## ESCI 441/641 Geophysical Data Analysis: Inverse Theory

Instructor: Colin A. Zelt

Department of Earth, Environmental and Planetary Sciences

P.O. Box 1892, Houston, Texas, 77251-1892, USA

**Texts:**

"Parameter
Estimation and Inverse Problems, Second Edition" by Aster, Borchers and Thurber (2012)
"Geophysical Data Analysis: Discrete Inverse Theory, 3rd Edition" by Menke (1989)
"Introductory
Geophysical Inverse Theory" by Scales, Smith and Treitel (2001)
"Global Optimization" by Scales (1997)
"Inverse Problem Theory and Methods for Model Parameter Estimation" by Tarantola (2004)
**1. Introduction**

what is inverse theory and what are inverse problems
what is not an inverse problem
terminology
simple problems
**2. Background**

linear algebra
probability
maximum likelihood principle
**3. Linear Inverse Theory**

least-squares solutions
prior information
regularization
singular value decomposition
example problems
**4. Non-linear Inverse Problems**

linearization
jumping and creeping
example problems
**5. Global Optimization**

grid search and Monte Carlo
simulated annealing
genetic algorithms
**6. Model Assessment**

errors
resolution
nonuniqueness
**7. Special Topics**

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