**EOSC 450** Potential Fields in Earth and Planetary Science Fall 2005

Professor: Mark Jellinek
(mjellinek@eos.ubc.ca, EOS South 257)

Meeting times:

Office hours: just ask.

Text: none.

Potential methods are used widely to analyze problems involving gravity, magnetics, heat and fluid flow. Applications of potential methods in the Earth, ocean, atmospheric and planetary sciences are varied and include geophysical exploration, satellite altimetry, the mechanical properties of planetary lithospheres, the structure and secular variation of the Earth's magnetic field, flow in the atmosphere and oceans, the flow of groundwater, long-term climate change (orbitally-forced ice ages on Earth and Mars), and the tidal triggering of Moonquakes. This course will provide the essential tools to address such problems.

1) Introduction to Potential Theory

a. Example Problems

b. Mathematical background for potential field analysis

c. Introduction to gravity and the gravitational
potential (Newtonian Potential).

2) Introduction potential field data processing
techniques

a. Review of 1D Fourier Transform

b. 2D Fourier Transform

c. Spherical Harmonics

3) Gravity, Isostasy and Flexure

a. Gravity field of the Earth and a Reference Earth Model

b. Gravity and Geoid measurements from space

c.
Gravity and Geoid anomalies

d.
Elasticity and Flexure

e.
Isostatic response functions and the gravity/topography transfer function (admittance)

f.
Mechanical properties of the Earth's lithosphere and the icy shell of Europa.

4) Magnetics

a. The Magnetic Potential

b. Magnetization of Earth materials

c. The geomagentic field

d. The Martian magnetic field

e. Crustal magnetization at a spreading ridge and
seafloor spreading

Assigned problems (4 problem sets) 35%

Quizzes (4 quizzes) 40%

Final Paper / Talk (Paper due on last day of class; Talk to be during the last week of class) 25%

There will be 4 quizzes over the course of the semester. Quizzes will address material from lecture and problem sets
and are intended to help students build essential knowledge from the course as
it develops. Students can bring 1 sheet (1 side of one page) of review notes to
each quiz. Students may drop the
lowest grade.

Students will submit a final
project that involves a 10 page (double-sided) paper and a 20 minute talk
during the last week of class.
Project proposals will be due *Wednesday October 26.*
Additional guidelines for the proposal and for the project will be
provided in due course. The goal
of this exercise is for each student to pursue in greater detail a topic of
their choice. ItŐs an opportunity
to think creatively and do some interesting or even cutting edge research. In previous years a number of final
projects have evolved into published papers.

No single text incorporates
the full range of subject matter we will encounter. Here are a few useful books. Most (or similar books) are available in the Geophysics
reading room.

*Potential Theory in Gravity and Magnetic Applications,*Blakeley. This book is a good one for establishing the basic tools of potential theory as it is applied to a range of geophysical problems in gravity and magnetics.*Physics of the Earth,*Stacey. A classic book. We will use material from chapters 3 and 7. The appendix has a reasonable discussion of spherical harmonics.*Isostasy and Flexure of the Lithosphere,*Watts. Thorough and modern approaches to the analysis of isostasy and flexure of planetary lithospheres.*Advanced Engineering Mathematics,*Wyllie and Barrett. One of my favorite texts.*Div, Grad, Curl and All That,*Schey. The title says it all.*The Fourier Transform and Its Applications,*Bracewell.