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GEOS 567, Inverse Problems in Geophysics

(alternating fall semesters, Randall M. Richardson & George Zandt Instructors)

Next offering fall 2007 (See http://www.geo.arizona.edu/geo5xx/geos567/ for current course)


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
  • 10% Class Participation

COURSE OUTLINE

INTRODUCTION
 
(REVIEW OF LINEAR ALGEBRA AND STATISTICS)
 
INVERSE METHODS BASED ON LENGTH
  • Least Squares Solution
  • Minimum Length Solution
  • Weighted Measures of Length
  • Variance of the Model Parameters
     
LINEARIZATION OF NONLINEAR PROBLEMS
 
EIGENVALUE PROBLEMS
 
SINGULAR-VALUE DECOMPOSITION (SVD)
 
THE GENERALIZED INVERSE AND MEASURES OF QUALITY
  • The Generalized Inverse Operator Gg­1
  • Measures of Quality for the Generalized Inverse
  • Resolution Versus Stability
     
VARIATIONS OF THE GENERALIZED INVERSE
  • Including Prior Information in the Generalized Inverse
  • Damped Least Squares and the Stochastic Inverse
  • Ridge Regression
  • Maximum Likelihood
     
CONTINUOUS INVERSE THEORY
 
OTHER COOL STUFF

Download Class Notes


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