16-20 February, 2009 – Five-day lecture course on Inverse Theory by Professor David D. Jackson – in Geophysics Library, School of Cosmic Physics, 5 Merrion Square, Dublin 2.

Lecture headings:

Lecture 1: Classical parametric inverse problems

• Nature, math models, interpretation
• Purpose of inversion: existence, optimal solutions, stability, uniqueness, boundary between ok and not ok, properties shared by ok solutions, predictions
• Least squares solution: algebraic solution, interpretation as max likelihood solution for Gaussian data
• Multivariate Gaussian variables
• Linear transformations, error propagation

Lecture 2: More on classical parametric inverse problems

• Extremal inversion; mostsquares etc.
• Correlated data
• Linear constraints, nested models, F-test

Lecture 3: Non-uniqueness

• Where it comes from
• How to recognize it
• How to deal with it
• How to limit the model space
• How to add constraints
• How to predict from the data space: Backus Gilbert, resolving kernels
• SVD
• Bayesian methods
• How these all relate

Lecture 4: Nonlinear problems

• How nonlinear is your problem?
• Mildly nonlinear problems: iterative techniques, asymptotic error estimates
• Tricks to make problems more linear
• Massively nonlinear problems: Monte Carlo, genetic algorithms, etc
• The bottom line: all relies on forward modeling; if an ok model doesn’t have your favourite new feature, sorry too bad