Geomagnetism: Topics and Notes from SIOG 229

 

 


 

SIOG229 is an introduction to potential theory in the context of gravity and geomagnetism at a level suitable for the advanced non-specialist in geophysics. It is taught by

 

Adrian Borsa (aborsa@ucsd.edu), Munk 318,   

and

Cathy Constable (cconstable@ucsd.edu), Munk 329,

 

But this web page only really deals with the geomagnetism part as taught by Cathy.

 

The subtext is to get you familiar with spherical harmonics, which are ubiquitous functions in global geophysics. After a brief warm-up we are going to introduce spherical harmonics, derive some of their properties and apply them to various problems in potential fields, with emphasis on the geoid. Along the way we will meet some old topics, like the precession of the equinoxes and classical problems of potential theory, as well as some newer ones, like satellite-derived geoid and gravity models of other bodies in the solar system.

 

Theoretical topics include multipole expansions, spherical harmonics, Laplace's equation, boundary-value problems on a sphere, and Fourier methods. Applied topics include the global geoid, gravity anomalies, geomagnetic field modeling and sources, and paleomagnetic observations.

 

Grading for this class will be based primarily on homework assignments.  Students may work together on assignments, but each student must turn in their own solutions based on their own work.  Any code written to complete assignments (e.g. Matlab routines) should be submitted along with results.  Short presentations of topics from the text or homework may be assigned, and a final exam may be given at the instructors' discretion. Prerequisite: graduate standing or consent of instructors.

 

Course Materials (Gravity) – Adrian’s Part – Check in with him for current notes. There are links old gravity notes below that are occasionally referenced in the geomag notes.

 

 

GEOMAGNETISM – Cathy’s Part

Course Materials:

Bob Parker’s Gravity notes: Part 1, 2, 3, 4, 5, including everything about spherical harmonics that you need to know for Geomag

Geomagnetism Notes - 2020

Useful Vector Relations

Spherical Harmonic Lore

 

 

Lecture G0- A few resources for getting started if you forgot (or never learned EM as an undergraduate)

Basic physics of magnetic fields, Chapters 5-7, of Introduction to Electrodynamics, David J. Griffiths,

4th Edition, Cambridge University Press, 2017.

Div and Curl Grant Sanderson on his Youtube channel 3blue1brown, which has some useful visualization and intuition about divs and curls.

More things are covered at an elementary level in Khan Academy

e.g., Laplacian intuition, …. Harmonic functions

https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/laplacian/v/laplacian-intuition

 

Lecture G1-

Topics: Introduction to Geomagnetism – internal fields

Reading:  Geomagnetism notes, pages 1-9 (Slides)

Geomag Homework1

 

 

Lecture G2 -

Topics: Classical Electrodynamics – Helmholtz Theorem and Maxwell’s equations

Forgotten all about vector calculus? Try this Kahn Academy video which has some useful visualization and intuition about divs and curls.

Reading: Geomagnetism notes, pages 10-14. For more serious details see Chapter 2 of Foundations of Geomagnetism by Backus et al. (1996).

Today’s Slides

 

 

Lecture G3

Topics: Classical Electrodynamics – the static case, and constitutive relations continued

Reading: Pages 10-14 of notes

Today’s Slides

Geomag Homework2   due 2/27/2019

 

Lecture G4

Topics Gauss’s Theory of the Main Field

Reading: Geomagnetism notes, pages 15-17

Today’s Slides

 

Lecture G5 -

Topics: Upward and Downward Continuation,

Reading: Geomagnetism notes, pages 17-21.

Today’s Slides

 

Lecture G6 –

Topics: Geomagnetic Field Modeling

Reading: Geomagnetism Notes pages 22-31 Today’s Slides

 

Lecture G7 –

Topics: The Geomagnetic Spectrum; Toroidal and Poloidal Fields

Reading: Geomagnetism Notes (pages 32-38). Today’s Slides

 

Geomag_Homework3 due 3/6/2019

Solution to Homework #2

 

Lecture G8 –

Topics: Magnetohydrodynamics in Earth’s Core

Reading: Geomagnetism Notes (pages 39-56). Today’s Slides

 

Lecture G9 –

Topics: Magnetohydrodynamics in Earth’s Core- the Geodynamo

Reading: Notes (pages 39-56). Today’s  Slides

 

Lecture G10 –

Topics: The Crustal Magnetic Field

Reading: Notes  (pages 57-64) Today’s Slides

Geomag_Homework4 due 3/15/2019

 

Lecture G11

Topics: The Magnetic Annihilator, Filter Theory for Magnetic Anomalies

Reading: Geomagnetism Notes #6 (pages 57-64). Today’s Slides

 

Lecture G12

Topics:   External Fields & Electromagnetic Induction

Reading:  Geomagnetism notes, revisit pages 1-9 and read 65-72 (Slides)

Link to article on US space weather policy

And to Nature news on auroras

 

 

Supplementary References, Gravity                                                                                               

 

Physical Geodesy

W. Heiskanen and H. Moritz

W.H. Freeman and Company, San Francisco, 1967

A thorough treatment of much of the gravity material covered in the class notes.

 

Treatise on Geophysics, Volume 3, Geodesy

Volume Editor: T. Herring. Editor-in-Chief: G. Schubert

Elsevier, Amsterdam, 2007

Technical summaries of many current topics in gravity research, written by the best in the field.

 

Potential Theory in Gravity and Magnetic Applications

Richard J. Blakely

Cambridge University Press, New York 1995

Another look at potential theory, specifically in the context of gravity and geomagnetism.

 

Supplementary References, Geomagnetism:

 

Foundations of Geomagnetism

George Backus, Robert Parker, Catherine Constable

Cambridge University Press, New York 1996

 

Introduction to Electrodynamics, David J. Griffiths,

4th Edition, Cambridge University Press, 2017.

 

Treatise on Geophysics, Volume 5, Geomagnetism

Volume Editor: M. Kono. Editor-in-Chief: G. Schubert

Elsevier, Amsterdam, 2015, 2nd Edition.

[available from ROGER (roger.ucsd.edu) in electronic format]

Technical summaries of many current topics in geomagnetic research.

 

Treatise on Geophysics, Volume 8, Core Dynamics

Volume Editor: P. Olson. Editor-in-Chief: G. Schubert

Elsevier, Amsterdam, 2015, 2nd Edition.

[available from ROGER (roger.ucsd.edu) in electronic format]

Technical summaries of many current topics in core dynamics.

 

Space Science reviews volume on Planetary Magnetism at http://link.springer.com/journal/11214/152/1/page/1

And Terrestrial Magnetism http://link.springer.com/journal/11214/155/1/page/1

 

Earth’s Electromagnetic Environment Surv Geophys DOI 10.1007/s10712-015-9351-1

 

Supplementary Reference, Gravity & Geomagnetism:

 

Potential Theory in Gravity and Magnetic Applications

Richard J. Blakely

Cambridge University Press, New York 1995

[available from ROGER (roger.ucsd.edu) in electronic format]

Another look at potential theory, specifically in the context of gravity and geomagnetism.