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Geos 567 | Inverse Methods in Geophysics
Fall 200

Randall M. Richardson

Office: Gould-Simpson Room 525
Phone: 621-4950
Office Hours: TBA
Lecture Times: Tuesday and Thursday, 12:30-1:45 pm, Gould-Simpson 209
Text: Inverse Problems in Geophysics: A Set of Lecture Notes, by Randall M. Richardson and George Zandt (download below)

This is a one-semester course on the fundamentals on inverse theory. Inverse theory can be loosely defined as the art of inferring as much as possible about a problem using everything that is known about the data and the relationship between the model and the data as expressed by some mathematical forward problem. Emphasis will be on the discrete linear problem, but both nonlinear and continuous inverse problems will be covered.

This course involves substantial homework, a term project, and the expectation of active class participation. The grading is based on the following: 60% Homework, 30% Term Project, and 10% Class Participation.

Tentative Homework Sets

Homework Set Title Due Date
Homework Set #1 Library / MATLAB TBA
Homework Set #2 Parameter-Space Searches TBA
Homework Set #3 Least Squares TBA
Homework Set #4 Constraints TBA
Homework Set #5 Covariance and Chi-Square Test TBA
Homework Set #6 Mapping Data Noise to Solution Error TBA
Homework Set #7 Singular Value Decomposition TBA
Homework Set #8 Inverse Literature Presentation TBA
Homework Set #9 Non-Linear Problem TBA
Homework Set #10 Generalized Inverse TBA
Homework Set #11 A Nasty Non-Linear Problem TBA
Homework Set #12 Noisy Data TBA
Homework Set #13 Weighted Generalized Inverse Analysis TBA
Course Outline and Class Notes

Download the class notes here (pdf format):
Chapter Title Pages and Size
Preface Table of Contents pages i-vi, 127k
Chapter 1 Introduction pages 1-11, 160k
Chapter 2 Review of Linear Algebra and Statistics pages 12-30, 263K
Chapter 3 Inverse Methods Based on Length pages 31-69, 319k
Chapter 4 Linearization of Nonlinear Problems pages 70-88, 228k
Chapter 5 The Eigenvalue Problem pages 89-122, 266k
Chapter 6 Singular-Value Decomposition (SVD) pages 123-149, 230k
Chapter 7 The Generalized Inverse and Measures of Quality pages 150-194, 440k
Chapter 8 Variations of the Generalized Inverse pages 195-238, 518k
Chapter 9 Continuous Inverse Theory and Other Approaches pages 239-265, 290k
All Chapters Complete set of notes as a single file pages i-vi & 1-265, 2.8MB


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