UPSC CGGE 2016 Question Paper Geo-Physics Paper III

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OiOLOGiST Exam-2013
No. r t r t h , r i ; ij) A-GSE-P-HQC
00 0 *130
GEOPHYSICS
Paper III

Time Allowed : Three Hours Maximum Marks : 200

INSTRUCTIONS
Please read each o f the follow ing instructions carefully
before attempting questions.
There are EIG H T questions divided under
TWO sections.
Candidate has to attempt SIX questions in all.
Question No. I and 5 are compulsoiy.
Out o f the remaining SIX questions, FOUR questions
are to be attempted choosing TWO from each section.
The number o f marks carried by a question/part
is indicated against it.
All parts and sub-parts o f a question are to be
attempted together in the answer book.
Attempts o f questions shall be counted in sequential
order. Unless struck o ff attempt o f a question
shall be counted even i f attempted partly.
Any page or portion o f the page left blank in the
answer book must be clearly struck off.
Answers must be written in ENGLISH only.
Neat sketches may be drawn to illustrate answers,
wherever required.
Unless otherwise mentioned, symbols and notations
have their usual standard meanings.
Assume suitable data, i f necessary and indicate
the same clearly.

Section - A -

1. (a) (i) Draw the characteristic gamma-ra®
spectra o f K, U, Th and show their
energy peaks.
(ii) What are the places, in India, where
uranium and thorium ores are found ? 5

(b) (i) Discuss briefly the use o f spinner
magnetometer for finding residual com­
ponent o f magnetization.
(ii) Discuss briefly the ferrimagnetism in
minerals, and give at least one example.
When a ferrimagnetic material will
behave as paramagnetic material ? 5

(c) (i) Some o f the high density oceanic
materials are having high velocity,
substantiate your answer with suitable
reason.
(ii) What is the principle o f designing an
inverse filter to remove the water
reverberations due to first reflector. 5

(d) What are the three adjustments made in
Bouguer gravity o f land survey compared to
the Bouguer gravity at an ocean floor site. 5

(e) (i) What do you mean by a digital filter ?
(ii) Define Discrete Fourier Transform
(DFT) and its Inverse Discrete Fourier
Transform (IDFT) for a given discrete
time series. 5

A-GSE-P-HQC 2 (Contd.)

? (f) What is z-transform ? Explain the z-transform
I for the sample values o f a wavelet or sequence
o f time series. 5
(g) Discuss the energy sources and radiation
principles involved in electromagnetic remote
sensing techniques. 5

(h) (i) What will be the colour o f water seen on
a photograph taken in a wavelength
between 0-75 ^ m - 1-3 f i m l What is the
spatial resolution o f IRS and Quickbird
sensors ?
(ii) If length between two photographs is
to be fixed as 0-85 km and speed o f an
aeroplane is 170 km/hr, what should be
the time interval between the opening
o f the shutter ? Find out how many
photographs will be snapped along a
profile line in 9 hours. 5

2. (a) (i) Explain deconvolution.
(ii) Compute the inverse filter for the
normalized dipole (1, 0-5) and show the
result o f deconvolution of the signal
X = ( 4 , 2, 0-5, 1, -1-5) using above
computed inverse filter response. 10

(b) (i) Write down the expression of Fourier
Transform for a 2-dimensional Bouguer
gravity anomaly.

A-GSE-P-HQC 3 (Contd.)

(ii) Explain the role o f low-pass and high-
pass filters for the separation o f r e g io n ^
and residual anomalies.
(iii) Show the example o f 2-dimensional
maps o f Bouguer, Regional and Residual
anomalies. 10

(c) (i) What do you mean by Auto-correlation ?

(ii) Find out the Auto-correlation o f finite
length wavelet, ^ = ( 1 , 4, 3, 1) and plot
the same. 10

3. (a) Define photogrammetry. Discuss briefly the
importance of photogrammetry. 5
(b) Derive an expression for parallax equation.
15
(c) A tall building manifests a parallax difference
o f 13-6 mm between its top and its base on
photographs taken from an altitude o f 4000
metres above ground. If the average photobase
is 108 mm, calculate the height o f building.
10

4 . (a) Describe the working principle o f a LaCaste-
Romberg gravimeter specially designed for
shipboard gravity survey. 10
(b) What does the ocean floor magnetic meas­
urements indicate in terms o f ocean floor
dynamics ? 5

A-GSE-P-HQC 4 (Contd.)

(c) At a station 200 metres away from out-
i cropping dyke, the spectrometric readings for
thorium and uranium are found to be as 25 and
36 counts/min. The constants k x and k2 for
thorium and uranium channels are 0-6 and
01 3 , respectively; and the stripping constants
(5,) for thorium y-rays in uranium channel is
one. Find the thorium and uranium contents in
parts per million. 5

(d) What is that factor on which the strength o f the
measured magnetic field depends in absorption
cell magnetometer ? Find out the gyro-
magnetic ratio o f electron for measuring the
earth’s magnetic field o f 50000 gammas with
precessional frequency as 1400 kHz. How
aero-magnetic survey is earned out for base
metal exploration? 10

Section - B

5 . (a) Prove that LX, L V = ih L z,
A A A

where Lx , Ly and Lz are the operators
corresponding to the x-, y-, and z-components
o f the angular momentum, respectively. 5
(b) Find the energy levels of a particle of mass tn
moving in the one-dimensional potential
+ oo, for a: < 0
v(x) =
I\m (j)2x 2, fo rx > 0 ,
.2
where co is a real constant. Give reasons for
your answer. 5

A-GSE-P-HQC 5 (Contd.)

(c) Intensity 1 of e.m. waves passing through
a laser active medium is expressed
/(z) = I(o)e~az where a is absorption coeffi­
cient and is a positive quantity;
n 2C 2
cc = — =— ( —A^2)- t is spontaneous relaxa-
co T
tion time and the laser cavity is along the
z-axis.

ho)

-> z

What is the basic requirement for amplifica­
tion o f e.m. waves ? 5

(d) The spatial part o f e.m. field in a cubic cavity
o f side L is governed by
V2w(„y, y, z) = - K 2 u(x, y, z) (Helmholtz equa­
tion). K is propagation vector. Solution o f the
equation yields
Ik , mn , , nn , ,
k = — , k = ---- and = — ; /, m and n are
* L y L 2 L
integers and represent number o f modes that a
standing wave has along the x, y and z-direc-
tions respectively.
Find the length o f a parallel plane cavity for
the longitudinal modes under resonance condi­
tion. 5

A-GSE-P-HQC 6 (Contd.)

(e) Explain, how the change between Crystalline
and Amorphous structure is used to record
the data in CDRW (Phase Change Device
Technology). 5

(f) Draw the voltage - current characteristics for a
solar cell with a variable load at fixed solar
insolation. Specify typical value o f efficiency
for modem solar cells in common use
nowadays. 5

(g) Draw a sketch for a non-inverting unity gain
amplifier using an operational amplifier and
minimum possible number of external com­
ponents. 5

(h) Define the following :

(i) Geo-stationary orbit

(ii) Gain o f an antenna

(iii) SFR in a microcontroller

(iv) Quantization error in A/D converter

(v) Thermister (NTC) 5

A-GSE-P-HQC 7 (Contd.)

6. (a) State the limitations o f Einstein’s theorv
for heat capacity o f solids. How were th esl
circumvented by Debye ? Obtain the expres­
sion for heat capacity based on Debye’s theory.
15

(b) The state of a particle o f mass m in an infinite
square well potential in one dimension

is described by

r 3n x ' ' nx'
cos
I 2a I,2 a ,
0, elsewhere

(i) Normalize the wave function and find A.

(ii) If energy is measured in this state, what
is the probability o f finding the particle
in the first excited state ?

(iii) What is the average value o f energy in
this state? 15

A-GSE-P-HQC 8 (Contd.)

a
Consider the transition from 2P(ml = +1, 0, -1 )
to the lower 2S state o f hydrogen atom. Using
the following data, find the radiative life time
o f the 2P state. Given
Ratio o f Einstein coefficients :

- = £a_J lCOab ^ g stands statistical weight
Bab gb n 2C~

V iP = 2
a0 (Bohr radius) = 5x10 u m
(oba = l-7 8 x l0 16 s~]
e = 1-6x10 ~19C ; h « 1 0 ~34Js
€0 =8-85x10-12 Fm~]; C = 3 x l 0 8 ms~]

where Dba is dipole moment expressed by

sin 3 0 = 3 s in 0 - 4 sin30 ; cos 26 = 2 cos20 - 1

15

A-GSE-P-HQC 9 (Contd.)

(b) N longitudinal modes in a resonator o f 1(
d, are mode locked with constant
difference, 6 and the modes have the same
average amplitude, A. The intensity o f such a
mode locked pulse is given by

where Aco is frequency separation between two
modes.

(i) Show that the temporal separation
between two mode locked pulses is equal
to one round trip transit time o f the
photon.

(ii) What is the length o f a resonator to
achieve mode locked pulses having the
peak temporal separation o f 10 ns ?

(iii) Assuming that time between the first
minimum and the first maximum is
approximately equal to the time duration,
td o f the total gain profile (FNHM),
find approximate number o f oscillating
modes for ^ = 0 -1 ns. 5x3

A-GSE-P-HQC 10 (Contd.)

8 ^ (a ) Draw functional block diagram o f an eight bit
9 microprocessor and explain its working. Show
timing diagram for reading an instruction from
the memory and executing it. 10

(b) Draw the truth table for logic expression
A -B + C
and realise it using basic logic gates. 10

(c) Explain the uses o f satellites placed (i) in the
geostationary orbit and (ii) in the low altitude
orbit. What are the criteria used for selection
o f uplink and downlink frequencies for the
satellite communication ?
Specify the most commonly used uplink and
downlink frequency bands for satellite com­
munication. 10

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