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Combined Geo-Scientist (Main)
5 BGSP-C-GPH
GEOPHYSICS
PAPER—III
Time Allowed : Three Hours Maximum Marks : 200
QUESTION PAPER SPECIFIC INSTRUCTIONS
Please read each of the following instructions carefully
before attempting questions
There are TEN questions divided under TWO Sections.
Candidate has to attempt SIX questions in all.
Question Nos. 1 and 6 are compulsory. Out of the remaining EIGHT questions, FOUR
questions are to be attempted choosing TWO from each Section.
The number of marks carried by a question/part is indicated against it.
Neat sketches may be drawn to illustrate answers, wherever required. These shall be
drawn in the space provided for answering the question itself.
Unless otherwise mentioned, symbols and notations have their usual standard meanings.
Assume suitable data, if necessary, and indicate the same clearly.
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a
question shall be counted even if attempted partly.
Any page or portion of the page left blank in the Question-cum-Answer Booklet must be
clearly struck off.
Answers must be written in ENGLISH only.
Constants which may be needed :
Kepler’s constant = 3.986004418 ೬105 10003 972
Mean radius of the Earth = 6378 km
Mass of electron (m,) = 911+171 kg
Charge of electron (e) = 1. 6022९1071१ ୦
Planck’s constant (h) = 6.62×10-34 Js
Boltzmann’s constant (k) = 1-38 (10723 J/K
Permittivity of free space (६0) = 8. 854 10-12 F 701
BGSP-C-GPH/64 1 [26
1. (a)
धि
(6)
(0)
(૭
(0)
(h)
2. (a)
(b)
SECTION—A
Define average, RMS and stacking velocities for a layered Earth model of
n layers. Express them in order of their increasing values. What is move-out
time? 5
What is path radiance? Describe the total radiance recorded by a remote
sensing sensor. ˆ 5
State and prove convolution theorem. 1+4=5
Given a dipole is situated at the centre of the Earth. Calculate the magnetic
potential and magnetic field at a distance r from the dipole in spherical polar
coordinates (7, 8, டு, where 7 : radius, 9 : colatitude and 0 : longitude. 5
A digital filter is given by y, =2x, ¬ 5ׄ _1 +1-3y,_,. The sequence of input
values fed to the filter is x9 =5, ੭) =1-8, 22 = -4, x3 = 3, 24 = 2. Write the
output sequence 90 to ہل of the above filter. 5
Find out the expected change in gravity caused by the presence of seawater of
depth 1:5 m. Assume density of seawater as 1:05 gm/cm°, density of rock
between sea surface and sea bottom as 2:5 gm/cm®. Explain how terrain
correction removes the effect of hill and compensates for valley. 3+2=5
Briefly explain the wavelength ranges used in remote sensing in which the
atmosphere is particularly transmissive. Describe the role of these ranges in
designing the remote sensing sensors. 5
Explain the phenomena describing interaction of photons with radioactive
atoms—photoelectric effect, Compton scattering and pair production.
Show in a plot when these processes dominate as a function of energy levels
between 10 2 MeV and 102 MeV of the gamma ray interactions of atoms.
3+2=5
Write brief notes on (i) recursive and (ii) non-recursive filters. 5+5=10
Describe the various elements of visual image interpretation of remote sensing
data.
Explain their relative degree of complexity in interpreting the data. 5+5=10
BGSP-C-GPH/64 2
4.
(0)
(a)
धि
(0
(0)
ધિ
0)
Consider P waves propagating through thick sediments below seafloor with a
velocity gradient. Draw the time-distance (t-x) curves and ray path diagrams
for reflected and refracted rays in a shallow water column, and diving rays in
the deep ocean.
Write the expression for the depth of maximum penetration, and travel time t at
a distance x from the source for diving rays. 6+4=10
Mention the different direct and indirect indicators of groundwater occurrences
on a satellite image. Describe the applications of remote sensing in
groundwater mapping. 5+5=10
Define the rectangular function, x(t), in discrete form and evaluate the
convolution of 0) with itself. Draw a rough sketch of the convolved output.
(0 Why is radon gas considered as an ideal tracer for groundwater studies?
Describe the applications of radon gas in hydrogeological investigations.
(ii) Why is the sensitivity of air-borne magnetometers greater than those used
in ground exploration? Briefly explain the advantages and disadvantages
10
5
of air-borne magnetics. 2+3=5
() Describe the relationship between grain size and capillary rise of water in
unconsolidated materials. Arrange the following in the order of increasing
grain size :
Fine gravels, Very coarse sand, Clay, Silt 2+3=5
(i) Differentiate between laminar flow and turbulent flow in porous media.
Explain the range of validity of Darcy’s law. 2+3=5
(0 A linear body extends to infinity in ர் direction. Using Laplace’s equation
in Cartesian coordinates (X, Y, Z), show that the gravitational potential
associated with it at a height h above the sea level decreases exponentially
with height than its value at the sea level.
8 Define Eétvés correction in gravity. Schematically plot its variation with
latitude (0°-90°) for a given speed of moving platform and for headings of a
moving platform at 5°, 30° and 90°.
Over a homogeneous half-space, show that the apparent resistivity is equal to
the true resistivity.
10
BGSP-C-GPH/64 3 [ P.T.O.
5. (a) (i) Given the absorption coefficient of seawater as 8 × 10 5 dB/wavelength,
and intensity of the signal as unity. Calculate the intensity of a pressure
signal at a distance of five times its wavelength. Diagrammatically describe
the behaviour of an impulse originated at the source as a function of
distance. 3+2=5
(ii) Assume that obliquely incident rays are reflected from two receivers
spaced X apart on the surface. Derive the relationship among offset (X),
dip of layer (9 and maximum frequency (ಗಟ) of seismic wave that is not
aliased. 5
(b) (0 Define analytic signal and show that its Fourier transform vanishes at
negative frequencies. 1+4=5
(ii) State and prove the time-scaling property of Fourier transform. 5
(© ¢ The wavelengths of a certain portion of the electromagnetic spectrum
range from 20000 nm to 40000 nm. Calculate the lowest frequency
(in MHz) associated with that portion of the spectrum.
Calculate the resistivity of the subsurface if an inducing electromagnetic
wave of 10 kHz frequency penetrates up to 4 km. 3+2=5
8 Derive the vertical component of the gravity field versus horizontal
distance from the centre. 5
SECTION—B
6. (a) (i) Justify that X-ray diffraction is a proof of wave nature of light.
(ii) The spacing between principal planes of NaCl crystals is 2:82 A. It is found
that the first-order Bragg reflection occurs at an angle of 10°. Calculate the
wavelength of X-rays. 2-3೯5
(૪) Draw the ‘practical’ circuit of a differentiator by using an operational amplifier
and briefly explain the working of this circuit. Where do you find the
applications of this circuit? 4+1=5
(© How do you obtain polarized output from He-Ne laser? Why are external
mirrors preferred in making some He-Ne laser resonators? 4+1=5
(୩ (9 What are the types of dispersion in optical fiber communication?
(ಗ) A 20mW laser beam passing through a 50km optical fiber link
experiences loss of 0:4 dB/km. Calculate the output power in dBm. 5
BGSP-C-GPH/64 4
(e)
(9)
(h)
7. (a)
(b)
(०
0
(1)
0
(1)
Realize a NOT gate by using a transistor.
Show that
4456 + 5 + 57 +ABD+AC=B+C
What are the features of a Molniya orbit?
Compare the applications of the Sun-synchronous and geosynchronous
orbits.
The radius of a nucleus is 10714 m. Assume that the maximum value of kinetic
energy of an electron emitted by a radioactive nucleus is of the order of 4 MeV.
Using Heisenberg uncertainty principle, show that such an electron cannot
exist inside the nucleus.
ஆ ৯ ୮୨ ਕਿ > = > ਕਿ
Take L = 7 xP. Find the three components L,, Ly and L, of orbital angular
> >
momentum operator L. Evaluate the commutation relation [L,, P,]. (Here P is
the momentum operator and 7 is the position operator)
(0
(1)
Explain the concept of forbidden energy gap. With neat sketch, give the
order of band gap in metal, semiconductor and insulator. How does the
band gap vary with temperature in the above solids?
If the Einstein’s temperature of a material is 157 K, find the value of
specific heat at constant volume (C,) for the material at 100 K in
cal/mole/K, using Einstein’s formula. Also find the value of Einstein’s
frequency.
What are the standard techniques for the pulsed operation of a laser? With the
help of a suitable illustration, explain the mechanism of producing high energy
pulse of width in the ‘nanosecond’ regime.
¢
(ii)
¢
Write down the truth table and draw the logic diagram of a half-adder.
Realize a half-adder by using NOR logic.
A target is moving with a speed of 108 km per hour. A CW radar operating
at 4:25 GHz is employed to measure the speed. Obtain the value of
Doppler frequency seen by a stationary radar.
Draw the neat sketch of a particle of mass m confined in a one-
dimensional potential box of side L with infinite height. Mention the values
of potential at different regions (x <0, x > 7, 8000 <x 57). Write down the
relevant Schrédinger equation used to solve for getting quantized energy
eigenvalue.
8 An electron is constrained to move in one-dimensional potential box of
0-1 nm side. Obtain the first three eigenvalues in eV.
3+7=10
10
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(b) ¢ Discuss briefly the different ways of biasing a depletion type MOSFET.
8 What is the role of Rg in the circuit given below?
+ ৮০০
Rp
a.c.
signal
7+3=10
(c) i) Discuss the importance of studying the laser rate equations.
(ii) If the duration of a pulse emitted from a 7:5 W ruby laser is 15 ns, find out
the number of emitted photons in that pulse. 6+4=10
9. (a) 0 (1) Convert 9810 to its binary equivalent.
(2) Convert (10-1011) to its decimal equivalent. 2+2=4
(ii) A low Earth orbit satellite is in a circular polar orbit with an altitude, 7, of
1000 km. Calculate the velocity of the satellite in the orbit. 6
(b) டு What are the limitations of use of time-independent perturbation theory?
(ii) Derive an expression for first-order correction to energy using the above
theory for non-degenerate case. 3+7=10
(જં ¢ Write down the Curie law and Curie-Weiss law. Plot 1 /% versus T using
these laws and give physical inferences. (Here % is the magnetic
susceptibility and T is the temperature in Kelvin scale) 5
(1) The voltage applied across the ೩.೦. Josephson junction is 80. Calculate
the frequency of the radiation emitted by the junction.
How can this result be used for practical application? 3+2=5
10. (a) (0 With suitable diagram, explain the lateral confinement technique
employed in heterostructure lasers. Where are these lasers mostly used?
5+1=6
(1) Discuss the phenomenon of laser spiking that takes place in ruby laser. 4
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(b) (¢ Why do you need A/D and D/A converters? Explain the different
sequential processes involved for A/D and D/A conversions with suitable
diagrams. 5
(i) With reference to radar systems, explain (1) range of resolution,
(2) Doppler frequency and (3) coherence. 5
(© (0 What is Fermi’s golden rule for time-dependent perturbation theory? 4
(i) Enlist some contrasting points between non-relativistic and relativistic
quantum theory. What are the limitations of Klein-Gordon equations?
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