Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Geophysical Mathematics and Potential Theory
Code ENVS201
Coordinator Professor RT Holme
Earth, Ocean and Ecological Sciences
R.T.Holme@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2022-23 Level 5 FHEQ Whole Session 15

Aims

To provide mathematical training required for geophysical research, with a specific focus on:

Mathematical methods, providing a bridge between Year One mathematics courses and geophysical applications in Year Three and Four.

The application of these methods, with particular emphasis on applied potential theory (gravity and magnetic methods).


Learning Outcomes

(LO1) Knowledge of mathematical methods appropriate for geophysical science.

(LO2) Advanced knowledge and understanding of the concepts of gravity and magnetic field potentials, fundamental mathematical framework of potential field theory, and application to data manipulation and interpretation.

(LO3) The ability to manipulate gravitational and magnetic data using potential field theory.

(LO4) Report writing from practical exercise, focussing on answering and reporting on conclusions of an associated scientific requestion

(S1) Problem solving skills

(S2) Numeracy

(S3) Communication skills

(S4) IT skills

(S5) Application of literacy, ability to produce clear, structured written work and oral literacy - including listening and questioning


Syllabus

 

Introductory material, including basic calculus, complex numbers, series expansions and matrices.

Eigenvalue and eigenvector analysis

First and second order ordinary differential equations.

Fourier methods.

Partial differentiation, vector calculus.

Curvilinear coordinate systems.

Introduction to partial differential equations.

Class test

Recap and review

Foundations of potential theory

Laplace's equation in cartesian coordinates

Applied methods - Gauss' theorem, Directoral Derivatives

Application practical one.

Application practical two.

Upward/downward continuation.

Whole Earth potential theory.

Spherical Harmonics

Elipticity / flattening / Geoid

Planetary magnetism

Class test

Recap and review


Teaching and Learning Strategies

Teaching Method 1 - In person lectures
Description:
Attendance Recorded: Yes

Teaching Method 1 - Pre-recorded lectures
Description:
Attendance Recorded: No

Teaching Method 3- Tutorial
Description:
Attendance Recorded: Yes

Teaching Method 4 - Laboratory Work
Description: Practical sessions in gravity and magnetism
Attendance Recorded: Yes


Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 20

  20

6

  4

4

20

74
Timetable (if known)              
Private Study 76
TOTAL HOURS 150

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Class Test, End of Semester 2 There is a Resit Opportunity.  90    25       
Class test at end of first semester There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When): Sem 1    25       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Maths problems 1 - vectors         
Problem set 2 - Ordinary differential equations         
Problem set 3 - Partial differentiation         
Problem set 4 – Fourier methods         
Curilinear coordinates         
Partial differential equations         
Gauss' theorem report derived from practical         
Application of potential theory methods - report from practical         
Spherical harmonics report from computer practical         
Problem shhet 7 - Spherical potential theory         

Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.