# Academic Programmes

## B.Sc. Honours Degree Programme Curriculum Topics

### Advanced Potential Field Methods

*Advanced Potential Field Methods: *Potential field theory: 2D and 3D gravitational and
magnetic potentials, equipotential surfaces, forces of attraction - gravity and magnetic, improper
integrals, Gauss's (divergence) theorem, Laplace's equation, Poisson's equation, Harmonic functions,
Gauss's integral formula, excess mass, transformations of potential fields (derivatives, Poisson's
relation, pseudo-gravity, reduction-to-the-pole, continuation, frequency filtering), ambiguity.

Gravity : Measurement of G and gravitational acceleration, units, figure of the earth, rock and mineral densities, reductions to gravity observations, gravity anomalies (Bouguer, Free air, Isostatic), isostasy, interpretation of anomalies (regional/residual separation, forward and inverse modelling), important southern African anomalies, case studies, applications to exploration and whole Earth studies.

*Geomagnetism* : Analysis of the earth's internal and external fields, units, basic physics,
magnetic properties of rocks and minerals (paramagnetism, diamagnetism, ferromagnetism, ferrimagnetism,
anti-ferromagnetism, susceptibility, coercivity, magnetic mineralogy, effect of grain size, Curie
temperature, induced and remanent magnetisation), time variations of the earth's field, palaeomagnetism,
magnetometers (fluxgate, proton precession, optically pumped, Overhauser), interpretation (rules
of thumb, forward and inverse modelling, magnetic fields of simple geometry, depth inversion),
design of ground and airborne magnetic surveys, image processing (applicable also to gravity data),
case histories and applications.

### Computer Programming

Introduction to computer hardware. Operating systems. Programming in Basic, Fortran, and C. Computer graphics.

### Geoelectrical Methods in Geophysical Exploration

This course provides background in fundamentals of geo-electricity. Geoelectrical methods deal with the propagation of electrical currents and of electromagnetic fields within the earth and its atmosphere. The course is divided in two sections to deal with the different physical phenomenology, namely: galvanic and electromagnetic. Course content extends the fundamental theory into more advanced topics in order to help the student generalise into real world problems. A strong emphasis is placed on geophysical applications in the mining, geo-hydrology, engineering and environmental disciplines.

### Global Geophysics

The role of geophysics in understanding plate tectonics and deep mantle plumes is reviewed. A variety of global maps - including seismicity, seismic tomographic, tectonic, geological, topographic, heat flow, geomagnetic, age, gravity, and the geoid - are studied to ensure that the student receives a fundamental grounding in their implications for global tectonics and structure, and up-to-date information on current research. The course also stresses important aspects of the deep structure of the earth, largely deduced from seismology, and processes within the core that controls the earth's magnetic field.

### Heat Flow

The course highlights the importance of heat generated in the earth by radioactivity, and its transport to the surface, for understanding terrestrial phenomena including: the earth's heat budget, the thermal evolution of oceanic plates and ocean floor bathymetry, the thermal structure of continents, thermal effects of magmatism, refrigeration of deep mines, and recent climate change. Students will learn how to apply the equation of heat diffusion to such problems, and develop computer software for such purposes.

### Mathematical and Computational Topics in Geophysics

This course provides the fundamental mathematical and computational knowledge required by most of the other geophysical courses. It is split into several parts:

*Image Processing* : Gridding and contouring techniques, histogram modification, colour
tables. Space domain image filtering, sun-shading, frequency domain filtering, principal component
analysis. Introduction to remote sensing - satellite platforms, multispectral data processing.
Radar systems, classification, registration.

*Inverse theory* : Forward and inverse modeling. Error surfaces. Linear and non-linear
problems, Moore-Penrose inversion. Ridge-regression. Over-determined and undetermined problems.
Applications to gravity, magnetics, and resistivity.

*Signal processing* : Fourier series, Fourier transforms, the FFT. Convolution, correlation,
and aliasing, and Hilbert transforms. Windowing of data and power spectrum estimation. Standard
geophysical filters. The 2D FT and 2D filters.

*Wavelet theory* : Walsh and Haar transforms. Wavelets in 1 and 2D. Applications to Geophysics

### Exploration and Applied Seismology

*Exploration seismology* : Acquisition (land and marine), geophones, seismic sources, the
Vibroseis method, marine and land-based interpretation of shot-gathers, seismic data processing
sequences, convolutional model, inverse filtering, least-squares inverse filtering, optimum Wiener
filters, practical predictive deconvolution, special filters, normal moveout, velocity analysis,
residual static corrections, refraction statics, seismic refraction interpretation methods, Kirchhoff,
finite-difference and fk migration, the double square root equation and pre-stack migration, dip
moveout, 3D seismic profiling slant stack, seismic resolution, vertical seismic profiling. Designing
and planning seismic surveys.

*Seismic stratigraphy* : Stratigraphic significance of reflectors, seismic sequence and
facies analysis, identification and age determination of depositional sequences, seismic facies
analysis, sea-level changes, transgressions, regressions, coastal onlap, geohistory analysis, depositional
system tracts.

### Rock Mechanics

Definition, application areas, stability, case studies, stress analysis, strain analysis, stress-strain relations, numerical simulations, geological deformations and displacements, geophysical techniques. Elasticity and strength of rock. Mohr's circle, strength characteristics of rocks, failure criteria, geotechnical classification of materials. State of stress, measurement of stress, stress field modifications due to tunnels, stresses and displacements induced by mining tabular deposits.

### Advanced Earthquake and Mining Seismology

Equations of motion for an elastic medium, propagation of plane seismic waves in layered structure, synthetic seismograms, attenuation, scattering, Q-coda, anisotropy, seismic tomography, structure of the Earth.

Seismicity, magnitude-frequency relations, seismic hazard, seismic source radiation, Green's function, near field, far-field, concentrated couples, moment tensor, pure shear slip, tension, energy balance, source function, kinematic models, dynamic models, asperity, seismic spectra, source parameters, elements of engineering seismology, site effect, prediction, seismic gaps, seismic event location, P and S wave picker.

Convolution, deconvolution, impulse response, time series analysis, methods for spectra calculation, forward and inverse approach.

### Ground Penetrating Radar

Theory of ground penetrating radar. Instrumentation. Survey design and field measurement. Applications in engineering, exploration, borehole geophysics and archaeology.

### Geophysics Field Course

An intensive field school and a field excursion are compulsory components of the course.
The field school has an exploration or environmental bias and students are given the opportunity
of operating a variety of up‑to‑date geophysical instruments on targets of economic
or environmental interest. The field excursion has a broader purpose and visits are paid to mines,
mineral occurrences and regions of specific geophysical interest. The field school and excursion
may be combined in certain years depending on departmental constraints.