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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