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Geodynamics
and Geomagnetism* *Note,
the course title is to be changed to
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Home I Course overview I News and highlights I Notes, materials I Websites I Lectures I Backup site |
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Lectures |
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October 27, 2016: Natalya finishes her series of lectures with “Ice”: Lecture 4 slides. The take-home midterm is assigned: Midterm-2016.pdf October 20, 2016: I (Olivia) shall miss today's sessions. Natalya will continue with her lectures on Sea Level Change: Lecture 3 slides. October 13, 2016: Natalya continues with a lecture on Sea Level Change: Lecture 2 slides Following the lecture, we encourage you to question/answer/discuss this topic and that of the week past. October 6, 2016: Now we move on to Geodynamics of Climate Change..., Natalya will open the module with a lecture concerning isostasy, ice-flow, rheologies... Lecture 1 slides For those who took Earthquakes and Structures last year, I also link the Rheologies and introductory Stress-Strain notesets. In recollection of an earlier version of GG510, Geodynamics and Tectonics . Following this lecture, we will complete the discussion started last day and led by you, the students. For the continuing sessions, the following papers are suggested: 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 Geoscience 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! Anny Cazenave and William Llovel, Contemporary Sea Level Rise Annual Review of Marine Science 2010 Vol. 2: 145-173 (doi:10.1146/annurev-marine-120308-081105) September 29, 2016: Your turn to lead discussions on papers and issues that interest you. September 22, 2016: Today's class will take the form of a discussion seminar. Please come ready to participate. No question you may ask or answer you might offer will be seen as “silly”. The topics for today's discussion that I shall lead are those of the suggested papers for Module 1:
September 8/15, 2016: Now, we start Module 1 with two lecture sessions leading to our discussion sessions of September 22 and 29. As we are not going to lecture this material, we ask you to pay attention to the topics linked below under heading “Some further review and tools”. Olivia continues with “A little math, a little physics” and then will start “Gravity”. Next day the lecture moves on to Chandler Data Modelling and the theory of AR-Inversion as we look for the driving “innovations” of the pole-path motion. You might look ahead to the paper by Smylie and Zuberi (earthquakes), Adhikari and Ivens (climate) and Chen et al. (ice melt) ... for September 22, we would like to open discussion of these papers. For September 29, we would like you to lead the discussions on other drivers of geodynamical changes. Some diagrams concerning Chandler and Annual wobbles: SimpleChandler Chandler innovated Annual noise free Annual 20% Noise Annual 20% Modulated 20% Noise 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 shall meet in FD Adams 348 to arrange our time-table for the course. Do come to this meeting. For week of September 6, 2016: When we find a time and place for the course, Olivia will offer the first lecture next week. It will deal with my/our expectations for the mathematics and basic physics that you are expected to know as you start this course. We don't ask for highly developed skills in mathematical manipulation but we do expect that you understand mathematical principles and the use of mathematical tools. You should come from this and the following lecture with almost all you need know about math and physics... and then we can get on with the course. You might review “A little math, a little physics” as was introduced in last year's Earthquakes and Structures course. Some further review and tools: Error analysis and significant figures: It is very important that one report the results of calculations and experiments properly in science. The advent of hand calculators and computer codes used in analysis has left many of us and you with extremely sloppy calculation habits. Read this and then know why the following numbers all represent different results: 2. , 2.0, 2.00, etc.. Everyone of these numbers means something quite different from the others. Wolfram|Alpha online search engine: Try this: enter "integrate 1/ln(x) dx" into the window. This "search" engine could prove very useful to you when managing some mathematical manipulations. For the week of September 13: Should we have a schedule with a 3-hour session, I (Olivia) would continue with the lecture that takes us into the topics of Module 1: “Gravity”. We shall, here, learn something about the dynamics of the Chandler Wobble and how it is that we might model it: Chandler Data Modelling. We shall recognize that we might sufficiently describe the wobble with an AR (autoregressive) model with a single complex-valued coefficient. The theory of AR-Inversion will be referenced.
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September 3, 2014: We shall meet in FD Adams 232 to arrange for a time and place that does not conflict with your schedules or mine. Until then, we can't know when or where we will be meeting. For week of September 8, 2014: Having found a time and place for the course, the first lecture next week will deal with my/our expectations for the mathematics and basic physics that you are expected to know as you start this course. I don't ask for highly developed skills in mathematical manipulation but I shall expect that you understand mathematical principles and the use of mathematical tools. You should come out of those lectures with almost all you need know about math and physics... and then we can get on with the course. You might review “A little math, a little physics” as was introduced in last year's Earthquakes and Structures course. Some further review and tools: Error analysis and significant figures: It is very important that one report the results of calculations and experiments properly in science. The advent of hand calculators and computer codes used in analysis has left many of us and you with extremely sloppy calculation habits. Read this and then know why the following numbers all represent different results: 2. , 2.0, 2.00, etc.. Everyone of these numbers means something quite different from the others. Wolfram|Alpha online search engine: Try this: enter "integrate 1/ln(x) dx" into the window. This "search" engine could prove very useful to you when managing some mathematical manipulations. September 10(?): Cancelled due to field trips September 16, 2014: Having finished the introductory lecture “A little math, a little physics”, I would now like to continue with the lecture which takes us into the topics of Module 1: “Gravity”. We shall, here, learn something about the dynamics of the Chandler Wobble and how it is that we might model it: Chandler Data Modelling. We shall recognize that we might sufficiently describe the wobble with an AR (autoregressive) model with a single complex-valued coefficient. The theory of AR-Inversion will be referenced. Assignment for next day: Read the paper by Smylie and Zuberi; we shall discuss this next day. Also, skim the paper by Wu and Peltier with the intention of trying to understand that they determined the cause of the J2-Spindown-deficit. More simply, I refer you to an excellent term paper submitted on the subject by three students, Baretto., Fortin and Iredale, from my Earth Physics course of 2010. September 18, 2014: As I am not rushing through these materials as quickly as I may have wanted to, we shall pick up the very last elements of Gravity, describe Chandler Data Modelling and show you the linear algebra that one might use in computing the AR coefficients (for Isabel who like linear algebra), AR-Inversion. We shall then discuss the papers starting mid-class and continuing through next day's period. Assignment for next Thursday, September 25: I ask you to group with one other person in the class and with your partner, prepare a short presentation (10 minutes, 6 or 7 slides) to offer to the class on some aspect related to the topics of this first Module on Global Geodynamics. You can address anything you like that you feel fits the question. I would like you to save your presentation in *.ppt (PowerPoint) format if you would like to use my computer for projection. If you are using either diagrams or images that might reside on your computer, you should be careful to bring them “in-line” in the PowerPoint file. If you are using diagrams or images that are on-line via the Internet, it shouldn't be necessary to bring them “in-line” into the file. If you are using Keynote on a Mac, you will have to export your presentation in *.ppt form or, better, use your own Mac laptop. I shall bring a MiniDV-to-HDMI or MiniDV-to-VGA adapter to class for Macs. 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. You might look to a brief explanation of Plate Bending and Flexural Rigidity: Bending of Plates and look to Sections 3.16 of Turcotte and Schubert's Geodynamics. Today, I am asking you to lead a discussion on a topic of your choice, selected from the text, relevant to static deformations of lithospheric plates. October 14/16, 2014: 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. See News and Highlights As we start the geomagnetism section, I refer you to a rather nice introductory lecture set on Dynamo Theory by Richard Allen of the Berkeley Seismological Laboratory: the noteset. You might recognize a rather elaborately confused field solution is obtained by the Glatzmaier-Roberts dynamo model. It attempts to describe a chaotic system. I bring you back to a question concerning chaotic systems. It is argued that the mathematical system that we have used to describe models of the geomagnetic dynamo, those models which actually reverse polarity, is inherently chaotic. Chaotic systems are often characterized by sticky solutions called “strange attractors”. The attractor solutions in the case of the geodynamo are the two metastable polarities that arise as the modelled systems evolve. One of the simplest chaotic systems is described by the recursion: xi = 4 xi-1 (1-xi-1). Starting this recursion with any number in the range (0, 1) except for (exactly) ¼ or ¾ which recurse to a stable attractor at ¾, or ½ or 1 which recurse to a stable attractor at 0,we seem to obtain “deterministically unpredictable” (an oxymoron) future values. Actually, in doing the calculation, using digital computers, one quickly excites this system with small random “round-off” error which leads to a computer-dependent series. That is, in the computer modelling, we can only approximate the evolution of the series. Change the resolution of your computer mathematics and the recursion changes though the attractors at 0 and ¾ are still closely approached over and over again in the recursion. The problem inherent in digital computer approximations to the mathematics is that computers are only able to describe rational fractions with a rather limited set of numerator and denominator values that can be described in binary form. Look to these WikiPedia explanations of floating point number formats: IEEE-754-2008 Single Precision format, IEEE-754-2008 Double Precision format. See also Noise and Chaos and the article by Crossley, Jensen and Jacobs: The stochastic excitation of reversals in simple dynamos October 23, 2014: Expecting that you have now completed your midterm, you might relax to a couple of lectures. First I shall offer a powerpoint set: Introduction to Geomagnetism. I argue that through geomagnetics, we have discovered much about the tectonics/geodynamics of our planet and, perhaps, something about Mars and Mercury. I have also produced a couple of notesets, one so-far incomplete, that should bring us to understand some basic theory concerning electricity and magnetism – a review of your physics.. Geomagnetics introduces some of the theory – but it doesn't take us to understanding dynamos yet! Another noteset, EM-MT introduces the theory of magneto-tellurics, currents excited within the body of the Earth due to variations in the external component of the magnetic fields. Magneto-tellurics offers a very useful tool for sounding the electrical and magnetic properties of the crust and upper mantle. Some of the introductory theory here overlaps with that in the previous Geomagnetics notes. I'll skip across the redundancy. I introduce the International Geomagnetic Reference Field – Generation 11. Maps of Declination/Inclination/Field and Projected Temporal Change . Based on that field model, the NRCanada calculator for local field and field component strength and orientations. October 28, 2014: The two notesets, EM-MT and Geomagnetics, are somewhat redundant. I'll introduce the EM-MT one and then quickly move through the Geomagnetics one while trying to skip redundancy but first, I'll finish off the IGRF discussion and lead you to calculators that provide reference field strengths and directions at any point on Earth. I referenced the NRCanada calculator last day (above); NOAA (National Oceanography and Atmospheres Agency) also provide a nice calculator. Earlier, in the Geodynamics-Tectonics noteset, we discussed the heat sources that drive the geodynamo. I shall leave you with another brief PowerPoint noteset from my 2010 Earth Physics course that discusses the Interior Heat and Temperature. October 30, 2014: It might be well to review the Earth Physics noteset, Interior Heat and Temperature, as it relates somewhat to one question that I shall ask on the take-home final. You might begin to think about this question: Given what we have estimated to be the thermal parameters of the layered Earth's interior and the post-perovskite transition temperature as determined by Kei Hirose (assigned at the top of the D'' layer), obtain a temperature profile throughout the Earth. For data, I shall give you this spreadsheet: PREM-Thermal.xls and leave you to think about how you might address this question. I shall ask 4 such math/physics questions on the final. Now, I would like to address the issue of the geodynamo. Following my incomplete noteset, Geomagnetics, I refer you to a nice noteset, better than my own, by Ramandeep Gill of Harvard: DYNAMO THEORY: THE PROBLEM OF THE GEODYNAMO and another from a short course given in Aquila, Italy by Dieter Schmitt in 2006: Geomagnetic Dynamo Theory. We shall then discuss the paper by Crossley, Jensen and Jacobs which deals with problems in computer modelling of chaotic dynamos. November 4, 2014: I have slightly extended the Noise and Chaos noteset and will discuss these extensions for a few minutes. Then in preparation for discussing the Crossley, Jensen and Jacobs paper, I would like to refer you to pages 24-26 in the Schmitt short course lecture. There are two styles of dynamo possible: alpha-Omega and alpha-squared which are distinguished one from the other by the sign of a scale factor (alpha) in the dynamo equation. We briefly describe the stochastic forcing of Olsen's alpha-squared disc dynamo though most of our paper deals with the alpha-Omega class. November 11, 2014: Today, I would like to infill the room left from whatever presentations you have decided to do today with a lecture on Spherical Harmonic Continuation. I would then like to discuss the Spherical Harmonic Power Spectrum of Earth's field. November 13, 2014: Ariane and, perhaps, Isabel may not be able to make their presentations today... they both have good reasons. I expect that Sophie, Kelian and Andres can offer their's today. Now, Andres came to me with questions that I couldn't answer concerning his presentation. When he showed me his PowerPoint slide-set, I fixated on “Geomagnetic Activity Index”. I didn't know how to define it so I looked for definitions with wonderful Google. Here is a USGS paper that describes some of the indices used by Aeronomers: Geomagnetic Indices. It might be interesting, as well, to note that we are continuously monitoring the solar wind as shown in real-time on the SOHO (Solar and Heliospheric Observatory) Spaceweather site and the ACE (Advanced Composition Explorer) satellite site. November 18, 2014: Following Ariane's presentation, I shall return to a lecture on Harmonic Continuation from the newly extended noteset. This should prepare us for the final Module 4 lectures on geophysics on a sphere. The model that we shall use in developing this story is based on a highly simplified model of seismic normal mode theory. We shall develop the normal modes of oscillation for a non-self-gravitating spherical fluid. You might note that, given a fluid, we should see no effects that arise due to material rigidity. This modelling shows how the spherical harmonic series arises through the analysis of the dynamical partial differential equations that describe oscillation. The relevant noteset: Harmonic Data Analysis. Another suggestion in preparation for the final take-home: Something to think about! November 20, 2014: I shall lead you through a solution of the wave equation for “seismic” oscillations of a “fluid Earth” model. The solution of the differential system in spherical coordinates leads to the description of spherical harmonic decomposition into “normal modes” of oscillation. The solution of the wave equation is dynamic whereas the solution of Laplace's equation is static (no time variation); on a sphere both solutions require spherical harmonic modal description. The noteset: Harmonic Data Analysis. Look to the section concerning Module 4 on the Course overview page. November 25 and 27, 2014: You might find these next two lectures mathematically tedious but I would like you to relax into trying to understand the mathematical/physical story that I am trying to tell you. I think it is important that you have some sense of how the differential systems that are used to describe and analyse geophysical phenomena on and within a spherical Earth are solved. This is really an example course in partial differential equations. The complexity that appears is in the realization of harmonic or modal analysis in spherical polar coordinate systems. Some of you may have encountered a similar, though even more complex analysis in your courses in Physical Chemistry. It is/was not unusual to develop the electron probability field of the 1H atom as an example of solutions to Schroedinger's equation in our mid-program Physical Chemistry courses. Relax for the next two lectures and absorb! Nothing of this detail is to be tested. Reference: Harmonic Data Analysis. 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. |
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Olivia Jensen, McGill University |
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