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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