UNIVERSITY OF EAST ANGLIA
School of Environmental Sciences
Main Series Undergraduate Examination 2012-2013
SOLID EARTH GEOPHYSICS
SOLID EARTH GEOPHYSICS with FIELDCOURSE
ENV-2A12/2A12K
Time allowed: 2 hours.
Answer THREE questions.
Write EACH answer in a SEPARATE answer book.
All questions carry equal weighting.
You may use any equation or data on the Equation and Data sheet included
in this paper in order to answer a question.
Provided:
- A4 graph paper
- ENV Data Book
If you use the A4 graph paper attach it to the relevant answer book.
Notes are not permitted in this examination.
Do not turn over until you are told to do so by the Invigilator.
ENV-2A12/2A12K
Module Contact: Dr Ana Ferreira, ENV
Copyright of the University of East Anglia
Version 1
2
1. a) A gravity survey conducted over the Irish Sea revealed a residual Bouguer
anomaly of Δgmax = -40 mGal.
(i) If the anomaly is interpreted as a sedimentary basin and a density contrast
of Δρ = -200 kg m-3 is assumed, estimate the thickness of the sediment.
[15%]
(ii) Discuss the potential limitations of such an estimate.
[10%]
(iii) Briefly explain how second derivatives might be used to help confirm the
interpretation made in (i).
[15%]
b) Explain the importance of the following in the context of gravity reductions:
(i) Free-air correction.
[15%]
(ii) Bouguer correction.
[15%]
c) A terrestrial gravity survey is planned along a 10 km transect in an attempt to
locate an intrusive igneous body. Outline an appropriate field procedure and
factors that need to be taken into account in order to undertake the survey
successfully.
[30%]
2. a) A vertical igneous dyke running east-west and of infinite depth intrudes into
surrounding non-magnetic sedimentary rock.
(i) Sketch the form of the total-field induced magnetic response you would
expect along a North-South profile across the dyke, at latitude 60° north.
[15%]
(ii) How would the profile of the magnetic response change if the dyke were
located on the equator? Explain your answer.
[10%]
(iii) How might the magnetic response be used to estimate the depth to the top
of the dyke?
[15%]
b) Explain how a forward model might be created for an observed magnetic
anomaly due to a buried brick wall on an archaeological site. Consider the
issues of remanent magnetization and ‘non-uniqueness’ and how the latter might
be addressed.
[30%]
ENV-2A12/2A12K
Version 1
3
c) Describe the physical principles and key advantages and disadvantages of the
following magnetometers:
(i) The fluxgate magnetometer.
[15%]
(ii) The proton-precession magnetometer.
[15%]
3. a) A 100 m long seismic refraction survey was undertaken across a flatbottomed river valley consisting of alluvial sediments overlying bedrock. The
data obtained from the survey are shown in Table 3.1.
Offset
(m)
Arrival
time
(ms)
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0 100.0
0.0
17.3
29.2
35.9
42.6
49.2
55.9
62.6
69.2
75.9
82.6
Table 3.1: Data from seismic refraction survey (Question 3a)
(i) Calculate the seismic velocity of each layer (v1 & v2), the thickness of the
alluvial layer (z1) and the depth of the bedrock (assume horizontal planar
layers).
[25%]
(ii) Using your answers from (i) above, calculate the critical angle and critical
distance along the sediment-bedrock interface.
[15%]
b) Describe the basic principles and field procedures of seismic reflection
methods that might be used to define horizontal layering as part of a terrestrial
seismic survey.
[30%]
c) Within the context of planning a terrestrial seismic refraction survey briefly
discuss the importance of:
(i) Choosing a suitable seismic source.
[15%]
(ii) The spatial deployment of geophones.
[15%]
PLEASE TURN OVER
ENV-2A12/2A12K
Version 1
4
4. a) A Ground Penetrating Radar (GPR) survey is planned to search for a buried
horizontal concrete layer using a 100 MHz GPR antenna. The dielectric
permittivity (εr) of the concrete layer is 6 and the relative magnetic permeability
(µr) = 1.
(i) Calculate the minimum layer thickness that the survey would be able to
resolve.
[25%]
(ii) Briefly explain the advantages and disadvantages of using a higher
frequency antenna for the survey.
[10%]
(iii) Describe the main sources of energy loss and attenuation in the context of
a GPR survey.
[15%]
b) Compare and contrast the geophysical principles of GPR and reflection
seismology.
[20%]
c) With reference to GPR survey data, briefly describe the following data
processing techniques, giving examples of when they might be applied.
(i) Time-zero correction.
[10%]
(ii) Migration.
[10%]
(iii) Depth conversion.
[10%]
ENV-2A12/2A12K
Version 1
5
5. a) Briefly describe an electrical resistivity survey method that will map the
subsurface geology and hydrogeology of the cross section in Figure 1. The
project design should be for surveys parallel to the coast. Justify your choice of
equipment, type of array and electrode spacing. State the relative true resistivity
values of the three main zones in the fissured chalk aquifer.
[35%]
Figure 1 Cross section of a coastal fissured chalk aquifer subject to sea water
intrusion and overlying a clay aquitard layer. Note the cross section scale.
b) Explain the problem of equivalence and how this may affect interpretation of
results from the survey.
[15%]
c) Describe how you would determine a down-hole salinity profile for the open
(uncased) borehole in Figure 1.
[25%]
d) Draw a sketch to show the likely borehole salinity profile for the depth interval
A-A’ in Figure 1 and describe the nature of the profile obtained.
[25%]
END OF PAPER
ENV-2A12/2A12K
Version 1
6
Equations and Data Sheet 2012/2013
Note that the inclusion of data or equations in this list does not necessarily mean
that they are relevant to a particular examination paper.
Gravity
G (Gravitational constant) = 6.67 x 10-11 m3 kg-1 s-2
1 mGal = 10 gravity units (g.u.) = 10-5 m s-2
Free-air effect = 0.3086 mGal m-1
Bouguer formula g = 2 Gh

z 

Gravity anomaly over a horizontal cylinder: g = 2 G R2   2
2 
z  x 
Maximum gravity anomaly over vertical cylinder: gmax = 2G (L + S1 – S2)
[where S1 = (R2 + D2)1/2 and S2 = ((D + L)2 + R2)1/2]
Smith Depth Rules:
2D: d < 0.65 .
g max
g ' max
3D: d < 0.86
g max
g ' max
Seismology
Compressional, P-wave velocity:
Shear-wave velocity:
Wyllie’s porosity equation:
ENV-2A12/2A12K
1
 1


V Vf
Vm
Version 1
7
Travel time of refracted wave, 2 layer case, horizontal interface:

V 2  V12
x
T=
 2z 2
V2
V1V2

1/ 2
Travel time of refracted wave, multilayer case, horizontal interface:
n 1
x

Tn =

Vn i 1


Vn2  Vi 2
2
z
 i
ViVn

alternatively Tn =

1/ 2



n 1
x
  (2 z i (cos θ i ) / Vi  where sin i = Vi/Vn
Vn
i 1
Travel time of reflected wave, 2 layer case, horizontal interface:
1 2
T=
(x + 4z2)1/2
V
Moveout
t2 – t1 ~ (x22 – x12)/(2 V2 t o)
 VRMS n 2 t n  VRMS n 1 2 t n 1 
Dix formula Vint = 

t n  t n1 


1/ 2
Electrical/Electromagnetic
Archie’s Law  = a ø-m s-n w
0.5 < a < 2.5, 1.3 < m < 2.5, n ~ 2
Electrical potential at a point = Vr =
I
2r
Skin depth () for em waves = 503 (f)-1/2 metres
Radar signal velocity through a medium (V) = c/[(µrεr)½].
Speed of light (c) = 3 x 108 m/s
Geodetic, gravitational and geomagnetic data for the Earth, together with
densities, magnetic susceptibilities and resistivities of common rocks and
minerals can be found in the ENV data book.
END OF EQUATION AND DATA SHEET
ENV-2A12/2A12K
Version 1