Master’s studies

# Syllabus for Inversion of Geophysical Data

Inversion av geofysiska data

## Syllabus

• 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.

## Content

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.

## Instruction

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

## Assessment

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

Applies from: week 26, 2016

• Menke, William Geophysical data analysis : discrete inverse theory

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

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Mandatory

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

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

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