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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. Jacksonin 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