Course Objectives: This course will cover the principles of geophysical inverse theory as applied to problems in the Earth Sciences. Both theory and applications will be covered. Inverse theory is a set of mathematical techniques used to obtain inferences about the Earth from physical measurements. The focus of this class will be on formulating and solving inverse problems, and understanding the nonuniqueness and resolution associated with inversions. We will not emphasize matrix inversion techniques, which are well covered in Applied Mathematics courses.

Prerequisites: Calculus, Computer Programming (any language), Matrix Algebra helpful

Course Format: The first two-thirds of the semester will be in traditional lecture format with homeworks. The first ten minutes of each class period will be devoted to a brief student presentation on an application of inverse theory from a recent published research article. The last third of the semester will consist of a series of guest lectures on application of inverse theory to various research problems, and student presentations.

Text: Geophysical Data Analysis: Discrete Inverse Theory (Revised edition), William Menke (available in bookstore, also on reserve in Earth Sciences library)

Grading:

Homeworks 40%

Class presentations 30%

Term paper 30%

Week Topics Reading

1. Jan 12 Introduction Ch. 1

2. Jan 19 Introduction / Linear Algebra Ch. 1

3. Jan 26 Probability Ch. 2

4. Feb 2 Least Squares Ch. 3 / Least Squares (smoothness, weighting) Ch. 3

5. Feb 9 Generalized Inverse Ch. 4

6. Feb 16 Nonlinear inverse problems Ch. 9

7. Feb 25 Dr. David Bahr, INSTAAR - genetic algorithms and application to glacier flow

Mar 2 Dr. Ken Dueker, CIRES - LSQR vs. SIRT

8. Mar 4 Nonlinear inverse problems Ch. 9

9. Mar 9 Nonuniqueness and localized averages Ch. 6

10. Mar 16 Singular value decomposition Ch. 7 / Dr. Doug Robertson, NOAA - precision gravity measurements / sparse matrix techniques

Mar 23 SPRING BREAK

11. Mar 30 Dr. Karl Ellefsen, USGS - cross-borehole tomography

Apr 1 Prof. Frank Evans, PAOS - simulated annealing with applications to remote sensing

12. Apr 6 Dr. Harley Benz, USGS - earthquake location/velocity structure

Apr. 8 TBA

13. Apr 13 Student Presentations

14. Apr 20 Student Presentations

15. Apr 27 Student Presentations

16. May 5 Term papers due

Back to home page