Master’s studies

Syllabus for Inversion of Geophysical Data

Inversion av geofysiska data


  • 10 credits
  • Course code: 1GE016
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Physics A1N, Earth Science A1N
  • Grading system: Fail (U), 3, 4, 5.
  • Established: 2007-03-15
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2015-10-19
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 25, 2016
  • Entry requirements: 180 credits including 80 credits in physics and mathematics.
  • Responsible department: Department of Earth Sciences

Learning outcomes

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

  • Explain the connection between linear regression, parameter estimation and inverse theory.
  • Derive the closed form solutions to a variety of linear least squares problems.
  • Explain the connection between continuous models and representers.
  • 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 critically interpret the trade-off between resolution, bias and uncertainty of the Tikhonov solution.
  • Explain 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.
  • Use Fourier transforms to solve the deconvolution problem by water levelling regularisation.
  • Give an account of and apply the basic methods for solving non-linear equations.
  • Solve a simple geophysical non-linear inverse problem by Occam regularisation.
  • Explain Bayesian approaches to inverse solutions and use apriori information to solve a simple geophysical inverse problem.


Short review of mathematical tools: linear algebra, statistics, and vector algebra; linear regression and linear inverse problems; discretisation of continuous inverse problems; the Singular Value Decomposition; Tichonov regularisation; other methods of regularisation; Fourier techniques; iterative methods, including the conjugate gradient method; non-linear regression and non-linear inverse problems, including Occam’s method; Bayesian methods.


Lectures, homework, problem solving and computer solution of simple geophysical inverse problems using MATLAB.


Oral examination (7 ECTS) and compulsory part (3 ECTS).

Reading list

Applies from: week 26, 2016

  • Menke, William Geophysical data analysis : discrete inverse theory

    Rev. ed.: San Diego: Academic Press, cop. 1989

    Find in the library


  • Aster, Richard C.; Borchers, Brian; Thurber, Clifford H. Parameter estimation and inverse problems

    2nd ed.: Waltham, MA: Academic Press, 2012

    Find in the library