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 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
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Last Updated: 22nd March 2016 by Anna
2009-02-16 – Five-day lecture course on Inverse Theory by Professor David D. Jackson
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
Lecture 2: More on classical parametric inverse problems
Lecture 3: Non-uniqueness
Lecture 4: Nonlinear problems
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