USU Geology 5670/6670 (Inverse Theory)
Course Materials, Spring 2021

Course Syllabus

Class Meets MWF, 1:30-2:20 pm in Geology 310

Resources:

  • Matlab scripts from Menke


  • Assignments:

  • Due 26 March at 8:30am: Assignment 1 & the data
  • Due 5 May at 5:30pm: Assignment 2 & some data: CAYA north positions.
  • The matlab script for Assignment 1 (for reference!)


  • PowerPoint Lectures and UPDATED Schedule:

  • 20 January: Introduction/Motivation for Inverse Theory
  • 22 January: Introduction/Motivation for Inverse Theory
  • 25 January: Introduction to Linear Inversion; The L2 Norm
  • 27 January: Ordinary Least Squares; the Pseudoinverse
  • 29 January: Gaussian Statistics and Model Parameter Error (OLS)
  • 1 February: Parameter Uncertainty and the Chi-Square Parameter
  • 3 February: Review: Matrix Notation; How We Got Here
  • 5 February: Parameter Uncertainty and Solution Appraisal
  • 8 February: Weighted Least Squares
  • 10 February: Confidence in WLS; the Generalized Inverse
  • 12 February: SVD & the Generalized Inverse
  • 17 February: SVD & The Generalized Inverse
  • 19 February: The Generalized Inverse
  • 22 February: Review: The Inverse Problem
  • 24 February: More on SVD...
  • 26 February: Inversion Parameter Resolution/Variance
  • 1 March: Linear Algebra Review; Damped Least Squares
  • 3 March: Damped Least Squares
  • 5 March: Maximum Likelihood
  • 8 March: Nonlinear Inversion
  • 10 March: Nonlinear Inversion: Gradient Approach
  • 15 March: Perils of the Gradient Search: Local Minima & Divergence
  • 17 March: Stabilizing Gauss-Newton (Gradient) Solutions
  • 19 March: Solution Appraisal for Nonlinear Inversion
  • 22 March: Simulated Annealing
  • 24 March: Linear Programming
  • 26 March: L1 and Inequality Constraints
  • 29 March: SVD and Quadratic Programming for (L2) Constrained Problems
  • 31 March: Quadratic Programming
  • 2 April: Inequality Constraints For Nonlinear Problems
  • 5 April: Stochastic Inversion
  • 7 April: Stochastic Inversion: Gravity Example
  • 12 April: Stochastic Inversion (Special Cases)
  • 14 April: Review of Assignment 1
  • 16 April: Joint Inversion
  • 19 April: Likelihood Filtering Example
  • 21 April: Bayesian Inversion
  • 23 April: Example: Double-Difference Hypocenter Location (Mitigating Data Error and Model Inexactness!)