# Syllabus for The Earth's Potential Fields

Jordens potentialfält

• 5 credits
• Course code: 1GE035
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Physics A1N, Earth Science A1N
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2015-03-12
• Established by:
• Revised: 2022-02-02
• Revised by: The Faculty Board of Science and Technology
• Applies from: Spring 2023
• Entry requirements:

120 credits including 75 credits in physics and mathematics. Proficiency in English equivalent to the Swedish upper secondary course English 6.

• Responsible department: Department of Earth Sciences

## Learning outcomes

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

• Describe gravitational and magnetic fields in terms of their potentials, Gauss' law and the Laplace equation.
• Develop the gravitational and magnetic fields in terms of Greens' identities and the Helmholtz decomposition.
• Give a detailed description of how the Earth's gravity and magnetic fields can be measured and analysed.
• Compare gravitational and magnetic field measurements using Poisson's relation.
• Analyse the potential fields in terms of harmonic functions (Fourier components and spherical harmonics).
• Apply and evaluate filtering techniques such as upward and downward continuation to enhance the responses of geological target structures.
• Design field campaigns using gravity and magnetic methods to map geological structures and processes in the Earth's interior.
• Describe the fundamentals of 3D forward modelling applied to the Earth's potential fields.

## Content

Energy, work and potential. Green's identities for scalar potentials and Helmholtz theorem for vector fields. Gravitational and magnetic force and potential. Gauss' law and the Laplace equation for gravitational and magnetic fields. Magnetization, magnetic permeability and susceptibility. Poisson's relation between the magnetic potential and the gravitational field. Spherical harmonic analysis and Fourier methods. Filtering techniques. The Earth's gravity field, the geoid and the shape of the Earth. Regional gravity fields and gravity anomalies. Origin of the global geomagnetic field and its variation in time and space. Measuring techniques for gravitational and magnetic fields. Forward modelling of gravitational and magnetic fields.

## Instruction

Lectures, homework, problem solving and computer exercises.

## Assessment

Written examination (3 credits), homework assignments (1 credit) and oral presentation (1 credit).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.