EOSC 550 · Linear Inverse Theory

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

• Overview
• Essential mathematics 1.1
• Minimum Norm Construction  2.0
• Discretizing the inverse problem  2.1
• Singular Value Decomposition  2.2
• Inversion with Inaccurate data 2.3
• Numerical Solution with SVD 2.4
• Finding the Regularization Parameter
• Non-linear Inverse Theory

Papers for Sensitivity Calculation

• Frechet Derivatives and Sensitivites
• Sensitivities for EM problems
• 3D DC inversion with Conjugate Gradients

Lecture Topics

1. Overview to linear inverse theory
2. Review of essential mathematics
3. Minimum norm construction using accurate data
4. Discretization and Singular Value Decomposition
5. Linear inverse problems with inaccurate data
6. Choosing a regularization parameter: (GCV, L-curve, discrepancy principle)
7. Basics for solving nonlinear inverse problems
8. Tuning the inversion algorithm: applications to geophysical inversions
9. Calculation of sensitivities and Frechet derivatives
10. Inverse problems with partial differential equations
11. General measures of misfit and model norm
12. Parameter estimation
13. Resolution analysis

See also the expanded syllabus

Labs

Problem 1:

Problem 2

Problem 3

Tomo Project 2009

•  Forward modelling
•  Data: Readme file
•  Test data

Nonlinear Inverse Problem

• Noise free data