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
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
Lecture G1-
Topics: Introduction to Geomagnetism – internal fields
Reading: Geomagnetism notes, pages 1-9 (Slides)
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
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.