USU Geology 5670/6670 (Inverse Theory)
Course Materials, Spring 2017

Course Syllabus

Class Meets MWF, 8:30-9:50 am in Geology 217a

Resources:

  • Matlab scripts from Menke


  • Assignments: Coming soon!

  • Due 3 March at 8:30am: Assignment 1 & the data
  • The matlab script for Assignment 1 (for reference!)
  • Reading for 20 March: Scales & Sneider, Geophysics, 1997
  • Reading for 27 March: Harding et al., Appl. Opt., 2014
  • Reading for 3 April: Tarantola & Valette, J. Geophys., 1982
  • Reading for 12 April: Curtis et al., The Leading Edge, 2006
  • Due 1 May at 8:30am: Assignment 2 & some data: CAYA north positions.


  • PowerPoint Lectures and UPDATED Schedule: Coming soon!

  • 9 January: Introduction/Motivation for Inverse Theory
  • 11 January: Introduction/Motivation for Inverse Theory
  • 13 January: Introduction to Linear Inversion
  • 18 January: L2 Norm & Ordinary Least Squares; the Pseudoinverse
  • 20 January: Gaussian Statistics and Model Parameter Error (OLS)
  • 25 January: Parameter Uncertainty and the Chi-Square Parameter
  • 27 January: Parameter Uncertainty and Solution Appraisal
  • 30 January: Solution Appraisal, Weighted Least Squares
  • 1 February: Confidence in WLS; the Generalized Inverse
  • 3 February: SVD & the Generalized Inverse
  • 6 February: The Generalized Inverse; Damped Least Squares
  • 8 February: Damped Least Squares; Maximum Likelihood
  • 10 February: Maximum Likelihood
  • 13 February: Nonlinear Problems
  • 15 February: Stabilizing Gauss-Newton (Gradient) Solutions
  • 17 February: Solution Appraisal for Nonlinear Inversion
  • 21 February: Simulated Annealing; L1 and Inequality Constraints
  • 22 February: Linear Programming for L1 and Inequality Constraints
  • 24 February: Quadratic Programming
  • 27 February: Stochastic Inversion
  • 1 March: Inequality Constraints For Nonlinear Problems
  • 3 March: Joint Inversion
  • 13 March: Review of Assignment 1
  • 15 March: Likelihood filtering Approach to Joint Inversion
  • 17 March: Likelihood Filtering Example; Bayesian Inversion
  • 22 March: More on Bayesian Inversion
  • 24 March: Example: Double-Difference Hypocenter Location (Mitigating Data Error and Model Inexactness!)
  • 29 March: Information Theory & Relative Entropy
  • 31 March: Minimum Entropy Inversion; Optimal Interpolation
  • 3 April: Tarantola & Valette (1982)
  • 5 April: Examples: Gravity kriging; "Simul Joint Inversion" (de Stefano et al., 2011)
  • 7 April: Tikhonov Regularization
  • 10 April: Assignments...
  • 12 April: Curtis et al.
  • 14 April: Joint inversion revisited
  • 19 April: Joint inversion revisited