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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
NOTE: This examination paper must be submitted inside your
examina-tion booklet, otherwise your examination will not be
marked.
School of Earth SciencesEXAMINATION
Semester 1 Final Examination, 2016ERTH2020 Introduction to
Geophysics
Examination Duration: 150 minutes (2.5 hours)Reading Time: 15
minutes
Answer 4 questions only.All questions are of equal value (20
marks) with part marks as indicated.
Exam Conditions:Closed book examination.During reading time,
writing is permitted only in this document, not in answer
booklet.No electronic aids (laptops, phones etc). UQ approved
calculators only.Materials supplied: 2 answer booklets.
Page 1 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 1
(a) How does gravitational potential relate to gravitational
potential energy. (1)
(b) Consider the derivation for gravitational potential at a
distance r from a point mass m.
(i) The derivation begins with the statement
dU =Gm
r2dr
With the aid of a sketch explain the meaning of this
statement.(ii) To determine the integration constant C we need to
use a boundary condition. This
defines the sign of gravitational potential. What is that
boundary condition? (2)
(c) Write down (do not prove) the resultant expression for
gravitational potential at a dis-tance r from a point mass m.
(1)
(d) Assume that to a first approximation the earth acts as if
all its mass was at the centre.Using the formula from (c) we are
able to calculate the potential at any distance from thecentre of
the earth. Write down an expression which would then allow us to
estimatethe earth’s vector gravitational acceleration (g) from the
potential (U ). (1)
(e) Using a numerical approach, based on Part (d), estimate the
gravitational acceleration(magnitude and direction) experienced by
a satellite orbitting 2500km above the surfaceof the earth.
Carefully explain the sign of your answer. (3)
(f) Gravitational acceleration can also be calculated directly
using the relationship
g = −Gmr2
r̂
Use this direct form to verify your result in (e). (2)
In magnetics, the observed B field is made up of a component BH
which would occur in avacuum, and an induced component BM resulting
from the susceptibility of the material.That is
B = BH + BM
where BH = µ0H and BM = µ0M.
A magnetic survey is being carried out in a region of SE Qld
where the BH vector has mag-nitude 52750 nT, and an Inclination of
-56 ◦. A NS profile is run across a high susceptibilitydyke, which
strikes EW. At a traverse point near the dyke, the BM vector has
magnitude1250 nT, and is acting horizontally, partially cancelling
BH.
(g) Sketch a section showing the dyke, and primary and induced
fields. Illustrate thegeneral location along the profile where the
induced field would be horizontal. (2)
(h) What would be the reading on a proton-precession
magnetometer at that location? (3)
(Q1 continued over page)
Page 2 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 1 (continued)
A magnetic survey is being carried out over a 2-day period. On
Day 1, all drift readings aremade at Base Station A. For logistical
reasons, a different base station (B) is used on Day 2.The
following table gives base station readings made on Day 2. The two
readings made atBase Station A were for the purpose of data
integration.
Base Station Time Reading (nT)
A 0755 52461B 0800 53350B 1000 53373B 1400 53373B 1700 53410A
1705 52519
(i) Why is the morning reading at Base Station A different from
the afternoon reading. (0.5)
(j) Why is the reading at Base Station A (at any given time)
different from that at B. (0.5)
The following table gives two of the field readings taken on Day
2.
Station Time Reading (nT)
F1 0900 53393F2 1635 52224
(k) Calculate the drift-corrected values, relative to Base
Station B, for stations F1,F2. (2)
(l) It is subsequently desired to adjust all Day-2 readings so
that they can be merged withthe Day-1 data. What are the final
corrected values for stations F1, F2 (relative to BaseStation A).
(2)
Page 3 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 2
(a) Explain the relationship between resistivity (ρ) and
resistance (R) for a wire of length land cross sectional area A.
(1)
(b) Figure 1 shows a point source of current (I) on a homogenous
earth having resistivity ρ.Using the result in (a) deduce the
resistance of a hemispherical shell of thickness dr at adistance r
from the current source. (1)
Figure 1: Current flow (red lines) away from a point
electrode
(c) Hence derive an expression for the change in electrical
potential dV across the shell.(1)
(d) Integrate in the radial direction, applying a reasonable
boundary condition to deducethe constant of integration. Hence
derive the expression for the potential V at a distancer from a
point source of current. (3)
(e) Sketch a general 4-electrode array (C1, C2, P1, P2), and use
the result from (d) to derivean expression for the potential
difference ∆V measured between the potential electrodes(P1, P2).
(3)
Page 4 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
The gradient-array is a very efficient means of profiling,
particularly suited for steeply-dipping resistive bodies. It is,
however, quite different to most other arrays, in that thecurrent
electrodes C1, C2 are fixed, while the potential electrodes P1, P2
move laterally.Figure 2 illustrates three stages of a particular
gradient-array experiment, as the P1 andP2 electrodes move from
left to right along the line.
Figure 2: Gradient-array profiling exercise. The three sketches
(top to bottom) show the situation at the start of the
profile(x=100m), mid-way through the profile (x=500m), and at the
end of the profile (x=900m). Current electrodes are fixed(C1 at 0m,
C2 at 1000m). Potential electrodes have a fixed spacing (P1P2 =
50m) and are moved horizontally between thecurrent electrodes,
moving by 10m between each reading. The plotting point (x) is
mid-way between the P1 P2 electrodes.
(f) For the experiment shown in Figure 2, imagine first that the
earth is homogenous, andthat the current is constant. The voltage
∆V measured along the profile will still change,because the
electrode geometry changes from reading to reading. Using your
formulafrom (e) show that the voltage reading (∆V ) will be about
an order of magnitude largerat the start and end of the profile,
compared to the centre. (3)
(g) Because of this changing electrode geometry, a simple
formula for apparent resistivity(ρα) is not possible. It must be
calculated using an expression
ρα = K∆V
I
where the geometric factor K varies continuously (and smoothly)
along the line.
For the experiment in Figure 2, calculate the geometric factor K
for x=100m, 500m, 900m.Then, assuming K changes smoothly along the
line, sketch the general form of K as afunction of x (4)
Page 5 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Now consider a real experiment based on Figure 2, where the
earth is actually changingalong the profile. Readings taken along
the central part of the profile are shown below. (Thelisted x
coordinate is at the plotting point, mid-way between P1 and
P2.)
x (m) ∆V (mV) I (mA)
400 13 420410 12 420420 13 419430 12 419440 12 419450 12 419460
23 418470 42 418480 27 418490 12 418500 11 417510 12 417220 11
417530 12 417540 12 417550 12 417560 12 417570 12 417580 13 416590
13 416600 13 416
(h) The current values seem relatively consistent from reading
to reading. Why is thisreasonable? (0.5)
(i) Give a possible cause for the slight decrease in current
over time . (0.5)
(j) What is the apparent resistivity of the country rocks in
this area. (1)
(k) A resistive dyke is present on this part of the profile.
Where is it, and what is itsapparent resistivity? (2)
Page 6 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 3
Resistivity sounding is being performed using the Schlumberger
array. An expression con-venient for field use is
ρα = πG∆V
I
where G is a geometric factor given by
G =(L2 − l2)
2l
Here L and l are the distances from the centre of the array to
the current and potentialelectrodes respectively.
(a) A reading is being taken with L = 220 m and l = 10 m. With
the current off, a steadyreading of 9 mV is observed on the
voltmeter. What phenomenon is being observed.
(1)
(b) When the current is switched on the voltmeter reads 47 mV,
and the current is 353mA.Calculate the apparent resistivity.
(2)
(c) For the purposes of error estimation we will assume that L2
� l2. Write down the for-mula for a simplified geometric factor G′
to be used in error estimation. The estimated er-rors in the
current and potential electrodes are ± 0.1m and ± 0.01m
respectively. Hence,estimate the approximate percentage error in
the geometric factor. (2)
(d) The accuracy of the meters is such that the estimated error
in each voltage reading is± 1mV. The error in each current reading
is ± 1mA. Calculate the absolute error in theapparent resistivity
estimated in Part (b). (3)
(e) The Schlumberger sounding is being recorded using the
following equipment:
• 1 x 12V battery• 1 x 12-500V converter• 2 x current cables• 2
x brass spikes• 1 x ammeter• 2 x potential cables• 1 x voltmeter• 2
x porous pots
Draw a sketch which indicates how these items are connected.
(3)
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 3 (continued)
Figure 3 shows the Schlumberger sounding curve obtained.
Figure 3: Schlumberger sounding curve
(f) Explain how many layers are indicated in this location.
Estimate the layer resistivities.(You may need to use ≤ or ≥
symbols) (3)
(g) Assume that for the Schlumberger array a nominal depth of
investigation is 0.125 *(total array length). Estimate approximate
depths to the interfaces, and sketch yourresultant model. (3)
(h) With reference to the concept of equivalence, give a
specific numerical example of howthe resistive layer in (g) could
be subject to non-uniqueness. (3)
Page 8 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 4
A short seismic refraction line has been recorded perpendicular
to the direction of a pro-posed road, to define the best location
for a road cutting. Figure 6 shows the measuredarrival times at
each geophone. The times are also tabulated below.
Figure 4: Refraction arrival times. Geophone spacing 10m. Shots
at 0m and 120m.
Coordinate (m) tF (ms) tR (ms)
0.0 82.010.0 23.0 78.020.0 35.0 74.030.0 37.5 70.540.0 41.0
68.050.0 46.5 67.560.0 54.0 68.070.0 59.5 65.580.0 64.5 61.590.0
69.5 58.5100.0 73.0 53.0110.0 79.0 23.0120.0 82.0
Page 9 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 4 (continued)
(a) Assuming a simple overburden - bedrock situation, estimate
the velocity in the surfacelayer (v1). (2)
(b) Which interpretation method is appropriate for the bedrock
layer, and why? (1)
(c) The reciprocal method cannot necessarily be applied at all
geophones on the spread.Why? (1)
(d) With the aid of a sketch (or sketches), explain how to
calculate:
(i) the velocity function at a geophone (tV )
(ii) the refractor velocity at a particular point along the
spread
(iii) the time depth function (tG) at a geophone
(iv) the refractor depth at that geophone (4)
(e) Compute and plot the velocity function (tV ) at relevant
geophones, and hence com-ment on any variations in the bedrock
velocity (v2). (You may use the grid below.)
(4)
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 4 (continued)
(f) Compute and plot the time-depth function (tG). (You may use
the grid below.) Calculatethe overburden thickness at its
shallowest and deepest points. (4)
(g) The road cutting needs to be 20m deep, and 30m wide. Suggest
the optimum location,giving two reasons. (4)
Page 11 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Question 5
Figure 5 shows part of a Vibroseis shot record from central
Australia. More details are givenin the figure caption.
(a) Examine the approximately linear events highlighted in blue
and yellow. Identify thetype of event (e.g. direct wave,
refraction, reflection etc..). Extend the marking along theevents
(Blue: approximately from Geophones 40-87. Yellow: 94-135). (2)
(b) Estimate the apparent velocities of the blue and yellow
events. Hence, comment on theorientation of the refracting
interface (approximately horizontal, dipping towards high-numbered
geophones etc.). Estimate the true velocity below this interface
(v2). (3)
(c) Draw in an axis at the shotpoint (between Geophones 90 and
91). Estimate the interceptsfor the yellow and blue events (which
should be similar). Direct arrivals around Geo-phones 92-94
indicate an approximate surface velocity (v1) of about 1200 m/s.
Estimatethe depth to the interface. What is the likely geological
significance of this interface? (3)
(d) What type of events are highlighted in pink and green?
Extend the markings as far aspossible in each direction (Pink:
Geophones 35 -70, Green: 52-72). (1)
Because of strong surface waves, it is hard to track these
events back towards the centre ofthe record. Hence, we cannot use
our normal method of determining velocity. We need todevise an
alternative approach.
(e) Figure 6 shows reflection ray paths to two geophones at
distances x1 and x2 from a shot.It also shows the zero-offset ray
path. Using the NMO concept, write down an equationwhich relates
the reflection time tx1, for the geophone at x1, to the zero-offset
time t0 andthe layer velocity v. Write a second equation for the
reflection time tx2, for the geophoneat x2. (1)
(f) Eliminate t0 from the equations in (e), and hence derive an
expression for the layer veloc-ity v in terms of the parameters x1,
x2, tx1, tx2. (4)
(g) Use the result in (f) to estimate the average velocity down
to the reflecting interface forthe pink event. Now, use the
standard NMO equation to estimate the zero-offset time (t0),and
hence the depth to the interface. (4)
(h) Repeat this process for the green event, to determine the
velocity above the reflectinginterface and its depth. (2)
Appendix: Formulas and Constants
G = 6.67 ∗ 10−11 N m2 kg−2ME = 5.97 ∗ 1024 kgRE = 6371 km
Page 12 of 14
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Figure 5: Part of Vibroseis shot record from central Australia.
Here the distance axis is geophone number (30-150shown). The
geophone spacing is 20m. The shot point is midway between Geophones
90 and 91. The time axis goes from0s to 1s in increments of 0.1s.
Selected events are highlighted. Note that, for these Vibroseis
data, the true arrival time ofan event corresponds to a black peak,
as marked.
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Semester One Final Examination 2016 ERTH2020 Introduction to
Geophysics
Figure 6: Reflection ray paths for two geophones at distances x1
and x2 from a shot. The zero-offset ray path is alsoshown. The
layer velocity is v.
Page 14 of 14