot of real average positions. as will be seen in other portions of the Storyboard.
Substantial different picture emerges
what the chart does not show is how the rate of change varies and the highly interesting fact that there is no detectable drift prior to 1900.
 

Mars wobble


http://www.geosociety.org/news/pr/05-37.htm
Mars' Climate in Flux: Mid-Latitude Glaciers
14 October 2005
GSA Release No. 05-37This figure illustrates the effects of axial precession on the seasons, relative to perihelion and aphelion. The precession of the equinoxes can cause periodic climate change (see Milankovitch cycles), because the hemisphere that experiences summer at perihelion and winter at aphelion (as the southern hemisphere does presently) is in principle prone to more severe seasons than the opposite hemisphere.
 

 

NEXT:  How geophysicists plot and study the wobble spirals

About The Earth's Tilt & Polar Motion In The Precession Of The Equinoxes:

There is another form of polar motion which is often confused with the Earth's near-annual wobbling  This is the relative "movement" of the Spin Axis in a very long cycle of 25,800 years which is called the "Precession of the Equinoxes".  Almost all of this "polar motion" is relative only to the stars and to the Sun, not to the surface of the Earth. 

This long cycle of movement of the Spin Axis relative to the stars was discovered by the ancient Egyptians and translated into the first written euro language in ~160 BCE by Hipparchus, an Hellenic scientist in the millennium before the Romans politically butchered date-keeping in what is known as the Common Era. 

It has long since been known as the "Great Platonic Year" which defines the astrological ages of human civilization.   During this long cycle, the Spin Axis very slowly shifts its orientation in a modest circle to what the ancients called "the fixed stars" in the North.  This "circle" which the Spin Axis "draws" on the fixed stars is the same size in degrees (as seen from the Earth) as the tilt or inclination of the axis.

The Egyptians thought that the entrance to Heaven was located there, where everything is unchanging and thus "eternal".   Polaris, of course, is the current fixed "pole star" towards which the Spin Axis points.  More precisely, Polaris is actually within about one half of a degree of an imaginary line which extends from the North Spin Axis out towards the stars. This line does not change position from day to day or even much by year to year but it does slowly change.  The line will make its closest approach to Polaris in 2017.

The Spin Axis maintains its orientation rigidly throughout the year, despite the fact the Spin Axis is tilted by 23.5 degrees to one side relative to the plane of Earth's regular rotation around the Sun. This rigid orientation and equally rigid tilt produces, of course, the annual seasons.  To maintain the rigidity of orientation of the Spin Axis toward Polaris, the Earth must pivot its daily spin cycle, which means it must simultaneously pivot the entire Spin Axis and the moving mass of the Earth, so that for one half of the year the the North Spin Axis tilts towards both the Sun and Polaris and during the other half the North Spin Axis tilts away from the Sun while maintaining its orientation towards Polaris. 

Thus for one half the year, the Sun is made to "appear" to be moving northward to warm the Northern Hemisphere more than the Southern, and for the other half of the year, the Sun "appears" to be moving southward to warm the Southern Hemisphere.  The maximum movement from the Equator in either direction is 23 degrees +27 arcminutes of Latitude, for a total swing of 46 degrees and 54 arcminutes. 

Go here for an image of the tilt and precession:
http://csep10.phys.utk.edu/astr161/lect/time/seasons.html

http://www.crystalinks.com/precession.html
As of February 8.2007, avoid Wikipedia on these discussions, the text is immature and somewhat misleading.

The timing for this annual "swing" lags by a minute amount each year (a little less than 1/60 of a degree) to create the Precession of the Equinoxes.  Thus, if you stood on the Equator at Noon on March 21 each year (when the Sun is exactly over the Equator), the moment of crossing (which is called the Vernal Equinox) would "appear" further and further to the West each year.  Currently, this annual  movement to the west is about 50.3 arcseconds per year or 1 degree (of the equatorial celestial vault) every 71.6 years.  Some 25,765 years later, after traveling around the Earth, the "moment" of the Vernal crossing would return to the same location.  Each year, accordingly, the  positions of stars on the Equator will slowly change their coordinates, swinging through a range of nearly 47 degrees during the Great Platonic Year.

What causes the Tilt and this Precession?  Amidst many factors, probably two fundamental causes are the most strongly at work.  These are difficult to definitively prove within the current limitations of human science, but the circumstantial evidence is fairly strong. 

For the Tilt, the magnetic fields of the Sun and its vast solar wind most likely interacts with the core magnetics of the inner planets to produce the "tilts" in their orientation. The closer to the Sun, the straighter and more parallel the axial tilts, as one would expect in elementary magnetic materials.  The further from the Sun, the greater the tilts, the less polarized the magnetic agents.  This table of axial tilts for the planets (drawn from NASA sources as published in Wikipedia) demonstrates the correlation.  The inner planets correlate well in this order but the outer planets are somewhat disorganized.  Jupiter is the major anomaly, perhaps the exception which proves the rule.  Its huge size and active electrical properties (it propagates infrared radiation) may overcome the distance and strongly polarize the planet with the magnetic field of the Sun nearly as sharply as Venus. As can be seen, the Earth is perhaps nearly at the distance where the polarization effect from the solar wind drops off and becomes nearly uniform out to Neptune.  Pluto is omitted because of its extreme eccentricity.

Planet Degree
of
Axis Tilt
Planet Degree
of
Axis Tilt
Mercury 0.01 Jupiter 3.13
Venus 2.64 Saturn 26.73
Earth 23.459 Uranus 97.7
Mars 25.19 Neptune 28.32

For the Precession, the gravitational forces of the Sun and Moon are the factors which have been traditionally said to  induce the Precession. The Sun and the Moon are constantly tugging at the Earth from different angles with various amounts of "pull" which varies with their orbital fluctuations.  The net result of this combined pulling is to retard the return of the Vernal Equinox, thus the apparent "Precession".   This effect is called "lunisolar precession".  The second  effect is to induce slight variations or bobbing oscillations into the precessional movement which reflect variations in the orbits of the Earth and Sun.  These effects, which are known as nutations, slightly alter the speed or rate of the procession and the tilt of the axis. The nutations are studied and reported upon for scientific and military purposes, primarily because the strength of them are somewhat unpredictable and because the nutations affect the accuracy of all digital navigation.  According to the IERS Agency in Belguim, measurement of the nutations are now done with an accuracy of .001 arcsecond, which is very very precise.

The largest nutation is 18.6 years and has an amplitude or "swing" in the heavens of 20 arcseconds.  This has long been observed, it is an effect of the Moon"s 18.6 year eclipse cycle.  During this cycle, the Moon swings through a complete range of orbital "tilts" above and below the equator of the Earth, reaching its maximum swing once every 18.6 years

Through these motions of the Spin Axis, there is virtually no change in the location of the Spin Axis on the surface of the Earth.  All of the motion is relative to the stars and the Sun. Accordingly, these motions have no effect on the Earth's Tectonic Plates and they have no impact on climate cycles.  There is one kind of orbital cycle (Precession of Perihelion) which does impact very long range climate cycles, but that is another story for another place.


 

IERS Databases:

All the charts, graphs, and various studies are based on databases which are calculated and maintained by an international consortium which is based on Belgium, closely thus allied with the European Union.\

The main databases

Sample-point Database Files

EOPC01 Series

http://hpiers.obspm.fr/eoppc/eop/eopc01/eopc01.1900-2006
EOPC01 (1900-NOW) - Product metadata

This data base is composed of EOP calculations from 1846 to now
For 1846 to 1889, based on 10 sample points per year
Sinchttp://www.iers.org/products/19/832/orig/eopc01.1846-1899
e 1890 based on 20 sample points in the year, beginning Jan 1 as point 0
It provides roughly a two week sample - EOC series.
Worth keeping up only to provide current comparisons with pre 1962 spirals

Daily Database Files

Internatinal Earth Rotation Service
Earth Rotatoin Parameters
EOP C04 series

This database is constructed from January 1, 1962 through to the end of the year from the EOPCO4
bulletins which provide the only consistant data series through this time series to the current
 

Statistical Averages

; locations and URLS have changed.  Suggest google for latest versions of  average location of the poles

ftp://michaelmandeville.com

wobbleplots_1846-now.xls

wobbleplots_1846-now.zip

this is an excel spreadsheet with multiple workbooks, contains both of the main data series of the IERS from 1846 to early 2007, both the EOPC01 sample point data and EOPC04 daily data.

For the latest partial year, my wobble database is composed of an appropriate selection of the "finals-all" file, which is a composite of all bulletins update daily since May 19, 1976
 

plus some statistical averages by IERS consortium members

.  conundrum on the samplepoint database

Y charts

THESE CHARTS ALL BASED ON Bull B Sample Points
These are the same as the X Plots in worksheet Bull B Sample Points 1846-2006
BUT WITH ONE BIG EXCEPTION - these are shifted to display the Y Axis
The Y Axis clearly shows the drift of the wobble.


X Plots

This data series by IERS and hence these charts are always about six months to a year behind.

The skinny appearance of the waves 1846 through 1889 is due to only 10 points per year. Cannot use pre-1890 data
 

 

 

Characteristics of the Earth's Wobble:
 

 

Scale of Measurement:

In this Storyboard, all measurements have been arbitrarily termed  as degrees of Longitude.  This keeps the story simple and there is no practical effect at the Poles by avoiding differences connected with counting in degrees of Latitude.

All notation is defined as what?:  Longitude, where?: West or East, how much?: 90.
For whole numbers, degrees are omitted as pointless oxymorons. This is a different style than most academic convention.  I use it because this is how I think about objects and how to locate them on the Earth.  It is superior to prevailing academic convention.

1 degree =  60 arcminute, 3600 arcsecond

1 arcminute = 1/60 of a degree =

1 arcsecond = 1/3600 of a degree = 30.87 meters

0.1 arcsecond =  meters 3.087 = feet 10.127 = inches 121.524;

0.01 arcsecond = 1.0 millisecond of arc = 1.0 mas (this unit is often used)
                            = 1.1 foot = 12.1 inches = 30.87 centimeters

.005 arcsecond = 0.5 mas

Accuracy of Measurement:

IERS CLAIMS:  "Variations in the wobble can be seen on a diurnal and semi-diurnal (daily and nightly) with amplitudes which have a fraction of millisesond of arc (mas) that are due to the oceanic tides." Also:  "Universal time and polar motion are available daily with an accuracy of 0.5 mas and celestial pole motion are available every five to seven days at the same level of accuracy - this estimation of accuracy includes both short term and long term noise. Sub-daily variations in Universal time and polar motion are also measured on a campaign basis."   ASSESSMENT: Reasonably true.

Chandler Amplitude:  This is the variation in the size of the wobble, usually measured on the X and Y Plots such as shown in Graph A2.   Typically the size ranges every 3.5 years between a small spiral and a large spiral:

Approximate Spiral Cycle in MIN phase size: typical 3 meters
(range 1.5 - 6)

Approximate Spiral Cycle in MAX phase size: typical 5 meters
(range 12 -24)

The size of the wobble from cycle to cycle varies significantly. The MIN and MAX phases, for instance, range broadly in size, as indicated.

Chandler Frequency:   0.843 cycle per year

Chandler Term - average length:  14 Months; 433-435 days, depending upon source.

Wobble Cycle - average length:  Very close to seven years or 84 months. Generally 6 "waves" of 14 months each can be found in the typical wobble cycle which is described on the X or Y plots.  A partial count of cycle length, based on X Peak to X Peak for a portion of Century 20 yielded an average of 7.1 years or nearly 85.5 months,    Since 6 X 14 = 84 months, there is a slight amount of variation in the waves, all of about one week per wave.  Absolute variation is somewhat larger than suggested by these numbers because sometimes there are less than 6 complete "waves" on the X or Y plot.  The updates and changes in the IERS database since 2005, however, most likely requires a new computation. Regardless, the "mean" is regular.  A count of any significant part of a century of wobble X waves returns the same number as the average for the century.

Most Significant Variations In The Wobble Since 1890: (a) variation in the sizes of the MAX and MIN phases; (b) a tendency to "time truncation" or "elongation" of the MIN phase; (c) variations in the average rate of drift; apparent acceleration in the rate of drift for discrete periods of time; (d) tendency of drift in the direction of Long. West 90, (e) with at least four episodes of hunting in the direction of  approximately (very roughly) Longitude West 135; (f) marked persistent changes in the wobble since a 20 year period of turbulence and phase-shift from 1925-1945, most especially larger wobble spirals and an increased rate of drift of the wobble; (g) a modest increase since 1935 in the size of the wobble spirals in the "lee side" of Solar Activity Cycles (the trailing edge of Solar Activity Cycles is typically and substantially more energetic in CME's, flares, and major magnetic storms than the rising edge of the Solar Cycle);

Variation In Mean Time Domain?:  Nothing significant is apparent

What Pumps The Wobble?:  Most existing reference books have it wrong, wholly or in part, or incomplete, or misleading. Wikipedia is incoherent on the subject.  During recent decades, a school of thought has been pushing the idea that the wobble's variations and energy are primarily "weather induced".  This is simply not true.  Here is the answer provided by the observations and principles of Vortex Tectonics.  The observations described here are all easily observed in Graph XZY

Based on the size, shape and timing of the wobble cycle during the past 116 years, the most probable main source of energy for the wobble is the result of a complex beat function between the Earth's spinning crust, the orbital gravity fluctuations from Solar Perihelion/Aphelion and Lunar Perigee/Apogee, and elastic rebound in the crust of the Earth.  The Wobble is the result of a destructive interference with the natural free spinning state of the rotating Earth.  The sources of the interference are the Sun and the Moon. Variations in the pull of their gravity combine at certain times to pull the Earth's Wobble into a greater or smaller size.  Their orbital gravity vectors subtract various amounts of energy from the wobble on a regular cyclical basis.  By far the most important influence on the Wobble is the increased solar gravity which drags on the Earth's mass at Perihelion (when the Earth is closest to the Sun during the first week of January).

If the Earth were perfectly rigid, the wobble would take on this exact period and be locked mainly to the Earth's Perihelion cycle, with many variations created by additions and subtractions to the drag on the Earth which are caused by orbital variations of the Moon.  However, the largest fluctuation in the wobble is created by the elasticity of the Earth. 

The elastic nature of the crust and upper mantle resists the wobble period and, with the assistance of the Moon, each year delays the gravity-based solar cycle by nearly 60 days, basically by the length of  two lunar cycles.  This retards the timing of the return of the Spin Axis in its circular jig around the top of the Earth and draws the wobble spirals out into 14 month periods rather than 12 month periods.

Some additional energy transference, both additive and subtractive, comes from seasonal variations in the atmosphere and the oceans.  This transference is  probably in the range of 1% to 5%, perhaps as much as 10% when augmented by intense periods in the Solar Activity Cycle.

When the wobble's 14 month timing synchronizes the Spin Axis  with  Perihelion (in the period December/January) while on or close to the Greenwich Meridian, the wobble receives its greatest addition of energy. In the next two or three succeeding spirals, which fall progressively two months later in each succeeding year, the wobble continues to receive greater energy.

But when the Spin Axis returns to the Greenwich Meridian after the Summer Solstice, the wobble progressively shrinks for the next two to three spirals.  The length of the cycle is unaffected but it continues to shrink on each spiral. Finally a "low" or "null" moment of movement in the Spin Axis synchronizes once again with Perihelion as it wanders near Greenwich Meridian. This almost always occurs seven years after the beginning of the first spiral of the wobble.

Why Perihelion?  the orbital cycle and the daily spin of the Earth are most closely  paralleled and synchronized in their motions at this time.  Thus increased solar drag on the southern hemisphere can more easily increase the size of the wobble at this particular moment (which actually extends for close to six months).

More probable than not, this is likely a reflection of the well known fact that the Earth is slightly bottom heavy. Despite the large expanse of oceans in the Southern Hemisphere, this side of the Globe is slightly heavier.  A part of the reason for this heaviness most likely is the three miles of ice which are piled up on Antarctica.  So all vectors add up (or substract!) most strongly at this time to pull the motion of the Earth's surface into a larger wobble.

Why Greenwich Meridian? (Or close thereof)  That is a very good question, for which there is no good answer. But probably there is only one possible TYPE of answer. In the quadrant which is formed by the intersection of the Atlantic Hemisphere side of the Earth and the Southern Hemisphere, something there is.  Is the Earth's mass here greater than in all other quadrants.  Precisely why requires some serious science to find the answer.  The ice alone on Antarctica may answer this question.

When the wobble cycle rebounds off the elastic   

Correlations With The Wobble 7 Year Cycle:

Solar Activity (11 Year Sunspot Cycle): modest influence, perhaps 5-10% influence on the lagging edge of the 11 year cycle

Global Air and Water Circulation & Tidal Forces:  perhaps 1% to 5% influence, additive and subtractive.,

El Nino:  very strong, strong enough to infer that underwater tectonic activity is induced by the Wobble sufficient to produce El Nino heat flux.

Global Warming:  drift of the wobble

Southern Hemisphere: Strong connection revealed through the Greenwich Meridian; bottom heaviness of Earth involved in the wobble

 Perihelion:  Most important vector which pulls the wobble out

 Lunar Cycles:  Clearly involved, mechanics not incorporated into this material

Elasticity of Earth's Structure and Mass:  Rebound dampens and pulls the wobble cycle into exhaustion;

Tectonic Quantum Events: wobble oscillations create long term tectonic "quantum" motion events which progressively shape-shift the Earth through  dual action of Great Rift splitting and upwelling and Subsidence Zone downwarping.

Other Schools Of Thought:
 

The geophysicists who write and produce the IERS documentation generally argue that the variations in polar motion (which includes all of the Wobble) are produced by the seasonal and lunar (tidal) movements of Earth's air and water.  Most recently, for instance, the Jet Propulsion Laboratory announced that "tidal" and "seasonal" loading and friction of currents on the bottoms of the ocean "appear" mathematically as if they could produce the variations in polar motion.  However, this school of thought casually neglects the 11 Year Solar Activity Cycle which has a deep and abiding effect on the atmosphere and the climate patterns of Earth.  If fluid motion shaped the Earth's Wobble, in part or in main, one would seen an obvious 11 year signature in the Wobble. Increased solar activity drives increased fluid flow.  This should be observable in the Wobble if fluid flow is driving the wobble.  In fact, there is some influence, but this signature does not support a "seasonal" connection.  See for instance Graph

More probable than not:  variations in lunar perigee/apogee/orbit-angle combining with variations in Solar barycenter, primarily at Perihelion, induce and sustain the Wobble and 90 of its variations as mass spin- reaction functions which are independent of the Precession functions.  With the Wobble, the energy function for the mass reaction is primarily between the spin energy and the gravity forces. Changes in electromagnetic flux sufficient to change the weather and drive seasonal changes must be largely self-cancelling on a daily or seasonal basis.

test variations of the Jupiter induced  barycenter with the variations in the size of the spiral waves.

More probable than not: 

 

Updating Charts Of X & Y Plots (every five days)

http://hpiers.obspm.fr/eop-pc/earthor/polmot/pm.html
http://hpiers.obspm.fr/eop-pc/earthor/polmot/polhody-x-fil.gif

 

 

 

 

 

IERS X & Y Plots of Wobble (Polar) Motion

 

The X Plot of Wobble Motion (2005-2007) - A2
as of February 1, 2007
click here for expanded version

NOTE: These plots show significant distortion from normal X & Y Plot waveforms. 

The wobbling motion of the Earth can be easily turned into a simple graph plot which moves across the sheet looking like a simple wave form.  In fact that is one of the most important ways to look at the wobble to study the correlation between the movement of the crust and other natural events, such as earthquakes, volcanoes, weather patterns, solar activity, etc.  as will be seen below

To reduce polar motion to a simple chart, geophysicists use the same conventions which govern the IERS chart of True Polar Motion (shown above).  The X axis = Greenwich Meridian, which is also called Longitude 0.  The Y Axis = Longitude West 90,   This enables scientists to look at the wobble in two different dimensions simultaneously to look for correlations. 

expanded charts below provide a better view.

The phase difference between X and Y.  A 90 degree difference, normally but not always, sometimes the wobble varies its phase, usually only a little.  But a few major phase shifts, such as the one in 2006 have been observed. Last one so large, still not possible to determine the amount of the phase shift.

Virtually a 180 degree phase differecne in the middle of the Graph, suggesting a 90 degree phase shift sometime between 2005 and 2006

Generally the average 90 degreee phase separation is equal  in time to  about one fourth of 14 months.  one fourth of a circle 360 degrees, 90 degrees, takes 14 months, or about 60 weeks one fourth of which is about 15  weeks.

These X and Y graphs are refeshed every few days on the IERS website.  It is based on data about polar positions which is published through the Iway and propagated through email to subscribers as "Bulletin A" or as Bulletin B. Bulletin A is considered advance information which is subject to further refinement.  Generally, the "final numbers" become final about a year later and are published in "Bulletin B".

Before sending the Bulletin A numbers, the plots are run through computer models and the predicted location of the Spin Axis is forecasted for the year ahead.   Since the Earth wobbles variations significantly through its spirals, the predictions are not really very precise after the first month or so.  To keep up with the ever-changing Earth, the predicted numbers are revised on a weekly basis.  This problem was acute during 2006 when the wobble spontaneously made a major anomalous shift in its tempo and phase.

What happens when the X plot and Y plots are combined on the same chart?  This can be done in what is known as an XY Scatter chart to show a spiral as in Graph A1.  Many interesting things can be observed about the the wobbling Earth. Or the two X and Y plots can be combined in a dual trace.  This is also creates an interesting way to spot and observe anomalies in the Wobble.

 

 

The Y Plot of Wobble Motion (2005-2007) - A3
as of February 1, 2007
click here for expanded version

 

 

A2. IERS X Plot of Wobble (Polar) Motion 2005-2007
This image sourced from running file: http://maia.usno.navy.mil/xplot2.gif
as of February 1, 2007
This image locally is: pm_xplot_by_iers_Jan07.gif
 

The X Plot graph to the right shows very well how the Chandler Amplitude varies in size (the size of the Wobble).  But because of the anomalous distortions in the wave form, the typical Chandler Term (length of the typical wave) cannot be readily understood in this time frame.  Historical plots in other parts of the Storyboard must be viewed to see the typical 14 month "Term".

The scale of this graph is on the left-hand side and the 0 point for this graph is nearly in the middle of the scale.

Becuase the numbers are small, typically about plus or minus 0.1 at the largest, we are obviously watching a Wobble MIN phase.

convert these numbers.

Anomaly xxx

 

to see a more normal X plot, go to

 

 

 

 

A3. IERS Y Plot of Wobble Motion 2005-2007
This image sourced from running file:  http://maia.usno.navy.mil/yplot2.gif
as of February 1, 2007
This image locally is: pm_yplot_by_iers_Jan07.gif

The Y plot to the right

Longitude West 90

 

Here the anomaly is seen mainly as....

undalations up and down the the Long.

or, one can see the changing size of the spiral loop of the wobble.

expansion and contraction.  Ideal perfect waveform for a perfectly balanced Earth would be a sine wave. 

Notice the numbers on the left of the graph.  Rather than balanced above and below the zero line, we see only positive numbers. 

This is an indication of the drift of the Axis down Long. West 90 which can be seen in the first chart.

to see a more normal Y plot, go to

 

 

 

 

 

 

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The IERS X Plot of Wobble (Polar) Motion 1900-2000
This image sourced from
This image locally is: wobble_xplot_iers_1900-1997.gif

 

The study of Earth's Wobble becomes far more interesting when you step back from the individual waves and build a comprehensive overview of the shifting wobble for many years at a lime.

Here is one such "overview" graph to the right.  It displays over 100 years of waves which are defined by the X plot data of the wobble. It also demonstrates how many geophysicists currently see and analyze the motion of the crust.

TOTAL MOTION:

The top graph line shows the X Plot of the Wobble, similar to the waves in the previous panels above, but these waves are compressed enough to show back to 1890.  Thus over 100 years of Wobble X waves can be seen.  One also can easily see nearly all of some 17 cycles of the Seven Year Wobble Cycle. By counting the center peaks in the undulations of the Chandler Amplitude on the top graph line, one counts 17 peaks in the seven year cycles from 1900 to about 1997.

 

One can see that the undulations vary significantly from wobble cycle to wobble cycle.  Each seven year cycle has a definite symmetry.  One can see also that there is a strong rhythm in the progressive change in the size of the Wobble cycles. This rhythm appears to be tapping out in sequences of three, roughly a 21 year cycle up or down in the size of the wobble.

The line which runs through the Total Motion band is called the trend.  It is the simple algebraic mean of the annual X Plot measurements. It shows a slight upward trend in the drift of the Wobble's focal point.  Other wise stated, this shows a tendency of the center point of the Wobble to drift toward England.

CHANDLER TERM:

This belt supposedly demonstrates the amount of the wobble which is created by the orbital beat between the gravity vectors of the Earth's crust, the Moon, and the Sun. At first blush, one might suppose that this belt is far too irregular to reflect the repeating orbital rhystem of the Moon and Earth.  But some geophysicsts have convinced themselves that energy which "feedbacks" from the changing seasons greatly influences the Wobble.

Notice the long anomalous truncation between 1925 and 1945, followed by a large expansion in the size of the wobble through to about 1960.  This anomalous period, which was predicted and described by Edgar Cayce decades before geophysicists could even describe it, shows up repeatedly over and over in a variety of ways.  Something profoundly important happened during the 1930's.  This may be happening again during the first decade of Century 21.

SEASONAL TERM:

Maybe.  Maybe not. With this part of the analysis we get perhaps into mathematical mysticism. The "Seasonal Term" appears to be an attempt to develop a paradigm of the wobble which is based on a feedback effect between the orbital factors and the physics of Earth's atmosphere and ocean circulation.  Many factors have been compiled into a complex modeling effort to define the energy in  this Seasonal Term. The problem with these theories is that we do not have a "null factor" to help us sort out fact from mathematical illusions.  The reality is we cannot really say how much the seasonal factor influences the Wobble, we can only guess speculatively at this time in humanities comprehension and scientific ability. Some geophysicists are quite authoritative in announcing their mathematical speculations in these things as facts.  But I personally cannot determine whether or not they have a bad case of circular reasoning.  By no means do we need to regard the calculations of the seasonal term as "facts".

 

RESIDUAL TERM:

Again, maybe, maybe not.  This is apparently the portion of the Wobble which did not fit the mathematician's calculations for the other two terms.  This 'TERM" was made available for other researchers to explain.  Some are attempting to explain this residual motion on tidal loading of the ocean bottoms and changes in ocean currents,

 

 

 

 

 

 

 

 

X Plots of Wobble Motion
 

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X Plot of Wobble Motion 1846-2006 - Area Graph
area plot in landscape orientation by MWM
pm_xplot_solid_846-2006.gif

A Table at 322 pix width

 

 

 

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X Plot of Wobble Motion 1846-2006 - Line Graph
line plot in landscape orientation by MWM
pm_xplot_line_1846-2006.gif

A Table at 322 pix width

 

 

 

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X Plot of Earth's Wobble 1890-2006 - Area Graph
area graph in landscape orientation by MWM
pm_xplot_solid_1890-2006.gif

A Table at 322 pix width

 

 

 

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X Plot of Wobble Motion 1846-2006 - Giant
giant area plot in landscape orientation by MWM
pm_xplot_solid_expanded_1846-2006.gif

 

 

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X Plot of Wobble Motion 1890-2006 - Giant
giant area plot in landscape orientation by MWM
pm_xplot_solid_expanded_1890-2006.gif

 

 

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X Plot of Wobble Motion 1846-2006 Expanded
expanded line plot in landscape orientation by MWM
pm_xplot_line_page_1846-2006.gif

 

 

 

X Plot of Wobble Motion 1846-2006 Giant
giant line plot in landscape orientation by MWM
pm_xplot_line_expanded_1846-2006.gif

 

 

 

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Y Plot of Wobble Motion 1846-2006
line plot in landscape orientation by MWM
pm_yplot_1846-2006.gif

A Table at 322 pix width

 

 

 

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Y Plot of Wobble Motion 1846-2006 Giant
giant area plot in landscape orientation by MWM
pm_yplot_solid_expanded_1846-2006.gif

 

 

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X Plot of Wobble Motion 1962-2007 Gigando
giant area plot in landscape orientation by MWM
pm_daily_xplot_expanded_1962-2007

 

 

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Y Plot of Wobble Motion 1846-2006 Giant
giant line plot in landscape orientation by MWM
pm_yplot_line_expanded_1846-2006.gif

 

 

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X Plot of Wobble Motion 1992-2007
line plot in portrait orientation by MWM
pm_daily_xplot_1992-2007

A Table at 322 pix width

 

 

 

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X Plot of Wobble Motion 1992-2007 Expanded
line plot in landscape orientation by MWM
pm_daily_xplot_expanded_1992-2007

 

 

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X Plot of Wobble Motion 1999-2007
line plot in portrait orientation by MWM
pm_daily_xplot_1999-2007

A Table at 322 pix width

 

 

 

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X Plot of Wobble Motion 1992-2007
line plot in portrait orientation by MWM
pm_daily_xplot_1962-2007

THIS CHART MUST BE REDONE

A Table at 322 pix width

 

 

 

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X Plot of Wobble Motion 1962-2007
expanded line plot in landscape orientation by MWM
pm_daily_xplot_page_1962-2007

 

 

 

 

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Spiral Charts of Wobble Motion
spiral xy scatter charts composed in two sizes by MWM

algebraic signs reverse of normal to correspond with IERS coordinates

two sizes,

in this file: book display size (displays in a 6x9 trade book without the need to alter the size

in another file which is linked to this file,  all the spiral charts display below can be found in full web page size

To access the full web page size, find and click on the link for   "expanded size".

 

For Chart 1861-2006

This chart shows clearly that the displacement of the wobble which began just after 1915 has continued to the current day
The current over-all displacement or drift of the wobble is in the range of West 65 to 80.
Other charts shows that from cycle to cycle the angle and the rate of displacement changes. So also does the size and symmetry of the wobble
Thus purely mathematical averages hide practically everything which is interesting about the drift of the wobble.
It is impossible to correlate or parallel other phenomena based on purely mathematical average changes in the location of the Spin Axis
The crux is the DYNAMIC flux of the change….the shape, the angle, the size, the rate of displacement…that is where all the action is.
Most likely the most important influences on the wobble are:

Here are the recorded sequences of the spiraling track of the North Spin Axis moving through its 7 year Wobble cycles . Displayed In arcseconds of Longitude; 0.1 arcsecond = 3.087 meters or 10.127 feet; composed from IERS EOP 2005/2006 data files; 20 points per year prior to 1964, daily numbers for all after 1964; copyright MWM, 2007 - michaelmandeville.com

The irregularity of the track, seen as angles and sharp bends for the early periods prior to 1890 are probably due to poor monitoring of polar coordinates prior to the 20th century.
During Century 20, the spiral tracks become cleaner and more regular, probably reflecting more scientific refinement in the monitoring process
None the less there were some jerky periods which probably also betray instability in the spin motion of the Earth and sudden shifting locus of the axis. moon gravity
sun gravity
solar activity flux




This is the core of the wobble spiral graphics
Shows a steady progressive drift of Chandler's Wobble since 1861
Each numbered cycle is measured from MAX year to MAX year, thus there is overlap of the trace in the MAX years
So each color spiral begins at the widest circle and spirals inside and then back out to the next maximum to change color for the next cycle.
To make these charts correspond to IERS algebra signs and build a counter-clockwise spiral, the following mirrors must be made:
1 The chart x and y axis must be formatted to "reverse signs" - MOUSE SELECT X OR Y FORMAT AXIS PROPERTIES
2 Then, to pull in data for the Chart X Axis, must use the IERS Y column
3 For Chart Y Axis, must use the IERS X column

Chart 1861-1944
No discernable drift in the wobble from 1861 until 1915
After 1915, there is considerable instability and anomaly in the spiral tracks through to 1938 (this is not shown on the chart)
From 1939, the track becomes more regular even as it demonstrates a strong displacement at roughly Longitude West 45.
wobspiral_cite_expanded_1861-1945.gif


These six sequences of the spiraling track of the North Spin Axis demonstrate that 1958-1963 was another pivotal year. The Wobble was larger once again but the center of the MIN phase was dramatically off-center and many pertubations shown in the seven year spiral track for Cycle 11

After the small size and apparent drift of the average location of the wobble during 1931-1945, the wobble suddenly increased in size and appeared to be stable in location during 1946 - 1957
Then in 1958, the wobble suddenly decreased in size again and by 1963 produces a Wobble MIN which is considerably off-center of the previous averages.
This sudden shift is very closely aimed down Longitude West 90.
wobspiral_expanded_1898-1963.gif
 

Here are some more defining sequences of the spiraling track of the North Spin Axis in its 7 year Wobble cycles .
This chart clearly demonstrates that the Changes In The Earth began to accelerate in 1958 and by 1970 drift of the Axis was ~25 since Cycles 1 & 2

Here the direction of the drift appears to be very nearly down Long. West 90
It is readily apparent that the rate of the drift is still much larger than during the preceding 70 years.
The black spirals should dead center in its overlap of the blue spirals
Instead, the latest sequence for Cycle 12 is off center once again to the left




Since Cycle 12 (1958 to 1963), shown in black on the chart, the wobble stayed about the same size while progressively moving down approximately Longitude West 90.
This progression in the drift or wander of the wobble can be seen in the succession of colors moving to the left.
Each seven year wobble cycle has a different color. The succession appeared to speed up during the 1990's but the rate clearly changed with the beginning of Cycle 18 in 2003
As can be seen, the maximum size of the wobble has once again shrunk and the Wobble MIN during 2005/2006 is offset to the left.
The inner loop, as shown in white in the graph, shows a profound anomaly.
The spiral forms what is termed in mathematics a "cartoid" loop. It curls tightly into a point, which can be seen in the nearly vertical line which forms "a hook" in the spiral loop and then begins to spiral back out again as it moves counterclockwise.
The tip of the "hook" may represent the most balanced true average location of the North Spin Axis.
For whatever combination of reasons, the wobble may have decayed to 0 at the end of 2005.
By March 2006, the gravity vectors of the Moon and Sun began to exercise enough leverage on the Earth to cause the Wobble to regenerate a new spiraling motion of continual change in its location.
If so, there most likely was a significant increase in the rate of drift or True Polar Wander.
The "jump" may have accelerated TPW by a factor of four times for a few years.
Whether this acceleration will continue is unknown.
Regardless, this jump is likely to produce, at least for a few years, a significant increase in earthquakes, volcanism, and global warming.
There may have been as much shifting in the location of the poles between 1983 and 2003 as between 1898 and 1964

This can be seen in TPW Drift rates
wobspiral_expanded_1890-1970.gif

 

Spiral Chart of Wobble Motion 1861-2006
spiral xy scatter chart by MWM
wobspiral_all_1861-2006.gif

Expanded Size

Hello there

 

 

 

 

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Spiral Chart of Wobble Motion 1861-1945
spiral xy scatter chart by MWM
wobspiral_cite_1861-1945.gif

Expanded Size

Hello there

 

 

 

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Spiral Chart of Wobble Motion 1898-1963
spiral xy scatter chart by MWM
wobspiral_1890-1970.gif

Expanded Size

Hello there

 

 

 

Spiral Chart of Wobble Motion 1890-1970
spiral xy scatter chart by MWM
wobspiral_1989-1962.gif

Expanded Size

Hello

 

Spiral Chart of Wobble Motion 1898-2006
spiral xy scatter chart by MWM
wobspiral_1898-2006.gif

Expanded Size

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Spiral Chart of Wobble Motion 1910-2006
spiral xy scatter chart by MWM
wobspiral_1910-2006.gif

Expanded Size

 

 

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Expanded Spiral Chart of Wobble Motion 1861-2006
full web page spiral xy scatter chart by MWM
wobspiral_all_expanded_1861-2006.gif

 

 

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Expanded Spiral Chart of Wobble Motion 1861-1945
full web page spiral xy scatter chart by MWM
wobspiral_cite_expanded_1861-1945.gif

 

 

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Expanded Spiral Chart of Wobble Motion 1898-1963
full web page spiral xy scatter chart by MWM
wobspiral_expanded_1898-1963.gif

 

 

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Expanded Spiral Chart of Wobble Motion 1890-1970
full web page spiral xy scatter chart by MWM
wobspiral_expanded_1890-1970.gif

 

 

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Expanded Spiral Chart of Wobble Motion 1898-2006
full web page spiral xy scatter chart by MWM
wobspiral_expanded_1898-2006.gif

 

 

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Expanded Spiral Chart of Wobble Motion 1910-2006
full web page spiral xy scatter chart by MWM
wobspiral_expanded_1910-2006.gif

 

 

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True Polar Wander

There area many other profoundly important and interesting things we can learn from the X and Y Plots of polar motion. Before exploring those through much larger charts, let us take another look at the drift of the average location of the Spin Axis.  In the first IERS chart, we saw the average location defined as the mean value for the  X and and Y plots for  each year. That is a simple and straightforward way to define the mean location.  One can then measure the distance between the yearly points and from that compute the rate of drift.

 

Many Sources of Data

 

Li & Wang, 2000

LI, Jinling & WANG, Guangli: “An Analysis Of The Polar Motion Series From VLBI

Observations”; Chinese Science Bulletin, Vol. 45 No. 21, November 2000, pp. 1945;

 Joint Radio Astronomy Research Laboratory, Shanghai Astronomical Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Shanghai 200030, Correspondance should be addressed to Li Jinling (e-mail: jll@center.shao.ac.cn); online version of document: http://www.google.com/search?q=cache:REYIQP0DtB4J:www.scienceinchina.com/ky/0021/ky1945.pdf+Gross+and+Vondrak&hl=en&client=firefox-a

 

August 1979 to the end of 1998

 

By applying a filter, the secular polar motion was

found to be (2.74 ± 0.01) mas/a towards (83.9 ±0.3) W longitude, which is smaller in rate and more westward in direction compared with those determined from optical observations or the combination of optical and space geodetic observations.

2.74 mas = .00274 arcsecond = 8.45838 cm/yr.

 

Li & Wang: It is believed that in the polar motion

series there exists the Markowitz wobble

with a period varying from 25 to 30 years

and amplitude about 20 mas.

 

 

Data Source Date Span Rate/mas Direction

[1] Hipparcos 1900-1992        3.51 ± 0.01      W 79.2 ± 0.2

[4] International Latitude Service           1899-1979       3.52 ± 0.09      W80.1 ± 1.6

[7] Space geodetic observations           1976-1994       3.39 ± 0.53      W85.4 ± 4.0

[8] Optical and space geodetic observations      1899-1994       3.33 ± 0.08      W75.0 ± 1.1

[9] VLBI          1979-1999       2.74 ± 0.01      W83.9 ± 0.3

 

1. DeMets, C., Gordon, R. G., Argus, D. F. et al., Effect of recent revisions to the geomagnetic reversal time scale on

estimates of current plate motions, Geophys. Res. Lett., 1994, 21: 2191.

4. Gross, R., Vondrak, J., Astrometric and space-geodetic observations of polar wander, Geophys. Res. Lett., 1999, 26: 2085.

7. Zhao, M., Dong, D., Chen, Y., A new research for the secular drift of the earth’s pole, Acta Astronomica Sinica (in

Chinese), 1986, 27: 352.

8. McCarthy, D. D., Luzum, B. J., Path of the mean rotational pole from 1899 to 1994, Geophys. J. Int., 1996, 125: 623. (Received March 20, 2000)

9. LI Jinling et al.: An analysis of the polar motion series from VLBI observations

 

Joachim Hopfner

 

Joachim Hopfner: Low-Frequency Variations, Chandler And Annual Wobbles Of

Polar Motion As Observed Over One Century;  Scientific Technical Report No.: STR03/01

 

 Table 6. Relevant characteristics of the Chandler and annual wobbles

Wobble Period Motion Type Numerical Semi-major Direction of the Semi-minor

(days) direction eccentricity axis (arcsec) semi-major axis axis (arcsec)

Chandler 410 ... 442 prograde quasi-circular 0.00 ... 0.70 0.03 ... 0.27 very variable 0.02 ... 0.25

Annual 356 ... 376 prograde elliptic 0.20 ... 0.80 0.05 ... 0.16 ,.-_/ _ ... ,.0_1 _ 0.04 ... 0.13

 

 

Table 7. Recent estimates of the linear rate of the motion of the rotation pole

PM time series Time span Linear trend rate Source

Magnitude Direction

mas/year _ West

POLE99(JPL) 1900 ... 1999 3.54 69.92 Vicente and Wilson (2002)

POLE2001(JPL) 1900 ... 2001 3.530 _ 0.019 70.46 _ 0.32 This study

EOP(IERS)C01 1900 ... 1992 4.43 _ 0.08 78.15 _ 1.00 Schuh et al. (2000, 2001)

EOP(IERS)C01 1900 ... 1999 3.35 76.3 Vicente and Wilson (2002)

EOP(IERS)C01 1900 ... 2000 3.901 _ 0.022 65.17 _ 0.22 This study

OA (AICAS) 1900 ... 1992 3.51 _ 0.01 79.2 _ 0.2 Gross and Vondr´ak (1999)

OA (AICAS) 1900 ... 1992 3.20 77.1 Vondr´ak (1999)

OA97(AICAS) 1900 ... 1992 3.31 _ 0.05 76.1 _ 0.8 Schuh et al. (2000, 2001)

OA (AICAS) 1900 ... 1992 2.84 73.03 Vicente and Wilson (2002)

OA (AICAS) 1900 ... 1992 2.86 75.4 Vondr´ak (2000)

OA99(AICAS) 1900 ... 1992 2.81 _ 0.04 75.4 _ 0.9 Schuh et al. (2000, 2001)

OA00(AICAS) 1900 ... 1992 2.250 _ 0.010 59.58 _ 0.24 This study

EOP(IERS)C04 1962 ... 2002 4.554 _ 0.008 68.93 _ 0.09 This study

SPACE96(JPL) 1977 ... 1997 4.123 _ 0.002 73.9 _ 0.3 Gross and Vondr´ak (1999)

SPACE2001(JPL) 1977 ... 2002 3.521 _ 0.014 81.42 _ 0.17 This study

 

Thus, the most reliable trend estimate is likely to be obtained

from that time series. Accordingly, the Earth's rotation pole is found to drift at a mean linear rate of 3.901 4 0.022 mas

per year (or ca. 12 cm per year at the surface) in the direction towards 65.17 4 0.22_ West longitude. The cause of this

westward secular polar motion is most likely post-glacial rebound (see, e.g., Nakiboglu and Lambeck 1980, Milne and

Mitrovica 1998).

Concerning the drift of the Earth's rotation pole, we determined a mean linear rate of 3.901 4 0.022 mas per year in

the direction towards 65.17 4 0.22_ West longitude. Concerning the low-frequency variations, our results re-con_rm a

wobble with a ca. 30-year period, but only ca. 15 mas in amplitude (semi-major axis) at a direction of ca. 15_ East

longitude. Other signals, in particular those at 9 and 18 years are rather unstable in both amplitude and period.

Except between 1925.1927, the

variation in the Chandler period is between 410 and 442 days over the analysis intervals.

 

 

True Polar Wander 1962-1998
xy scatter chart in portrait by MWM
axisdrift_ave_annual_plot_1962-1998.gif

REDO THIS CHART FOR THE ENTIRE CENTURY OF DATA from iers.

 

HELLO THERE

 

problem is, this plot is a mathematical fiction, an illusion.

As can be seen in the next two charts, the Wobble MAX and Wobble MIN spirals revolve aournd a focal point which is not the same as the annual average points. 

 

For IERS stat average
This computation below creates an entirely different impression
of the drift of the North Spin Axis.
I think it mainly shows considerble annual instability. The X or Y MIN points
probably show the Spin Axis at its most stable points. Accordingly,
X MIN to X MIN, as above most likely show the best track for measuring the drift
 

 

True Polar Wander 1846-2003
computed from Wobble MAX phase
axisdrift_MAX_plot_1846-2003.gif

 

By comparing this chart with the previous one, we can easily see that the MAX phase spirals revolve around a focal point for the Spin Axis which is distinctly different than the mathematically created annnual "mean".

 

However, this chart is every bit as illusionary as the average one, even somewhat delusionary.

 

 

 

True Polar Wander 1894-2005
computed from Wobble MIN phase
axisdrift_MIN_plot_1846-2006.gif

 

Using the average annual positions is simple but it may not be the best method for describing the drift.  As can be seen in the spiral charts, the wobble has many complexities and patterns of variations.  

 

 

If we compute the average position of the Spin Axis during the Wobble MIN phase, we get a third answer. 

Which is the best method of calculation?  Probably this one for the following reasons.

When is the Earth MOST stable in the Wobble?  When is it is closest to its best balance?  Most likely this is when it is not wobbling or is wobbling the least. In other words, Wobble MIN phase is most likely the Earth at its best possible balance point. That point probably best defines the Earth's average Spin Axis every seven years.

Accordingly, if we calculate the mean X and Y Plot values just for the MIN years, and graph them as is done in this chart, we may be looking at the locations of the Spin Axis when the Earth is most stable. As can be seen, this definitely provides a different view of the path of the Spin Axis down Long. West 90. We can see a few fits and starts, which interestingly enough appear to trend at roughly a 45 degree angle upward toward the left.  And we can see that the rate of drift from stable point to stable point (MIN to MIN) has changed relatively dramatically during the past 112 years. As can be seen, most of the linear drift has occurred since 1948, and the greatest portion of this has occurred since 1958. Or, in other words, tectonic changes in the Earth have accelerated the most since 1958, the rate of change has varied from MIN to MIN, speeding up, then slowing down, then speeding up again, and most recently the graph shows a slower rate of change since about 1980.

What will it do next?  We really have no assured way to predict it using our databases and primitive understanding of the morphology of the Earth.  Our database is far too slim to make a strongly assured prediction. However, we can try to make some astute guesses. The Anomaly of 2005/2006 is of sufficient size, that it may be a harbinger of a period of greater chaotic motion.  The wobble may for the next 20 years become more chaotic in a manner similar to the wobble tracks between about 1925 and 1945. and late 50ls. It may well have the same kind of results.  A period of first a decrease in the size of the wobble and then an expansion of the wobble....an acceleration in the rate of drift,  greater tectonic activity, expansion of earthquake numbers, greater Rifting and subsidence, more volcanic activity and an acceleration of Global Warming.

Looking into the greater framework o fthe past several millenia, it is likely that the Earth is ON an upward curve in activity.  This upward curve could easily continue for the next several hundred

 

 

 

 years.

table in wobbleplots_1846-now.xls

 
Table Derived From the Graph:  Drift In The Average Position of the Spin Axis - As Calculated At Wobble MIN
these rates determined by mechanical method from the graph      
be careful, not all points are labeled on the chart.   TPW    
X MIN Wobble X MIN Wobble Difference Time In Ave/Yr    
Year Cycle Year Cycle Distance YRS Arcseconds Centimeters/Yr
1890 1 1919 6 0.05 29 0.0017 5.32  
1919 6 1927 7 0.07 8 0.0088 27.01  
1927 7 1942 9 0.08 15 0.0053 16.46  
1942 9 1961 12 0.05 19 0.0026 8.12  
1961 12 1968 13 0.075 7 0.0107 33.08  
1968 13 1974 14 0.03 6 0.0050 15.44  
1974 14 1980 15 0.075 6 0.0125 38.59  
1980 15 1993 17 0.0175 13 0.0013 4.16  
1993 17 2005 19 0.052 12 0.0043 13.38  
                 
1890 1 1942 9 0.1425 52 0.0027 8.46 worthless - hides exceptional variation
1919 6 2005 19 0.4495 86 0.0052 16.13  
1942 9 2005 19 0.2825 63 0.0045 13.84  
1993 17 1999 18 0.0245 6 0.0041 12.61  
1999   2005   0.02 6 0.0033 8.95 Don't use this bottom line as the ending year is uncertain

a)      Citations:    The constant of 12.13 centimeters used in this graph trend line is  the rate of drift or True Polar Wander of the Spin Axis calculated as the mathematical average for the period 1900-1999 by  Joachim Hopfner in his special report titled  “Low-Frequency Variations, Chandler And Annual Wobbles Of Polar Motion As Observed Over One Century"; published as “Science Technical Report ISSN 1610-0956”; January 2003 by the IERS (www.iers.org, International Earth Rotation Service, the world cooperative body which is the sole source of authoritative information on the location and behavior of the Spin Axis). Other geophysicists, using a shorter base of years during early parts of the 20th century, have computed rates which range between 10.05 and 10.4 centimeters per year.  For other discussions related to the drifting of the pole see articles posted at the IERS site and see also discussions in the “Return of the Phoenix:  Book Three – The Prophecies” and “Vortex Tectonics”  by MW Mandeville, published by MetaSyn Media at www.michaelmandeville.com

Table Derived From the Graph:  Drift In The Average Position of the Spin Axis - As Calculated At Wobble MIN
these rates determined by mechanical method from the graph      
be careful, not all points are labeled on the chart.   TPW    
X MIN Wobble X MIN Wobble Difference Time In Ave/Yr    
Year Cycle Year Cycle Distance YRS Arcseconds Centimeters/Yr
1890 1 1919 6 0.05 29 0.0017 5.32  
1919 6 1927 7 0.07 8 0.0088 27.01  
1927 7 1942 9 0.08 15 0.0053 16.46  
1942 9 1961 12 0.05 19 0.0026 8.12  
1961 12 1968 13 0.075 7 0.0107 33.08  
1968 13 1974 14 0.03 6 0.0050 15.44  
1974 14 1980 15 0.075 6 0.0125 38.59  
1980 15 1993 17 0.0175 13 0.0013 4.16  
1993 17 2005 19 0.052 12 0.0043 13.38  
                 
Some Period Comparisons            
1900   1999 authoritative average for 20th century 12.16 Joachim Hopfner, see cite below
1890 1 1942 9 0.1425 52 0.0027 8.46 worthless - hides exceptional variation
1919 6 2005 19 0.4495 86 0.0052 16.13  
1942 9 2005 19 0.2825 63 0.0045 13.84  
1993 17 1999 18 0.0245 6 0.0041 12.61  
1999   2005   0.02 6 0.0033 8.95 Don't use this bottom line as the ending year is uncertain

 

 

 

 


True Polar Cartoid Wobble Wander 1894-2006
computed from cartoid moments in the Wobble MIN phase
axisdrift_cartoid_plot_1894-2006.gif

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
Points derived from cartoid identification on the graphs - this is original data here
Prior to 1962, the EOPC01 series used, from 1962 to now the EOPC04 series is used
             
date x y        
2/5/1894 -0.00487 -0.04409        
2/23/1907 -0.00947 -0.02518        
4/20/1942 -0.01117 0.03393        
6/16/1967 -0.00225 0.16335        
8/27/1974 0.00857 0.20797        
1/13/2006 0.04854 0.380364        
date date Delta Period Rate Centimeters/Yr
1894 1907 0.02 13 0.001538 4.749231  
1907 1942 0.06 35 0.001714 5.292  
1942 1967 0.125 25 0.005 15.435  
1967 1974 0.045 7 0.006429 19.845  
1974 2006 0.17 32 0.005313 16.39969  
1907 2006 0.4 99 0.00404 12.47273 QUALIFICATION:  This sum excludes 1894-1907
2000 to 2006 = about .015 >>>>>>>>>>>>>>>>>>>>>> Note for this line:  this is by eyeball
2000 2006 0.0175 6 0.002917 9.00375  

 

     computed from "cartoid moments" in the Wobble MIN

 

 phase

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
2/5/1894 -0.00487 -0.04409        
2/23/1907 -0.00947 -0.02518        
4/20/1942 -0.01117 0.03393        
12/5/1961 -0.01871 0.14559        
6/16/1967 -0.00225 0.16335        
8/27/1974 0.00857 0.20797        
1/13/2006 0.04854 0.380364        
             
ALT TABLE WITH 1961 INCLUDED - problem with this one is the non-linear hop during 60's
date date Delta Period Rate Centimeters/Yr
1894 1907 0.02 13 0.001538 4.75  
1907 1942 0.06 35 0.001714 5.29  
1942 1961 0.11 19 0.005789 17.87  
1961 1967 0.022 6 0.003667 11.32 this cartoid only has a moment of about two days?  is it real?
1967 1974 0.045 7 0.006429 19.85  
1974 2006 0.17 32 0.005313 16.40  
1907 2006 0.407 99 0.004111 12.69 QUALIFICATION:  This sum excludes 1894-1907
2000 to 2006 = about .015 >>>>>>>>>>>>>>>>>>>>>> Note for this line:  this is by eyeball not from database
2000 2006 0.0175 6 0.002917 9.00375  
             
1967 2006 0.215 39 0.005513 17.01808  
1961 2006 0.237 45 0.005267 16.2582  

 

 

 

True Polar Cartoid Wobble Wander 1894-2006
computed from cartoid moments in the Wobble MIN phase
axisdrift_cartoid_plot_1894-2006.gif

Two trial preliminayr tables to spur discussion on this topic.  Some serious mathematical inquiry is highly appropriate here...

 

 

 

 

 

 

 

 

 

 

 

 

 

 
Points derived from cartoid identification on the graphs - this is original data here
Prior to 1962, the EOPC01 series used, from 1962 to now the EOPC04 series is used
             
date x y        
2/5/1894 -0.00487 -0.04409        
2/23/1907 -0.00947 -0.02518        
4/20/1942 -0.01117 0.03393        
6/16/1967 -0.00225 0.16335        
8/27/1974 0.00857 0.20797        
1/13/2006 0.04854 0.380364        
date date Delta Period Rate Centimeters/Yr
1894 1907 0.02 13 0.001538 4.749231  
1907 1942 0.06 35 0.001714 5.292  
1942 1967 0.125 25 0.005 15.435  
1967 1974 0.045 7 0.006429 19.845  
1974 2006 0.17 32 0.005313 16.39969  
1907 2006 0.4 99 0.00404 12.47273 QUALIFICATION:  This sum excludes 1894-1907
2000 to 2006 = about .015 >>>>>>>>>>>>>>>>>>>>>> Note for this line:  this is by eyeball
2000 2006 0.0175 6 0.002917 9.00375  

True Polar Wobble Wander 1894-2006 Deduced From Nine Cartoids
computed from 9 cartoid moments in the Wobble MIN phase (1961 added)
axisdrift_9cartoid_plot_1894-2006.gif

 

This alternative analysis graph helps us understand that there is some variation in the drift from wobble cartoid to cartoid.  It is also helps us to understand that there may be a problem of subjectivity is "seeing" some of the cartoid moments.

 

This graph is identical to the one above which is labeled simply "Cartoid Moments" with one exception.  A point was added for a cartoid in the MIN phase year of 1961.  This "cartoid" was not included in the first chart because the duration is only about two days.  This seemed a tad short and I excluded it to come to a "tighter" more objective number for True Polar Wander.

 

Later, after observing the apparantly powerful impact of Solar Activity Cycles 18 and 19 (peaks 1947 and 1958) on the Earth's Wobble, I decided to find numbers for the drift which included as much of the years after 1958 as possible.  The result is this graph of "Nine Cartoid Moments". 

 

As can be seen in the graph, the drift between 1942 and 1967 takes on a decidedly different twist, one which is more compelling in some ways than the first chart.  First, we see that from 1907 through to 1961 the drift is more linear and is moving briskly down Longitude West 95 (briskly compared to before 1907).  The greatest acceleration occurs after 1942 while the tracks of the X and Y Axis have begun to rapidly separate.  During 1947, a record high Sunspot Peak (Cycle 18) appears to increase the size of the wobble spirals and keep the pace of planetary change high. Both volcanism and earthquake activity above 4.0 begin to increase each year, establishing new tectonic trends.  Then the greatest solar event of Century 20, the peak of Sunspot Cycle 20  in 1958 appears to "set" the wobble towards a new direction.  This is not yet seen in the track in 1961 but the ensuring Wobble Cycle (#12) paints the track very well.  Point to point, 1962 to 2006, the angle of drift about 14 degress ( Long. West 76), point to point tween 1907 to 2006 (which is probably the best average), the apparant angle of drift is 7.5 degress (down Longitude West 82.5).

 

 

To see the sunspot cycle (annual average counts) in an expanded scrolling graph, see SUN.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
2/5/1894 -0.00487 -0.04409        
2/23/1907 -0.00947 -0.02518        
4/20/1942 -0.01117 0.03393        
12/5/1961 -0.01871 0.14559        
6/16/1967 -0.00225 0.16335        
8/27/1974 0.00857 0.20797        
1/13/2006 0.04854 0.380364        
             
ALT TABLE WITH 1961 INCLUDED - problem with this one is the non-linear hop during 60's
date date Delta Period Rate Centimeters/Yr
1894 1907 0.02 13 0.001538 4.75  
1907 1942 0.06 35 0.001714 5.29  
1942 1961 0.11 19 0.005789 17.87  
1961 1967 0.022 6 0.003667 11.32 this cartoid only has a moment of about two days?  is it real?
1967 1974 0.045 7 0.006429 19.85  
1974 2006 0.17 32 0.005313 16.40  
1907 2006 0.407 99 0.004111 12.69 QUALIFICATION:  This sum excludes 1894-1907
2000 to 2006 = about .015 >>>>>>>>>>>>>>>>>>>>>> Note for this line:  this is by eyeball not from database
2000 2006 0.0175 6 0.002917 9.00375  
             
1967 2006 0.215 39 0.005513 17.01808  
1961 2006 0.237 45 0.005267 16.2582  

 

 

 

Analysis Of The Cartoid Moment Which Ends/Begins
The Seven Year Wobble Cycle
giant line plot in landscape orientation by MWM
 

What is a "cartoid"

can be said to be the ending of one spiral and the spontaneous generation of another.

or the Yin Yang begin end transition of flux

use dictionary definition

copy from graph

Incorporate two small pix of two in this panel on the right side

abstract pix

pix of wobbletrack 2006 cartoid

Major Charts Which Demonstrate The Cartoid Moments In The Earth's Wobble

1.  Unmarked Seasonal X Plot 1890-2006

filename:  pm_seasonal_xplot_1890-2006.gif

 

This chart is the base chart which was used for the cartoid analysis.  It is the same chart as the Sunspot/Xplot correlation chart except that it has been expanded horizontally to show each quarter of the year distinctly enough to spot seasonal fluctuations in the wobbling of the Spin Axis.  This is necessary for finding visually the key transition moments in the wobble.  This clean chart is provided for suitable mark-up.  Look for the cartoids and then compare with the author's picks.  You come up with a better list, the author did not try to define every cartoid moment, only a few to illustrate the concepts and main findings.

 

2. Cartoids In The Earth's Wobble on the X Axis 1890-2006
filename:  pm_cartoids_xplot_1890-2006.gif

 

This chart probably reveals the moments of absolute stability in the Spin Axis every seven years which may be the best positions for plotting the true, absolute drift in the location of the Poles.

 

Once spotted, as circled on this graph, go to the database

(wobble dahdah.xls) and find the transistion points

where the motion reverses itself.  going trom neg to pos or from pos to neg as the case may be.

 

define the exact spot of transistion....add 14 months backwards and forwards (a total of two "average" wobble spirals) to define the entire Wobble MIN phase, then use the dates to spin out a wobble spiral using suitable graph in spreadsheet or in wobbletrack. beforehand, use red, after the key date, use green, defines the Yin-Yang of the Spiral.  As can be seen, the Earth's zen moment is not exactly exact.

 

Varies in size, varies in length, has many irregularities which show as "dents".  These are probably related to weather, magnetic, seasonal, lunar changes in the mass or spin rate of the Earth.  If the Earth is close to its "perfect" balance point, all of these typical surface effects should be reflected in the exact location and motion of the Spin Axis, and it would appear from the irregularities in the track that they indeed can be seen and thus measured in the polar motion data.

 



As one patiently scrolls back and forth through the X Plot for Century 20, a few things become reasonably clear:

Several Cartoid functions appear in the MIN phase

spot them by looking for a sudden short reversals of motion on the X plot

 

first example

 

here is what one looks like as a spiral track.  red- 14 month spiral track curls down into a small track and then begins a reversal of motion in what appears to be a very small jiggle, which is actually a spiral track. 

 

show this example in wobble tracker format to the right.


The cartoid functions which are circled in red define the classic spiral transistion from Yin to Yang (End to Begin), which is the point when the curling inward track line of the spiral changes into an outward expanding line,. Within each read circle there is an exact "cartoid moment"j. Some of the exact moments can be seen in this graph but it takes spiral charts to see that they are in fact somewhat imperfect caritoid functionsl These points most likely represent the Spin Axis at its most stable point of balance, all mass vectors momentarily balanced, hence these cartoid points may be the best definitions of the absolute average positions of the Spin Axis. If so, true migraton of the Spin Axis can be easily (and best) calculated from these points, allowing long-term analysts to ignore all other spiral plot data.

 


The cartoids are obvious during the smallest MIN phases and become less obvious the larger the MIN.

In a few of the MINS, the smallest spiral is so large and smooth, the cartoids cannot be distinquised

Wobble Cycles 3, 4, and 5
priod to Wobble MAX in 1916

W6 in 1918 east ti spot
W6-W7, chaotic transistion
major time shift, at least two minor cartoids, perhaps three
1925-1928 as if an additional year inserted into the Wobble Cycle

 

 

Length Of Day 1623-2005 
line graph in portrait orientation
file name:
http://hpiers.obspm.fr/eop-pc/earthor/ut1lod/lod-1623.jpg
site source: http://hpiers.obspm.fr/eop-pc/


Long term variation in the length of day from 1623 to 2000 
(reference value is 86400s TAI)

Scale:  milliseconds

Value:  computed as the average annual deviation centered at mid-year

Like the coordinates of location for the Spin Axis, the Length of Day is unstable from week to week. The "averages" filter out significant variations.  These variations are probably the best key for connecting to how the cosmos triggers and fluxes the rate of rotation of the Earth (Length of Day).

MWM has not taken up this study as of 2007.

Obvious Observations: 

1.  There does not appear to be any significant short term correlation in the LOD with cycles of less than 40 years.  There may be correlation with long term Solar Activity and/or as defined by changes in the orbital cycle of Earth and its near neighbors.

2.  There is a degree of similarity (isomorphism) between the LOD long term curve and the curve of sufur dioxide ions in Greenland Ice core from 1800 to 2000.  Does this indicate a tectonic connection via volcanic activity?  This is worth some additional study but it is not a speculation I can build upon at this moment.

3.  There is also a degree of similarity between the LOD curve and the 200-year deVries Solar Activity Cycle. [click to see graph]  In this cycle, the 11 year Solar Activity Cycle becomes relatively high for 100 years and then relatively low for 100 years.  This cycle is clearly significant, such as pointed out by (Vasil’ev et al., 1999 and Wagner et al., 2001, because it produced the well known major climate variations of the past several hundred years, including the Maunder Minima in solar activity which produced the so-called "Little Ice Age".  There is a good fit between the curves for the "Little Ice Age" during the 1600's.  There is a small correspondence for the next cool period during the early 1800's. 

4.  If there is a correlation here, it must be based on the alteration of Earth's dynamic spin/orbit of rotation in some synchronicity with a 200 year shift in the average magnitude of the Solar Activity.  Is this correlation as simple as long term changes in the average solar wind which acts to load or lighten average drag on Earth's magnetosphere and/or atmosphere?  Again, this is worth further investigation but is not usefully used in speculation as of 2007.