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i’mmIBlR UFIIVERSITY

OF SCIENCE FII'ID TECHNOLOGY

FACULTY OF HEALTH AND APPLIED SCIENCES

DEPARTMENT OF NATURAL AND APPLIED SCIENCES

QUALIFICATION: BACHELOR OF SCIENCE

QUALIFICATION CODE: 07BOSC LEVEL: 7

COURSE CODE: GPH70lS COURSE NAME: GEOPHYSICS

SESSION: JUNE 2017 PAPER: THEORY

DURATION: 3 HOURS MARKS: 100

FIRST OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER(S) Dr. Nortin Titus

MODERATOR:Mr. Robert Mwanachilenga

INSTRUCTIONS

1. Answer ANY FOUR questions.

2. Write clearly and neatly.

3. Number the answers clearly.

PERMISSIBLE MATERIALS

Non-programmable Calculators

THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page and attachment)

QUESTION 1 [25]

(a) Geophysics is a combination of three fields of study. Give a basic definition of

Geophysics and name the three fields of study ranking these fields from most

important to least important. (6)

(b) Give three examples of physical properties of the earth and provide a short

description of each example. (9)

(c) Give a basic description of the following terms used in Geophysics: (10)

(i) Gravity

(ii) Magnetics

(iii) Radiometrics

(iv) Electromagnetics

(v) Seismology

QUESTION 2 [25]

(a) A test particle moves in a gravity field from P1 (1,3,2) to P2 (3,2,5); draw the

displacement vector. (2)

(b) In another galaxy, two magnetic fields are described by the vectors if = (2,-2,6) and

E = -3i + 4]}. Calculate 214i —- 31—3". (2)

(c) An asteroid passes a planet (P) and its moon (M). The two gravity fields that the

asteroid experiences as it hurtles through space is given by 1—5 = i - 2]“ — IE and I)? =

(2,0,-3). Calculate the scalar product of these two vectors. (2)

(d) Calculate the vector product of]3 and A7. (2)

(e) Determine the angle between I3 and IV. (3)

(f) The potential in the ionosphere is given by the function f(x, y, z) = x2y324. Determine

the electric field. (4)

(g) Calculate the divergence of the vector function 53 = = x2 2+ 3xzzj— 2x2]? (3)

(h) Prove that the curl of a gradient is always zero using the potential given in 2(f). (4)

(i) Determine the Laplacian of F = x2 + 2xy + 32 + 4. (3)

QUESTION 3 [25]

(a) Explain the concept of ’a potential’ and why it is convenient to talk about potential

fields in Geophysics. (5)

(b) The fundamental theorem for gradients f:§f- df = Kb) — fCa') says that the

integral of a derivative is given by the difference of the values of the function at the

end points. You determined that the potential is given by the function T = xyz.

Starting at A, the origin (0,0,0) and ending at B, the point (2,1,0), prove that

T(B) — T(A) = 2. (12)

(c) The potential fields of gravity and magnetic have a similar form. Write down the

expressions for the fields proportional to gravity and magnetic and define all the

terms used. (6)

(cl) Explain qualitatively using either the expression for gravity or magnetic in (c), what

happens when the distance between the source and the observation point is

changed. (2)

QUESTION 4 [25]

(a) Sketch the exponential decay law and use it to explain radioactivity. (5)

(b) What is a decay chain and give an example ofan element that decays in this way. (3)

(c) Name the three naturally occurring radioelements and give the gamma-ray energies (in

MeV) of each radioelement. Which isotopes are responsible for the gamma-ray

energies? (9)

(d) Airborne geophysical surveys only measure gamma—radiation. Why gamma- radiation

and not alpha- and beta—radiation as well? Also explain what cosmic radiation is. (5)

(e) Apart from potassium, thorium and uranium radiometric maps, name the other two

standard radiometric maps produced during a radiometric survey. (3)

QUESTION 5 [25]

(a) What is a seismic wave? Also sketch a seismic waveform. (2)

(b) Explain triangulation and how it is used to determine the location of an earthquake.

You may explain by using a sketch. (3)

(c) Name for types of elastic waves. (4)

La.)

(d) Define the seismic velocities for the two main body waves, the P-wave and S-wave if

q

3(1—20‘)K and] are defined as K = and = K + 3'5. Define all the symbols used. (10)

(e) Use the definitions above to prove that S-waves cannot travel through liquid. (3)

(f) What is a reflector and use it to explain the difference between the reflected wave

and refracted wave in seismic surveys by way of a sketch. (3)

END OF EXAM