Geodynamics and Geomagnetism*
Autumn Term 2016

*Note, the course title is to be changed to
Global Geodynamics and Climate Change

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News: 2016


November 1, 2016: All the midterms are in and we are beginning to grade them. What was expected? Olivia's answer to Question #1.

Note that next day's lecture (November 3) will be given by Erik Chan. We shall post his slideset as soon as we receive a copy from Erik.

October 27, 2016: Today, we assign the take-home midterm test. It is worth 20% of your grade. It is due on Monday, the 31st at noon. For question #1, should you take it to the fussy level of physics, taking into account the Moon's orbital eccentricity, you might look to the Michael Fowler (UVa) noteset on elliptical orbits.

Natalya's slideset for today's lecture are here: October 27.

October 13,20, 2016: Natalya's lecture slidesets are available online here: October 6, October 13, October 20. On November 3, Erik Chan will be giving a lecture that extends what both Natalya and I have brought to you and introduces Geomagnetism. He suggests the attached papers (available in *.pdf form here and in myCourses):

Sabine Stanley, Linda Elkins-Tanton, Maria T. Zuber, E. Marc Parmentier, Mars' Paleomagnetic Field as a Result of a Single Hemisphere Dynamo, Science  26 Sep 2008: Vol. 321, Issue 5897, pp. 1822-1825 (doi: 10.1126/science.1161119)
J. Turadano, Hum from the Quiet Zone, Nature Geooscience Vol 5 March 2012 (News and Views)
W. Kuang, W. Jiang, J. Roberts, and H. V. Frey, Could giant basin-forming impacts have killed Martian dynamo? Geophysical Research Letters 2014, p. 8006-8012. (doi:10.1002/2014GL061818)

October 6, 2016: Now as we move into Module 2 (Geodynamics of Climate Change), Natalya has arranged a new series of papers. They are available on the myCourses site in *.pdf form and are listed here in reference form:

J. Mitrovica et al., Reconciling past changes in Earth’s rotation with 20th century global sea-level rise: Resolving Munk’s enigma Science Advances  11 Dec 2015: Vol. 1, no. 11, e1500679 (doi: 10.1126/sciadv.1500679) also here!,
Tamisiea ME, Hughes CW, Williams SDP, Bingley RM. Sea level: measuring the bounding surfaces of the ocean. Phil. Trans. R. Soc. A 372: 20130336. 2014 (doi:10.1098/rsta.2013.0336)
P. U. Clark, J. X. Mitrovica, G. A. Milne, M. E. Tamisiea , Sea-Level Fingerprinting as a Direct Test for the Source of Global Meltwater Pulse IA, Science 29 March 2002 VOL 295 (doi: 10.1126/science.1068797)
Jerry X. Mitrovica, Mark E. Tamisiea, James L. Davis & Glenn A. Milne, Recent mass balance of polar ice sheets inferred from patterns of global sea-level change, Nature 22 February 2001 VOL 409
Kurt Lambeck,, Marco Anzidei, Fabrizio Antonioli, Alessandra Benini, Alessandra Esposito, Sea level in Roman time in the Central Mediterranean and implications for recent change, Earth and Planetary Science Letters 224 (2004) 563– 575
Jacqueline Austermann, Jerry X. Mitrovica, Konstantin Latychev and Glenn A. Milne, Barbados-based estimate of ice volume at Last Glacial Maximum affected by subducted plate Nature Geoscinece JULY 2013 VOL 6 (doi: 10.1038/NGEO1859)
Robert M. DeConto & David Pollard, Contribution of Antarctica to past and future sea-level rise, Nature 31 March 2016 VOL 531 p. 591 (doi:10.1038/nature17145)
... and Jeff Tollefson (In Focus News item), Trigger seen for Antarctic collapse, Nature 31 March 2016 VOL 531 p. 562 (doi:10.1038/531562a)
Robert Steven Nerem, Éric Leuliette, Anny Cazenave, Present-day sea-level change: A review C. R. Geoscience 338 (2006) 1077–1083, also available here!

September 29, 2016: For this evening's session, we are asking each of you to bring, either singly or in groups, a topic to the table and lead a discussion on the topic. In the past few days, topics that bridge from Module 1 into Module 2 have been in the news: 1. Greenland ice sheet melting 7% faster than believed , 2. Melting Greenland ice changing ocean circulation and Earth's gravitational field , 3. 'Out of time', (a political story), 4. Climate Change Is Moving the North Pole

If you haven't chosen your topic to bring to discussion, perhaps you find some interest in these. You might look to the papers referenced in these news items.

And more: on Precambrian rotation, on Tidal Rhythmites ..., on Precambrian length of day and the validity of ..., on Surface temperature and rotation rate..., from Medieval Eclipse records, and from J.X. Mitrovica: Eclipses and Sea Level... If it is already 4:30 and you have nothing, pick off one of these...

September 22, 2016: Please look to the Course overview page (in banner above) for the three papers we shall discuss this week. In preparing for discussions, I ask you to read them.

D.E. Smylie and M. Zuberi, Free and forced polar motion and modern observations of the Chandler wobble, Journal of Geodynamics 2009 48/3-5 226-229 (doi: 10.1016/j.jog.2009.09.028 )
S. Adhikari and E. R. Ivins, Climate-driven polar motion: 20032015, Science Advances 8 April 2016; Vol. 2, no. 4, e1501693 (doi: 10.1126/sciadv.1501693) also here!
L. Chen, et al., Rapid ice melting drives Earth's pole to the east , Geophysical research letters, Volume 40, Issue 11, 16 June 2013, 2625–2630(doi: 10.1002/grl.50552)
Some other references:
Yoder et al., Secular variation of Earth's gravitational harmonic J2 coefficient from Lageos and nontidal acceleration of Earth rotation, Nature Volume 303, no. 5920, June 30, 1983.
Qu, W. and Wu, B., Analysis of the characteristics of the harmonics coefficient J2 of the Earth’s gravity field in different periods, Chinese Science Bulletin, Vol. 57, p 1626, 2012.

Mitrovica, J., Milne, G. and Davis, J., Glacial isostatic adjustment on a rotating earth, Geophys. J. Int. 2001, 147, 562–578 and here!
Gross, R. and Chao, B., The rotational and gravitational signature of the December 26, 2004 Sumatran earthquake, Surveys in Geophysics, Vol. 277, no. 6, 615-632, 2006 ... and here!

Illustrative data and plots (EOP CO4 Combined series) from Earth Orientation Centre, Paris Observatory – current.
On post-glacial rebound and Earth's changing shape. Search “post glacial rebound” with Google Images....
The following papers might be alluded to but they are offered only as reference.
P. Wu and W.R. Peltier, Pleistocene deglaciation and the Earth's rotation, The Geophysical journal of the Royal Astronomical Society 1984 76/3 753 -791 (doi: 10.1111/j.1365-246X.1984.tb01920.x)
V. Dehant et al., Considerations concerning non-rigid Earth nutation theory, Celestial mechanics & dynamical astronomy 72/4 245-310 (doi: 10.1023/A:1008364926215 )
Should you become interested in the detailed analysis of the Earth's gravity field and what our knowledge of that field informs us about the mass distribution within the Earth, you might look to Chapter 2 from the “book” served by Brad Hager in his comprehensive introductory graduate course “ 12.201/501  ESSENTIALS OF GEOPHYSICSgiven at MIT in 2002.

September 9, 2016: When I translate from calendar days to a continuous series of equal length days that closely and integrally fit the year on a relatively short cycle, I use the length of year to be 365.2422 days. This causes a 1-day step out every 45,000 years. The Gregorian calendar of civil use has for reasons of simplicity chosen 365.2425 days for the length of year. It accumulates a 1-day step out every 3300 years. Online, I found a very interesting high-school-level exercise on calendar design. It might interest you: How many days are in a year?

September 8, 2016: Today, Olivia will lecture on math/physics expectations and Gravity. Of more interest: Come to the Departmental BBQ on Saturday!

September 7, 2016: We have a time for the course that accommodates most of us. Unfortunately, it does not serve all of us. We lost one student to this time. We are meeting Thursday evenings, 5:30-8:30PM. We should be able to take room FDA 232 (preferred) or FDA 348 (backup).

September 6, 2016: We are choosing our course time... Here is a starting schedule: Weekly_timetable.xls

As we complete the first lecture, expecting that you will review Olivia's story so far, she offers another story that you might find intriguing. This short lecture on Pythagoras' Theorem leads to Relativity Theory: Gravitation.

Bill Minarik alerted me to a website that shows the Sun's orbit about the barycentre (COM) of the Solar System.

August 29, 2016: On September 6 at 5:30PM in Room FD Adams 348, we should meet to choose a time and place for this course. Tentatively, it is scheduled for 5:30-8:30PM on Wednesday evenings. This might not be convenient or even possible for all of us so we will look for a schedule that can work for everyone. We will accommodate you!

April 27, 2016: This course is now scheduled for the Autumn term of 2016. The website will be redacted to reflect this change during the next few weeks.

February 9, 2016: It was reported that the Honshu-2011 earthquake measurably changed the Earth's rotation axis and the length of day: LOD record. Pole path and Excess LOD plots show little unexpected variations due to the event, in my opinion. Data on pole position and variation is rotation rate are available from the IERS.


News: 2014


August 7, 2014: The course lectures should begin during the first week of September but we, first, have to schedule lecture places and times. I propose that we do this at 5:00PM on Wednesday September 3 in FDAdams 232.

September 16, 2014: We are now meeting on Tuesdays and Thursdays, 5:30PM to 7:00PM in FD Adams 348. For lecture topics of the day, click on Lectures in the banner above.

September 17, 2014: I have edited and extended with one diagram the Chandler Data Modelling note.

September 18, 2014: We have now been assigned FDAdams 232 as our classroom for the rest of term. Still, there may be a few sessions for which we are asked to retreat to FDA 348.

September 23, 2014: We have something of the theory of polar motions; today, I open the floor for discussions and explanations (as far as I am capable) and introduce another paper of some interest in that it argues for a climate signal in the recent polar motion: Rapid ice melting drives Earth's pole to the east

September 25, 2014: Today, we shall receive your presentations. Please keep them short enough to give us some time to discuss them following. I suggest 12-15 minutes followed by 15-12 minutes of discussion. I shall have a Mac miniDV-to-HDMI adapter, a Mac miniDV-to-VGA adapter but I don't yet have a microHDMI-to-HDMI adapter for the MicroSoft Surface or for the department's Lenova laptop. You can bring your presentation on a USB stick but do be careful to include all diagrams that you might be using on the memory stick as well.

September 30, 2014: We start Module 2 with a short presentation: Geodynamics-Tectonics. This is a topic that most of you are familiar with so let us share our insights. I shall try to ask you leading questions that bring you to a somewhat deeper questioning and understanding of what you and I think we know about mantle and lithospheric dynamics.

October 7, 2014: Skim through the first chapter of Geodynamics with a view to bringing critique to my story as I continue to tell it via the Geodynamics-Tectonics PowerPoint lecture. Break in on my story whenever and often.

October 9, 2014: I shall finally finish the Geodynamics-Tectonics lecture (far too long and slow), invite you into a discussion about that material before taking you to something of the History and Story of Plate Tectonics.

In preparation for next week's classes, I ask that each of you take on a description of a problem in lithospheric geostatics/geodynamics and lead a short discussion on your topic during next Tuesday and/or Thursday classes. For reference, I suggest the text (online: Geodynamics edition 2) or the current edition 3 which is available in the library. I gave my copy to Christie. She might lend it to you for a few days. I don't ask you to delve deeply into the mathematical/physical arguments but I would like you to try to understand the results of these analyses.

Problems suggested:

    1. 3.16 Bending of the Elastic Lithosphere under the Loads of Island Chains: This problem gives us a measure of the the “equivalent” thickness of the oceanic lithosphere. Actually, it allows us to obtain a measure of the flexural rigidity, D. D is a parameter that combines the elastic properties and thickness of an equivalent uniform plate (eqn. 3.72, Geodynamics ed. 2). Recall the description of elastic constants from Earthquakes and Structures: Relationships among elastic constants.

    2. 3.17 Bending of the Elastic Lithosphere at an Ocean Trench: This problem describes the bulge of a subducting plate before it reaches the trench. The analysis follows that of the previous section.

    3. 8.4 Anderson Theory of Faulting: This problem and description might be particularly appropriate to those of you who are interested in seismology. We did not cover this analysis in Earthquakes and Earth Structures but you could address it now and here. Subduction faults seem to show very low coefficients of friction[1], [2], [3]

    4. 4.24 Changes in Sea Level: In the last lecture, we dealt with the problem of the thickening oceanic lithosphere. The isostatic adjustments involved in the cooling of the lithosphere have important implications for “sea level”. This might offer something of an enlarged view with respect to just what does control sea-level. There is more to it than accumulation and melting of grounded ice.

    5. 5.14 Forces Required to Maintain Topography and the Geoid: Continents are under a generally tensile lateral stress field even in orogenic zones of “relative” compression. This introduces a classical problem in in-situ stress measurement. For this topic, you might have to do a little digging earlier in the text.

    6. And/or then anything: that you find interesting with respect to geostatics and geodynamics that you might like to discuss in Tuesday's class.

For interest: http://www.humboldt-foundation.de/web/kosmos-humboldtians-in-focus-102-3.html

October 14, 2014: Today, I am asking that we discuss some of the problems listed above with each of you directing one discussion. This exercise will substitute for the “presentation” for the Mantle/Lithosphere Geodynamics module. The essential equation describing the flexure of a plate is shown in this brief page: Bending of plates. As in most physical problems, the basic differential system can appear as very simple very mathematics; the art of the physicist is in applying physical constraints for the solution through boundary and/or initial conditions. A general solution of this particular system is essentially quite a simple sequential integration. As it is a fourth order system, though, the geophysicist is faced with recognizing four boundary conditions that establish the four constants of sequential integration.

October 16, 2014: Today, October 16, we should finish up our brief exploration of mantle and lithospheric tectonics with Ariane's story today.

Note: I have scheduled the take-home midterm for Tuesday, October 21 to be handed in during the class of Thursday, October 23. I ask that each of you provide a short question for the midterm and either a reference link in partial explanation of the context of the question or your classroom *.ppt presentation.

Also note that last week's News and Highlights page crashed and this is a much shortened facsimile.

For October 21, 2014: I am just now composing the short midterm based on your questions relating to the presentations you gave in the Global Geodynamics module. I am, at the moment, still missing a question from Kelian and Ariane. As soon as I get them, I'll re-edit the midterm. We shall discuss the midterm tomorrow in class. Link to Midterm .

For October 23, 2014: I shall expect your midterms to be handed in during the Thursday lecture. Then we/I shall begin the story of Geomagnetism. I would like you to review, read or glance through the first 10 or so pages of this EM summary... and introduce yourself to Self-exciting Dynamos. While geophysical electromagnetics is not the immediate topic, for interest, I refer you to a lecture module that I produced for Earth Physics when I last gave that course: EM-MT. We have the Geomagnetism module and the “Spherical Earth” module yet to cover. I shall ask you to address the Geomagnetism module with a presentation in mid-November; the subsequent “Spherical Earth” module is not intended to be so much studied as informed. That is, I would like you to carry away some understanding of the major tool for geophysical analysis on a spherical Earth: Spherical Harmonic Decomposition.

October 23, 2014: On November 6 at 6:00PM, Nobel Laureate (2012) David Wineland delivers the Anna McPherson public lecture in Physics. His evening lecture is entitled “Quantum Computers and Schroedinger's Cat. While this lecture might not be especially relevant to our course, his PhysSoc lecture on Friday afternoon could well be: “Single Atom Optical Clocks. His work leads to our very best atomic time standards. As the Anna McPherson lecture series is the pre-eminent in Physics at McGill, I would like to suggest that we take in his evening lecture on November 6 rather than the lecture in this course and if you can find the time, his PhysSoc lecture Friday, November 7.

October 28, 2014: Today, I shall return the midterms to you and briefly discuss them and the strategy and style in marking. Everyone does very well – no one should worry about getting good grades at the end of term. I shall then return to my lecture stories and open up the papers that I suggest for the Geomagnetism module.

October 30, 2014: Note that next Tuesday Andre Pellerin defends his Ph.D. thesis in this room from 2:30 onwards. The defence will surely be over by our course time but, as always, when a Ph.D. student finishes his degree, we celebrate. I invite you to take some part in the celebration that will be taking place in the hallway outside this room but then to join our class at 6:00PM.

Also, next Thursday, I would like you to join me for the lecture by David Wineland (see link above) which takes place at the very same time as our course. Wineland is a Nobel Laureate in Physics and should give a good talk.

November 4, 2014: Again, let me remind you that I am asking that you attend David Wineland's lecture at 6:00PM in Leacock 132. The Anna McPherson public lecture in Physics is the major event on the Physics calendar each year. Usually these talks by Nobel Laureates and other major scientists who might well win such acclaim over the next few years are very well delivered. While this topic is not directly relevant to our course, the following lecture on Friday afternoon is not too distant from the stories that I have been lecturing. Ever more accurate time keeping is extremely important in Physics and the geophysical relationship to atomic time is one of our responsibilities as global geodynamicists.

November 11, 2014: The final take-home exam is centrally scheduled as follows: EPSC 510 001 Geodynamics and Geomag Dec 08 9 am HOME I shall, however, post the exam on Friday December 5 on the course website so that those of you who are trying to catch flights home can receive and complete the exam early.

November 13, 2014: Rosetta: perhaps the event has most excited earth scientists in the last days is that of the landing of Philae on Comet G67. This event probably excites the geochemists and cosmochemists among us as much as a Mw ~ 8 event on the San Andreas would excite our seismologists. Geo(cometary)magnetism is not entirely irrelevant to the Rosetta/Philae mission. We are interested in the primordial magnetic field conditions in which G67coalesced and how the comet's magnetic field, as small as it must be, interacts with the plasma of the solar wind (RPC-Mag experiment).

November 18, 2014: Last day, we did 4 of 5 presentaions. Only Ariane's is left to do. Expecting that Ariane will offer her final presentation, I shall take the final hour of the class to extend my lecture on Harmonic continuation. The noteset has been somewhat expanded so I suggest that you might replace that that you may have saved with the new version.

November 20, 2014: Our last lecture is scheduled for December 1. For that lecture, I would like to engage you in a conversation about all 4 Modules of the course. For next Thursday's lecture, I should have finished all I wanted to lecture to you and so might offer to discuss the questions and expectations that I have referenced for the final take-home exam.

November 25, 2014: Two more lectures, then on Tuesday next, I'll answer any questions you have concerning the course materials past and introduce you to questions 1 and 3 for the final take-home exam. Question 2 was addressed in the last class. While it has nothing at all to do with this course, I shall be giving a lecture/presentation in Psychology 436 on Thursday morning at 10:00AM. The course room is Stewart Biology Building w2/2 (enter through main doors on Penfield Avenue, just “west” of Peel.)

December 2, 2014: Last lecture! I am in the process of constructing the final exam. It will have 4 questions, one from each of the 4 Modules of the course. I am open to answering any questions that you may have about the final here today. I would like you to do the exam without any further help or explanation from me. I shall post the exam on this website on Friday afternoon or Saturday morning with link here: Final-2014 . I shall also provide printed copies of the exam in the main office for 9:00AM, Monday, December 8.







For news and highlights items from previous year's courses, click here!



 

 

 

 

 

  News and highlights

© Olivia Jensen, McGill University
Images: Courtesy NASA/JPL/USGS
Web concept: Witold Ciolkiewicz
updated: 01/11/2016 12:24:16