**Inverse Theory (NMT Geophysics 529/Math 519)
**

*Parameter Estimation and Inverse Problems*

Second Edition Textbook available January 2012

### Richard Aster

*Geophysics Program
*

Department of Earth and Environmental Science

### Brian Borchers

*Mathematics Department*

*
New Mexico Institute of Mining and Technology
*

Socorro, New Mexico

### Cliff Thurber

*Department of Geology and Geophysics*

University of Wisconsin-Madison

**Learning Objectives**

**Fundamental concepts:** Theoretical and practical understanding of linear and nonlinear discrete parameter estimation, ill-posed, and/or rank-deficient problems, and their solutions.

**Skills and Capabilities:** Ability to produce and interpret solutions to parameter estimation and inverse problems using high-level programming languages. Understanding and application of fundamental mathematical

techniques from linear algebra, probability and statistics, and multivariate calculus. Ability to understand and assess parameter estimation and inverse problem solutions in professional literature. Ability to summarize present

additional topics in the field.

**Specific Topics:** Overviews of pertinent linear algebra, probability and statistics, and calculus. Classification and examples of parameter estimation and inverse problems, and challenging aspects of their solution. Linear regression. Discretizing continuous inverse problems. Rank deficiency and ill-conditioning. Tikhonov regularization. Iterative methods. Additional regularization techniques. Fourier techniques. Nonlinear regression. Nonlinear inverse problems. Bayesian methods.

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