Entry requirements

Mathematics, 20 points, Physics, 30 points, and Fundamentals of Geophysics MN1 or Solid Earth Physics NV1, 10 points.

Learning outcomes

After successful completion of the course, the student is expected to:

- Understand the connection between linear regression, parameter estimation and inverse theory.

- Derive the closed form solutions to a variety of linear least squares problems.

- Derive the Singular Value Decomposition, describe the properties of the natural inverse solution and implement an algorithm for solving a simple geophysical linear inverse problem.

- Describe the principles of Tikhonov regularisation and understand the trade-off between resolution, bias and uncertainty of the Tikhonov solution.

- Understand the basic principles behind iterative methods for solving large linear systems of equations and use the conjugate gradient method to solve a simple geophysical linear inverse problem.

- Understand basic methods for solving non-linear equations.

- Solve a simple geophysical non-linear inverse problem by Occam regularisation.

- Understand Bayesian approaches to inverse solutions and use apriori information to solve a simple geophysical inverse problem.

Content

- Short review of mathematical tools

Linear algebra

Statistics

Vector algebra

- Linear regression and linear inverse problems

- The Singular Value Decomposition

- Tichonov regularisation

- Other methods of regularisation

- Iterative methods, including the conjugate gradient method

- Non-linear regression and non-linear inverse problems including Occam's method

- Bayesian methods

Instruction

The course consists of lectures and (compulsory) exercises.

Assessment

Oral examination. The oral examination corresponds to 6 ECTS and the compulsory part 1.5 ECTS.