CroninProjects.org/ Vince/ PlateKinematics/ KinematicsCourse/

A course on the kinematics of the lithosphere and continental crust

This course is taught by Professor Vince Cronin


Introduction

This course will consider the kinematics of the lithosphere and continental crust. My immediate goal is for all of the participants to be able to successfully perform a series of quantitative tasks related to plate/crustal kinematics. This will entail some vector math that includes matrix math. It is assumed that students have access to a computer (whether personal or Baylor-owned) that is connected to the web and that has a working copy of Mathematica version 11 or 12 and Microsoft Excel ± MatLab .

Dr. Cronin does not assume that students have math background in excess of the national standards for high school mathematics; however, this is an upper-level undergraduate-to-graduate science course, and science is a quantitative endeavor. Dr. Cronin will teach the basic math needed to do the work, and will demonstrate some Mathematica programming skills. Fuller development of Mathematica skills is up to each student, who can utilize publications and on-line tutorials/information produced by Wolfram Research ( https://www.wolfram.com/support/learn/ and https://www.wolfram.com/broadcast/screencasts/handsonstart/ ).

A number of university nerds have created online resources for learning about Mathematica including the following:
https://www.cs.purdue.edu/homes/ayg/CS590C/www/mathematica/math.html
https://www.math.harvard.edu/computing/math/tutorial/
https://www.thiel.edu/mathproject/mathematica/index.htm
https://help.unc.edu/817
and other resources that you can find by "googling" the words Mathematica tutorial .

In addition to demonstrating proficiency in generating correct answers using Mathematica code that they have written, students will be required to complete a study of an area (approved in advance) that incorporates the quantitative techniques developed in this course. A fuller discussion of grading will be provided in a future edition of this document.

This is not primarily intended to be a course on the history of the development of plate tectonics, which is a very interesting topic that is well covered in several of the references listed below. We will cover the most important early developments of plate kinematics, to supply historical context and to give credit where credit is due. It is also not meant to be a survey of current understanding of the tectonic context of plate boundaries worldwide. It is also not a course in geodynamics: the physics of the mechanisms of plate tectonics.


Order of Topics Taught in 2021 Course

  1. February 2, 2021
  2. February 18, 2021 (near the end of the Little Ice Age of 2021)
  3. February 21, 2021
  4. February 23, 2021
  5. February 24, 2021 -- See the code GeogCartGeog.nb, accessible via https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/GeogCartGeog.nb
  6. February 28, 2021
    1. Assignment (HW04): What is the azimuth from Neenach in southern California (34° 44' 24"N, 118° 37' 24"W) in the direction of the shortest straight-line path to Pinnacles in west-central California (36° 29' 13"N, 121° 10' 01"W). The azimuth of a bearing is measured in a clockwise direction relative to true north.
      Write a Mathematica notebook that analyzes the input data to complete the following tasks.
      (a) Convert the given geographic coordinates of Neenach and Pinnacles to decimal geographic coordinates (see section 2.2.3).
      (b) Convert the decimal geographic coordinates to unit location vectors (locVectNeenach and locVectPinnacles), recalling that south latitudes and west longitudes are negative numbers (see section 2.2.3).
      (c) Determine the circumferential distance of the shortest great-circle path from Neenach to Pinnacles (see section 2.3.4).
      (d) Determine the azimuth of the shortest great-circle path from Neenach to Pinnacles (see section 2.4.3).
      This assignment should be completed and submitted by around March 10.
      The template for this homework is available via YourName-HW04.nb
    2. Revisions of the following documents are available for download. Please discard or "archive" the old versions and start using the new versions.
    3. The following new documents are also available for download, cranial digestion, contemplation, and use
  7. March 3, 2021
    1. Read the document https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Kinematics-Chapter-3.nb.pdf
    2. Assignment (HW05): The template for this homework is available via YourName-HW05.nb
      This assignment should be completed and submitted by around March 17.
  8. March 7, 2021
    1. Read the document https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Kinematics-Chapter-4.nb.pdf
    2. Assignment (HW06): The template for this homework is available via YourName-HW06.nb
    3. Assignment (HW07): The template for this homework is available via YourName-HW07.nb
      These assignments should be completed and submitted by around March 20.
  9. March 14, 2021
    1. Read and play with the Mathematica notebook TangentialVelocity.nb, revised on March 14 and accessible via https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/TangentialVelocity.nb
    2. Assignment (HW08): This homework is a direct extension from the information contained in the Mathematica notebook TangentialVelocity.nb as revised March 14 (see link above). The template for this homework is available via YourName-HW08.nb
    3. The Kreemer, Blewitt, and Klein (2014) paper from G3 (A geodetic plate motion and Global Strain Rate Model) is on the thumb disk you were given early in the semester.
    4. The supplemental table S2 from Kreemer et al (2014) recast in an Excel spreadsheet https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/KreemerEtAl2014TableS2.xls
      or in its original form https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/KreemerEtAl(2014)TableS2.html.
    5. Read the old Chapter 5 of the Mathematica version of my kinematics primer:
      in PDF form or
      in Mathematica notebook form
    6. Read and play with the Mathematica notebook TangVelGPS.nb, written on March 14 and accessible via https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/TangVelGPS.nb
  10. March 30, 2021
    1. A good recent version of a relative plate-motion model is in supplementary table 2 from the paper by Kreemer, Blewitt, and Klein (2014). Another is the MORVEL model by DeMets et al (2010) as modified by Argus et al (2011).
    2. A good recent version of a NNR reference frame is in supplementary table 2 from the paper by Kreemer, Blewitt, and Klein (2014): https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/KreemerEtAl2014TableS2.xls
    3. A reasonable example of a hotspot reference frame is the paper by Alice Gripp and Richard Gordon (GrippGordon2002.pdf), which is based on the DeMets et al model NUVEL-1A.
    4. An "accepted MS" prior to final copy editing from Jason Morgan and his son about the hotspot reference frame: MorganP4AcceptedMS.pdf
    5. Code for finding the instantaneous angular velocity from one plate to another plate (where neither plate is the Pacific plate): https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/FindingAngVelVectors.nb
    6. Code for the modules that handle circular rotation of a point around an arbitrary axis: https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/CircularRotationModules.nb
    7. Code for chapter 12 of my old kinematics textbook: https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/KinematicsCh12.nb
  11. April 1, 2021
    1. The long-promised long-awaited link to the mapping app GeoMapApp is here! Actually, it is accessible via http://www.geomapapp.org. Look on the left side of the window to find the list of download links.
    2. An explanation of how to export and import to a Mathematica notebook, how to adjust the number of dimensions (levels, layers) of a dataset, and how to reference specific elements in a dataset is accessible via https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Exporting-Importing-and-Referencing-Data.nb
    3. The part of Supplementary Table 2 from Kreemer et al. (2021) that we need is accessible as a png graphic at https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/TableS2-Original.png, or in its original form https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/KreemerEtAl(2014)TableS2.html.
    4. The sample dataset for the notebook Cycloids.nb containing Peter Bird's (2003) boundary points along the Eurasia-North America plate boundary in Iceland is accessible via https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/IcelandBoundaryBird2003.csv
    5. The Cycloids.nb code, which takes an external CSV file of point location data expressed in geographic coordinates and uses the Kreemer et al (2014) NNR plate velocity model to model the position of the imported points at times other than the present, is accessible via https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Cycloids.nb. This version exports results to external CSV files.
  12. April 5, 2021

    Measuring instantaneous crustal strain: Background on using GNSS/GPS data in plate kinematics and crustal deformation studies

    1. A good online source of information about GPS technology and its use in geoscience is the UNAVCO Spotlight site accessible via https://spotlight.unavco.org
    2. What can GPS tell us about future earthquakes? https://www.unavco.org/education/outreach/animations/Japan-vs-PacificNW_What-can-GPS-tell-us.mp4
    3. Sendai/Tohoku-oki earthquake displacements using 1 Hz data (by Ronni Grapenthin): https://youtu.be/rMhhyb6Yy94
    4. GPS as an essential component of Cascadia earthquake early warning: https://www.unavco.org/education/outreach/animations/GPSEarthquakeEarlyWarning.mp4

    Measuring instantaneous crustal strain: Introduction

    1. The primer on instantaneous strain in 1D, 2D, and 3D can be downloaded from https://croninprojects.org/Vince/Geodesy/GPS_Strain_Primer.pdf
    2. Algorithm for triangle-strain analysis (revised April 2021): https://croninprojects.org/Vince/Geodesy/TriangleStrainAlgorithm.pdf (.pdf, 767 kb)
    3. The video showing the GPS strain analysis of three sites just west of Portland in Cascadia is on YouTube at https://youtu.be/gNGs7oW9aAU
    4. The video showing a simple visualization of a GPS strain analysis is on YouTube at https://youtu.be/HGnr4dSE92I
    5. Reminders
      1. Rigid-body deformation = translation + rotation
        • positive rotation is anti-clockwise (right-handed rotation)
      2. Non-rigid-body deformation = translation + rotation + volume strain (dilation) + distortion (change of shape)
        • positive rotation is anti-clockwise (right-handed rotation)
        • positive dilation is an increase in volume
    6. Different triangle-strain scenarios: https://croninprojects.org/GETSI-EER2018/gps_triangle_strain_ellipse.pdf

    Measuring instantaneous crustal strain: Tools

    1. Video "How to find GPS velocity data from UNAVCO station overview pages": https://youtu.be/BYzCZh3RpyU
    2. NOTA GNSS/GPS Stations Network Monitoring
      https://www.unavco.org/instrumentation/networks/status/nota/gps
    3. Interactive PBO GPS network map: https://www.unavco.org/instrumentation/networks/status/pbo/gps
    4. Nevada Geodetic Laboratory site to access GNSS/GPS data from stations worldwide: http://geodesy.unr.edu/NGLStationPages/gpsnetmap/GPSNetMap_MAG.html
    5. Generic datasheet for velocity data from 3 GPS/GNSS sites: https://croninprojects.org/Vince/Geodesy/GPS-strain-datasheet.pdf (pdf file, 125.8 kb)
    6. GPS strain Calculator in Mathematica: https://CroninProjects.org/Vince/Geodesy/Calculators/gps-strain-calculator-mathematica.nb
    7. How to interpret the strain calculator output: https://d32ogoqmya1dw8.cloudfront.net/files/getsi/teaching_materials/gps_strain/explanation_gps_strain_calculator.v3.pdf (.pdf file)
    8. Strain ellipse visualization tool ( https://d32ogoqmya1dw8.cloudfront.net/files/getsi/teaching_materials/gps_strain/strain_ellipse_visualization_t.zip ), which requires a free copy of Wolfram CDF Player ( https://www.wolfram.com/cdf-player/ )

    Measuring instantaneous crustal strain: Cookbook instructions for analysis of GNSS/GPS stations P146, P149, and P150, located near Stampede Reservoir (just north of Lake Tahoe)

    1. Download a copy of the generic datasheet: https://croninprojects.org/Vince/Geodesy/GPS-strain-datasheet.pdf
    2. Go to the NOTA GNSS/GPS Stations Network Monitoring site: https://www.unavco.org/instrumentation/networks/status/nota/gps
    3. Either use the map or scroll through the table below the map to find Site P146, then click on the blue P146 link.
    4. On the P146 - Overview/Station Page, find the box labeled "Station Data," then the item "Time Series Data," then click on the "NAM14_CSV" link to go to the CSV (comma separated values) file that lists data for P146 in the North American Datum of 2014.
      Note that there is a video titled "How to find GPS velocity data from UNAVCO station overview pages" that is accessible via https://youtu.be/BYzCZh3RpyU
    5. In the 11th line from the top of the header of the CSV file -- the line that starts with "Reference position" -- find the latitude and longitude data and copy those coordinates onto your generic data sheet.
    6. Return to the P146 - Overview/Station Page and locate the graphic under the heading "Station Position," and click on the graphic. It will expand into a full-size page. Use the navigation arrow on the right side of the window to get to the third page of time-series graphs -- the one that includes the velocity and standard deviation above each of the time-series graphs. Copy the north velocity and σ (standard deviation), and the east velocity and σ onto your generic data sheet.
    7. Move on to the P149 and P 150 Overview/Station Pages. The easiest way is to change the last several characters in the URL of the P146 overview page. So, for example,
      https://www.unavco.org/instrumentation/networks/status/nota/overview/P146
      would be changed to
      https://www.unavco.org/instrumentation/networks/status/nota/overview/P149
      to allow you to access the P149 - Overview/Station Page.
    8. When you have all of the input data recorded on your generic data sheet, open the GPS Strain Calculator in Mathematica and input your data. The Mathematica version is available at https://CroninProjects.org/Vince/Geodesy/Calculators/gps-strain-calculator-mathematica.nb.
    9. After all of the new data is input to the strain calculator, it will generate results. Copy those results onto your generic data sheet, and work on trying to understand their meaning. (This might be of some help: https://d32ogoqmya1dw8.cloudfront.net/files/getsi/teaching_materials/gps_strain/explanation_gps_strain_calculator.v3.pdf)
    10. Compare your results with those of other students in this course. Identify and resolve any discrepancies, or ask for help.

  13. April 20, 2021

    Modeling Finite Motion Across Plate Boundaries
    Excerpts from Chapter 13 of the draft primer on plate kinematics

    1. Mathematica code https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/DraftCh13-PlateBoundary-Kinematics
    2. Keynote presentation https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/1.PlateBoundaryKinematics.key
    3. PDF of Keynote presentation https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/1.PlateBoundaryKinematics.pdf

    Triple Junctions
    Excerpts from Cronin (2020)

    1. Publications
    2. Mathematica codes
      • Afar triple junction https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Modeling-Afar-2021.nb
      • Mendocino triple junction https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Modeling-Mendocino-2021.nb
      • Code from BS thesis by Ryley Collins: https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/AfarTJ-22MyrTo5Myr.nb
      — — PDF of code from BS thesis by Ryley Collins: https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/AfarTJ-22MyrTo5Myr.pdf
      • Code from BS thesis by Ryley Collins: https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/AfarTJ-22MyrTo10Myr.nb
      — — PDF of code from BS thesis by Ryley Collins: https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/AfarTJ-22MyrTo10Myr.pdf
    3. Keynote presentation https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/2.TripleJunctionKinematics.key
    4. PDF of Keynote presentation https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/2.TripleJunctionKinematics.pdf

    Instantaneous Relative Motion Along a Plate Boundary
    from Collins and Cronin (2018)

    1. Mathematica codes
      • Offset of isochrons on the North American Plate https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Isochron-TF-Offset-NOAM.nb
      • Offset of isochrons on the Nubian Plate https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Isochron-TF-Offset-Nubia.nb
      • Zonal-Meridional-Velocity Map https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Zonal-Meridional-Velocity-Map.nb
    2. Keynote presentation https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/3.AngVelOfMidoceanRidges.key
    3. PDF of Keynote presentation https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/3.AngVelOfMidoceanRidges.pdf

  14. April 23, 2021

    Angular velocity of mid-ocean ridges, and the changing length of ridge-ridge transform faults

    1. Publication references
    2. Mathematica codes
    3. Presentation file:
      • Keynote file https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/AngVelOfMidoceanRidges.key
      • PDF file https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/AngVelOfMidoceanRidges.pdf

    Modeling the long-wavelength shape of oceanic fracture zones

    1. Publication references
      • Cronin, V.S., 1988, Cycloid tectonics: Fracture zones as flow lines of transform faults [abs.]: EOS (American Geophysical Union Transactions), v. 69, p. 1415.
    2. Mathematica codes
    3. Presentation file
      • Keynote file https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Oceanic-Fracture-Zones2021.key
      • PDF file https://CroninProjects.org/Vince/PlateKinematics/KinematicsCourse/Oceanic-Fracture-Zones2021.pdf


Draft textbook: A primer on the kinematics of the lithosphere and continental crust

All of the original content in the documents directly accessible via this web page, including the content of the draft textbook, is © 2021 by Vincent S. Cronin

The draft textbook is available via https://CroninProjects.org/Vince/PlateKinematics/KinematicsPrimer/


Some Important Papers from First-Gen Plate Tectonics

  1. Hill, M.L., and Dibblee, T.W., Jr., 1953, San Andreas, Garlock and Big Pine Faults, California: Geological Society of America Bulletin, v. 64, p. 443-458.
  2. Hess, H.H., 1962, History of ocean basins, in Engel, A.E.J., James, H.L., and Leonard, B.F., editors, Petrological studies: A volume in honor of A.F. Buddington, p. 599-620.
  3. Wilson, J.T., 1962, Cabot fault: an Appalachian equivalent of the San Andreas and Great Glen faults and some implications for continental displacement: Nature, v. 198, p. 925-929.
  4. Wilson, J.T., 1963a, Hypothesis of Earth's behavior: Nature, v. 198, p. 925-929.
  5. Wilson, J.T., 1963b, Continental drift: Scientific American, v. 208, p. 86-100.
  6. Wilson, J.T., 1965a, Evidence from ocean islands suggesting movement in the Earth, in Blackett, P.M.S., Bullard, E.C., and Runcorn, S.K., [editors], A symposium on continental drift: Philosophical Transactions, Royal Society of London, series A., v. 258, p. 145-167.
  7. Wilson, J.T., 1965b, A new class of faults and their bearing on continental drift: Nature, v. 207, p. 343-347.
  8. Bullard, E.C., Everett, J.E., and Smith, A.G., 1965, The fit of the continents around the Atlantic, in Blackett, P.M.S., Bullard, E.C., and Runcorn, S.K., [editors], A symposium on continental drift: Philosophical Transactions of the Royal Society, London, series A, v. 258, p. 41-51.
    Compare this with Moulin, M., Aslanian, D., and Unternehr, P., 2010, A new starting point for the South and Equatorial Atlantic Ocean: Earth-Science Reviews, v. 98, p. 1-37, doi: 10.1016/j.earscirev.2009.08.001
  9. Le Pichon, X., 1991, Introduction to the publication of the extended outline of Jason Morgan's April 17, 1967 American Geophysical Union paper on "Rises, trenches, great faults and crustal blocks," in Hilde, T.W.C., and Carlson, R.L., [editors], Proceedings of the 1987 Geodynamics Symposium: Tectonophysics, v. 187, p. 1-22
  10. Morgan, W.J., 1968, Rises, trenches, great faults, and crustal blocks: Journal of Geophysical Research, v. 73, p. 1959-1982.
  11. McKenzie, D.P., and Parker, R.L., 1967, The north Pacific -- An example of tectonics on a sphere: Nature, v. 216, p. 1276-1280.
  12. Le Pichon, X., 1968, Sea-floor spreading and continental drift: Journal of Geophysical Research, v. 73, p. 3661-3697.
  13. Le Pichon, X., 1970, Correction to paper by Xavier Le Pichon "Sea-floor spreading and continental drift": Journal of Geophysical Research, v. 75, p. 2793.
  14. Heirtzler, J.R., Dickson, G.O., Herron, E.M., Pitman, W.C., III, and Le Pichon, X., 1968, Marine magnetic anomalies, geomagnetic field reversals, and motions of the ocean floor and continents: Journal of Geophysical Research, v. 73, no. 6, p. 2119-2136.
  15. Isacks, B., Oliver, J., and Sykes, L.R., 1968, Seismology and the new global tectonics: Journal of Geophysical Research, v. 73, p. 5855-5899.
  16. McKenzie, D., and Sclater, J.G., 1971, The evolution of the Indian Ocean since the Late Cretaceous: Geophysical Journal, Royal Astronomical Society, v. 25, p. 437-528.
  17. Chase, C.G., 1972, The n-plate problem of plate tectonics: Geophysical Journal, Royal Astronomical Society, v. 29, p. 117-122.

Reference List

Overviews, compilations and textbooks of tectonics and whole-Earth structure

Some references concerning the early history of plate tectonics and continental drift.


Other Resources


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All of the original content of this website is © 2017 by Vincent S. Cronin