Course Description
Model construction, appraisal of nonuniqueness, and inference in linear problems. Tomographic inversions.
Instructors
Oldenburg, Douglas W
Time and location:
- Wednesday/Friday
- Time: 2:00-3:30
Textbook
See references in the course outline.
Course Content
Course outline
See also the expanded syllabus
Class Notes
Papers for Sensitivity Calculation
Lecture Topics
- Overview to linear inverse theory
- Review of essential mathematics
- Minimum norm construction using accurate data
- Discretization and Singular Value Decomposition
- Linear inverse problems with inaccurate data
- Choosing a regularization parameter: (GCV, L-curve, discrepancy principle)
- Basics for solving nonlinear inverse problems
- Tuning the inversion algorithm: applications to geophysical inversions
- Calculation of sensitivities and Frechet derivatives
- Inverse problems with partial differential equations
- General measures of misfit and model norm
- Parameter estimation
- Resolution analysis
See also the expanded syllabus
Labs
Problem 1:
Problem 2
Problem 3
Tomo Project 2009
Nonlinear Inverse Problem