# Geophysics

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MSc Programme in Geophysics.

Areas of specialisation:

• Groundwater Exploration

• Environmental Geophysics

• Mineral Exploration

• Oil and Gas Exploration

Title of Programme: M. Sc. (Geophysics)

The Department of Physics offers graduate programme leading to the award of M. Sc. (Geophysics).

COURSE DESCRIPTION

1ST YEAR/FIRST SMESTER

PHY 541 Geology for Physicists 3 CREDITS

• Introduction to Physical Geology, Mineralogy, Petrology and the principles stratigraphy

• Simple geological structures – faults, folds, joints; igneous intrusives, geosynclines; dip and strike

• The geological features and origin of selected types of mineral deposits – gold, bauxite, diamond manganese, limestone, iron-ore, uranium, etc.

• The nature of oil accumulation; types of oil bearing structures – fault trap, anticline, salt dome etc.; basic principles of the search for oil and natural gas.

• The physical and chemical properties of selected types of economic minerals

• Introduction to the Geology of Ghana and West Africa

• Laboratory exercises on interpretation of geological maps, structural problems and the identification of types of rocks in situ, crystals and the common rock and ore forming minerals in hand specimens

PHY 543 Fundamentals of Mathematical Geophysics 3 Credits

A. Introduction to Geophysical Data Analysis

• Time Series Analysis

• Fourier Series and Fourier Transformation: Forier series and Fourier intergral of functions; complex form of Fourier

series.

• Laplace transformation: the Laplace integral; basic properties of the Laplace Transform;

• The inversion problem and convolution theorem;

• Filtering of Signals

B. Review of Polar, Cylindrical and Spehrical Coordinates

• Polar coordinates; cylindrical coordinates and spherical coordinates; the Laplacian

C. Review of Vector Calculus

• Vector Analysis, Gradient, Divergence and Curl; physical meaning

• Surface and Volume Integrals; Integral Theorems: Gauss, Stokes’ and Green

D. Partial Differential Equations

• Partial Differential Equations: Examples from Geophysics; The Wave Equation; Laplace and Poisson Equations the Diffusion and Heat Equations;

• Spherical Functions; cylindrical and spherical coordinates; the common boundary-value problems; Legendre Polynomials; Bessel functions; Associated Legendre functions and spherical harmonics;

E. Fundamentals of Potential Theory

• The role of gravitational and magnetic fields in Exploration Geophysics

• Gravitational and magnetic fields of the Earth; derivation of field from potential; Green's Theorem and Laplace Equation; Spherical harmonics;

• Inverse Problem of Potential Theory: Forward and Inverse Methods

• Wave number domain handling of gravity and magnetic anomalies (wavelength filtering); field continuation methods in gravity and magnetics.

PHY 547 Numerical Methods and Statistics 2 Credits

A. Numerical Methods

1. Curve-Fitting and Approximation of Functions

• Least-Squares Regression

• The Monte Carlo Method

• Spline Interpolation

2. Numerical Solution of Ordinary Differential Equations

• Runge-Kutta Methods

• Systems of Equations

• General Methods for Boundary-value Problems

3. Numerical Solution of Partial Differential Equations

• Finite Difference: Elliptic equations, Laplace equation; Parabolic equations, Heat conduction equation

B. Statistics

1. Sample Mean, Sample Variance

2. Estimation of Parameters

3. Confidence Intervals

4. Normal Distribution

5. Testing of Hypotheses

6. Goodness of Fit – χ2 - Test

PHY 549 Geophysics Laboratory and Field Work I 2 Credits

A. Geophysical Instrumentation Practical

• Electrical Resistivity Model Experiments

• Outdoor Gravity Measurements: Variation of gravity with altitude

• Outdoor Magnetics: Variation of Earth’s magnetic field over a buried magnetised body.

B. Minerals and Rocks Classification and Identification

• Definition: Mineral, Crystal and Rock

• Basic Crystal Systems

• Concepts of Classification and Identification of Minerals and Rocks – Laboratory Work

• Identification of Minerals and Rocks in the Field

• Concepts of Strike and Dip

PHY 551 Mathematical Methods for Physics 3 Credits

(only some selected topics are treated depending on the previous mathematical background of the students concerned)

1. Linear Spaces: Vector spaces, bases, coordinates; Linear operators, matrices, inverses; Change of bases; Inner product; Orthogonality; Unitary operators; Generalized orthogonality; Egenvalue problems; Diagonalization, Hilbert spaces; Matrix representation of linear operators, tensor algebra and calculus

2. Introduction to the Theory of Distributions (Generalized Functions): Strongly-peaked functions and the Dirac delta function; Delta sequences; representation of delta functions; weak convergence; correspondence of functions and distributions; properties of distributions

3. Elementary second-order partial differential equations: Classification. The Cauchy problem and the characteristic surfaces.

Second-order hyperbolic equations: The wave equation; the method of separation of variables; Second-order elliptic differential equations; the Laplace and Poisson equations; Second-order parabolic differential equations; the diffusion and heat equations; Use of Fourier and Laplace Transforms, Method of eigenfunction expansions and transforms; Vibrations of a membrane: Degeneracy, the Helmholtz equation

4. Special Functions: Cylindrical and Spherical Coordinates; the common boundary-value problems; the Stourm-Liouville problem;

Self-adjoint operators; Legendre polynomials; Bessel functions; Associated Legendre functions and spherical harmonics; spherical Bessel functions; Neumann functions; modified Bessel functions

5. Green’s functions: Green’s function G(x / ξ) for the Sturm-Liouville operator; Series expansion for G(x / ξ); Green’s function in two dimensions; Green’s functions for initial conditions; Green’s functions with reflection properties. Green’s functions for boundary conditions.

6. Introduction to the theory of Integral Equations

PHY 591 Global Geophysics 3 Credits

• Introductory: The Solid Earth, its surface features, - continents and oceans; the internal structure of the Earth (crust, mantle and core).

• Gravimetry: Gravity field of the Earth; Gravity as gradient of the geopotential; the International Gravity Formula (IGRF); the shape of the Earth (geoid and spheroid); the Earth's gravity anomaly; Principle of Isostasy.

• Geomagnetism and Paleomagnetism the Earth's magnetic field and theories of its origin, the dynamo theory; the main and external fields; analytical representation of the internal field; spatial and time variations of the geomagnetic field; rock magnetism and paleomagnetism as tools for recording the ancient geomagnetic field.

• Koenigsberger ratio; hysteresis properties of ferrimagnetic minerals; magnetic susceptibility and remanence.

• Thermal properties of the Earth; thermal conductivity of rocks; field and laboratory measurement of thermal conductivity; conductive heat flow; calculation of simple geotherms; global heat flow; convection in the mantle.

• Geochronology; General theory; rubidium-strontium; potassium-argon; lead-uranium/thorium; fission track methods.

• Seismology; measuring the interior of the Earth; Seismic waves; Earthquake Seismology.

• Geodynamics; Theory of Plate Tectonics; Sea-Floor Spreading

MAS 533 Human Resource Management 3 Credits

This course is offered by the Department of Economics and Industrial Management.

• Introduction to Management & Management Thought: The definition, nature, role and scope of management; recognising its interdisciplinary approach. Relationship of management to administration. Elements/functions of management as perceived by different management authorities. Understanding of management/organisational theory highlighting on the different schools of thought - scientific, human relations, systems, contigency, etc. Goals of business organisations - economic and social responsibilities of management.

• Decision Making: The importance of decisions in the management process. Meaning and types of management decisions; some basic processes in decision making. Models and / or techniques of making decisions; and influence on decisions.

• Organisation and Design: The nature and types of organisations. Basic principles and their importance in structuring organisations - organisation charts, objectives, scalar chain, span of control, line, staff and functional organisation, departmentation, centralisation and decentralisation, authority, responsibility and accountability, etc. and their implications for organisational administration. Concept of bureaucracy as applied to large scale organisations.

MAS 561 Leadership and organisational Behaviour 3 Credits

• Organisational Behaviour/Human Relations: International and,' group processes/ Group dynamics, and its relevance to organisational psychology. The application of the theories, skills and concepts. like leadership, motivation, communication, morale, organisational climate - their implications for managing people and organisation. Managing stress including self and time management. Managing change - a consideration for the organisational need for change. Reasons/causes of change in individuals and organisations, strategies for effecting change/innovation. Analysis of causes for change/innovation failures in organisation, models for the establishment of appropriate for managing change/innovation.

• Management Controls: Meaning of management controls and reasons for their application in management. Processes of control and other forms of information for management. Uses and applications of some control devices/techniques; factors to be considered in effecting some of the techniques, and their inherent problems for instituting them.

YEAR ONE: Semester TWO

PHY 542 Seismic Methods 3 Credits

• Introduction: elastic properties; the elastic constants, their interrelation and relations to seismic wave velocities; attenuation of seismic waves through rocks; seismic energy reflected at interface between two layers of rock media.

• porosity, factors affecting porosity, the time-average equation.

• Seismometers, basic principles of penduium and electromagnetic instruments~ geophone, hydrophone, analogue and digital.

seismic amplifiers, analogue and digital data recording, digital-to-analogue conversion.

• propagation of seismic energy through bounded media types of seismic waves attenuation of seismic energy

• ray paths in layered media, refraction and reflection at boundaries, reflection coefficients; critical refraction; diffraction.

• Seismic reflection survey: Introduction; geometry of reflected ray paths single and multiple. horizontal reflectors dipping reflector, ray paths of multiple reflections multichannel reflection profiling;

• the reflection seismogram (seismic trace); seismic section; survey design parameters

• CDP profiling and stacking; time corrections to seismic traces; migration of reflection data

• processing and interpretation of reflection survey data.

• Seismic refraction survey: Introduction; geometry of refracted ray paths, planar interfaces- two, three, multilayer horizontal interfaces; dipping layer with planar interfaces; faulted planar interfaces; profile geometries for studying planar layer problems geometry of refracted ray paths; irregular (non planar) interfaces.

• methodology of refraction profiling; field survey arrangements; recording scheme; weathering and elevation corrections; display of refraction seismograms; refraction interpretation; ambiguities in refraction interpretation- the blind and hidden layer problems.

PHY 544 Radiometric Methods and Borehole Geophysics 3 Credits

• Radiometric; Introduction; theoretical background; radioactivity of rocks; radiation detectors, Geiger counter, scintillation counters and spectrometers; measurements of radiation;

• field procedure; reduction of data, interpretation, radio- element assay, Compton scattering and stripping coefficients, radon measurements; airborne radioactivity measurements.

• Borehole Geophysics.;. Introduction; permeable zones; Archie's Law; Permeability-zone logs, resistivity and conductive logs, porosity logs, density logs etc.; basic log interpretation procedure

PHY 546: Advanced Programming 2 Credits

Introduction of high level programming languages (Fortran, Pascal, C++, SQL). Programming design. Structural design. Developing an algorithm - define problem, design a solution algoritlim, checking the solution algorithm. Names and data types. Control structures - simple IF statements. ELSE statements, combine IF statements, nested IF statements, the CASE structure. Repetition control structures - DO WHILE structure. REPEAT .. UNTIL structure, combined repetition constructs.

Modularization-hierachy charts or structure charts. Steps in modularisation. Programming examples using modules. Module design consideration. Array and matrices. Characters and strings. Procedure and functions. Files. List processing (pointers). Enumerated and set types. Records. Search and sorting. Iteration and recursion. Graphics. Modelling and simulation.

PHY 550 Geophysics Laboratory and Field Work II 2 Credits

Field Work

• Use of Electrical Resistivity, Electromagnetic, Magnetic, and Shallow Seismic Refraction Techniques in Groundwater and Mineral Exploration, Foundation Studies, etc.

Practical Exercises

• Analysis and Interpretation Techniques of Seismic Data for Oil and Gas Exploration, Analysis and Interpretation of

Earthquake Data.

Geological Structures, Maps and Profiles - Practical Exercises and Field Work

• Geological structures: Identification in the Field

• Determination of Strike and Dip

• Maps and profiles: Geological mapping techniques

• Geological Cross-Section

• Interpretation of Geological Maps.

PHY 568 Gravity and Magnetic Methods 3 Credits

Gravity:

• Introduction: the place of gravity in ground water, mineral and oil exploration; basic theory; gravity units; density of rocks, and its determination - its importance in gravity surveys; relation to gravity anomalies.

• Gravimeters, stable and unstable types; use of zero length spring in commercial instruments; calibration of gravimeters, absolute and relative measurements of gravity; measurement of gravity on lakes and at sea, gimbals methods, stabilised platforms.

• gravity anomalies of regular geometrical and irregular shapes;

• procedure of gravity exploration on land and at sea; reduction of gravity survey data;

• interpretation of gravity anomalies, the inverse problem regional fields and residual anomalies; direct and indirect interpretation; examples of typical gravity anomalies for some geological features; examples of gravity investigation problems; applications of gravity surveying.

Magnetic:

• Introduction: Basic concepts and units; magnetic properties; magnetic minerals in the Earth's crust; induced and remnant (residual) magnetism in rocks and minerals.

• Magnetometers, field. and laboratory instruments, spinner magnetometer, vibrating sample magnetometer, fluxgate and proton magnetometers; gradiometers, thermo-magnetic balance.

• magnetic anomalies; ground magnetic surveys; aeromagnetic and marine surveys

• reduction of magnetic observations; interpretation of magnetic anomalies for dipoles and sheets, qualitative and quantitative interpretation; examples of magnetic investigation problems.

PHY 578 Electrical and Electromagnetic Methods 3 Credits

Electrical:

• Resistivity: Basic concepts and units; apparent resistivity

• electrical properties; resistivity factors affecting resistivity of rocks, Archie's Law, Formation Factor; skin depth; electrical conductivities, electronic, electrolytic, dielectric; electrical polarization- in rocks; laboratory measurement of resistivity and dielectric constant.

• Theory of current flow in the ground; two media of different resistivity;

• Resistivity -electromagnetic-induced polarization instruments, the terrameter; very low frequency (VLF) instrument, coil systems, the four electrode system of measurement, types of electrode configuration; resistivity survey on land, vertical electrical sounding and constant separation traversing.

• interpretation of resistivity data, resistivity master curves; problems of ambiguity; limitations of the resistivity method; applications.

• Induced Polarization (IP); Basic concepts and principles; mechanism of IP; time and frequency domain; measurement of IP; field procedure; interpretation of IP data; problems and applications.

• Self Potential (SP): Introduction; mechanism of SP; field survey procedure; interpretation of SP anomalies.

Electromagnetic (EM):

• Fundamentals of Electromagnetic Theory.

• Introduction: Electromagnetic induction; basic principle of EM survey; Elliptic polarization; depth of penetration of EM fields; detection of EM fields; tilt angle methods; VLF, AFMAG methods; phase measuring systems

• ground survey procedure; airborne EM surveying; interpretation of EM data; limitation and applications; brief introduction to the telluric and magnetotelluric methods.

Requirements for Graduation:

1. The minimum time for completing the M.Sc. (Exploration Geophysics) Programme is two (2) calendar years. The credit hours for the course is 55 maximum.

2. Students are expected to obtain a minimum of 50% in all the courses and an aggregate of at least 55%.

3. Students should complete a research project leading to an externally/internally examinable thesis. Students should successfully defend the thesis at an oral examination.

Resources Available Apart from Human Resources:

The Department has the following geophysical equipment:

1. Worden Gravimeter for gravity survey

2. Bison Instruments Inc.

3. Signal enhancement earth resistivity meter SAS 3000C

4. Proton Precession Magnetometer

5. High temperature furnace (1500 DC)

6. Very Low Frequency (VLF) equipment

7. Seismic refraction equipment

8. Ground Penetrating Radar

9. Geonics EM 32-3 equipment