GATE 2021 Question Paper GG Geophysics

General Aptitude (GA)

Q.1 - Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 The people ___________ were at the demonstration were from all sections of
society.

(A) whose

(B) which

(C) who

(D) whom

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Q.2

A transparent square sheet shown above is folded along the dotted line. The
folded sheet will look like ________.

(A)

(B)

(C)

(D)

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Q.3 For a regular polygon having 10 sides, the interior angle between the sides
of the polygon, in degrees, is:

(A) 396

(B) 324

(C) 216

(D) 144

Q.4
(
Which one of the following numbers is exactly divisible by 11 + 1 ?
13
)
(A) 1126 + 1

(B) 1133 + 1

(C) 1139 − 1

(D) 1152 − 1

Q.5 Oasis is to sand as island is to ________
Which one of the following options maintains a similar logical relation in the
above sentence?

(A) Stone

(B) Land

(C) Water

(D) Mountain

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Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q.6 The importance of sleep is often overlooked by students when they are
preparing for exams. Research has consistently shown that sleep deprivation
greatly reduces the ability to recall the material learnt. Hence, cutting down
on sleep to study longer hours can be counterproductive.
Which one of the following statements is the CORRECT inference from the
above passage?

(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser
benefit.

(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.

(C) If a student is extremely well prepared for an exam, he needs little or no sleep.

(D) To do well in an exam, adequate sleep must be part of the preparation.

Q.7

In the figure shown above, each inside square is formed by joining the
midpoints of the sides of the next larger square. The area of the smallest
square (shaded) as shown, in cm2 is:

(A) 12.50

(B) 6.25

(C) 3.125

(D) 1.5625

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Q.8 Let X be a continuous random variable denoting the temperature measured.
The range of temperature is [0, 100] degree Celsius and let the probability
density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.
The mean of X is _____

(A) 2.5

(B) 5.0

(C) 25.0

(D) 50.0

Q.9 70
60
60
50 50
50

40

30

20
10
10 5 3
0
Year 1 Year 2 Year 3

Pass Fail

The number of students passing or failing in an exam for a particular subject
are presented in the bar chart above. Students who pass the exam cannot
appear for the exam again. Students who fail the exam in the first attempt
must appear for the exam in the following year. Students always pass the exam
in their second attempt.
The number of students who took the exam for the first time in the year 2 and
the year 3 respectively, are __________.

A) 65 and 53

(B) 60 and 50

(C) 55 and 53

(D) 55 and 48

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Q.10 Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that
order. The cars T and U should be parked next to each other. The cars S and
V also should be parked next to each other, whereas P and Q cannot be
parked next to each other. Q and S must be parked next to each other. R is
parked to the immediate right of V. T is parked to the left of U.
Based on the above statements, the only INCORRECT option given below
is:

(A) There are two cars parked in between Q and V.

(B) Q and R are not parked together.

(C) V is the only car parked in between S and R.

(D) Car P is parked at the extreme end.

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Geophysics (GG)

Q.1 - Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 Which of the given planets has the highest average density?

(A) Mercury

(B) Venus

(C) Earth

(D) Mars

Q.2 In a multi-electrode resistivity tomography (ERT) survey, using equally
spaced electrodes, which of the given configurations will provide the
maximum number of data points?

(A) Wenner array

(B) Axial Dipole-dipole array

(C) Axial Pole-dipole array

(D) Schlumberger array

Q.3 In Electromagnetic methods of prospecting, which one of the given options
is CORRECT about frequency and type of current source for the Primary
field used?

(A) High frequency A.C.

(B) Low frequency A.C.

(C) Both high frequency A.C. and D.C.

(D) Low frequency D.C.

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Q.4 ‘Group’ is a unit of:

(A) Lithostratigraphy

(B) Sequence stratigraphy

(C) Biostratigraphy

(D) Chronostratigraphy

Q.5 Furongian is an Epoch of:

(A) Cambrian

(B) Ordovician

(C) Triassic

(D) Cretaceous

Q.6 The stage of textural maturity of a clay-rich sandstone containing poorly-
sorted and angular framework grains is:

(A) Mature

(B) Supermature

(C) Immature

(D) Submature

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Q.7 Which one of the following structures indicates Synsedimentary
deformation?

(A) Festoon bedding

(B) Flaser bedding

(C) Tabular bedding

(D) Convolute bedding

Q.8 Low value in SP log as observed in dispersed shales is mainly due to the
impeded movement of:

(A) Na+ ion

(B) Cl ion

(C) K+ ion

(D) OH- ion

Q.9 In Radiometric survey, the g-ray spectrometer count rate depends on:

(A) Cracks present in the target rock volume

(B) Solid angle of the target rock about the spectrometer

(C) Temperature in the target rock

(D) Pressure in the target rock

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Q.10 The dimension of radiant emittance of a blackbody as per Stefan-
Boltzmann law is:

(A) M0L1T-1

(B) M1L-1T-2

(C) M1L2T-2

(D) M1L0T-3

Q.11 A surface geological process that can create a landform called Cirque is:

(A) aeolian deposition

(B) fluvial deposition

(C) glacial erosion

(D) deposition of volcanic ash

Q.12 If  and  are P- and S-wave velocities, respectively, then 2 – (4/3)2 is
equal to:
( is the bulk modulus,  is shear modulus and  is density)

(A) /

(B) /

(C)  + /

(D)  - /

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Q.13 Which one of the following phases is P-wave that converts to S-wave during
passage through the solid inner core?

(A) PKIKP

(B) PKJKP

(C) PKiKP

(D) PKPPcP

Q.14 In reduction of gravity data, the latitude correction is maximum at:

(A) 35° latitude

(B) 45° latitude

(C) 55° latitude

(D) 65° latitude

Q.15 The most coaliferous unit of the Gondwana Supergroup is:

(A) Talchir Formation

(B) Barakar Formation

(C) Karharbari Formation

(D) Panchet Formation

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Q.16 - Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.16 A vertical borehole encounters a shale bed of uniform thickness occurring
at a depth of 5 m and dipping 60o. The borehole pierces through this shale
bed for a length of 10 m to reach a sandstone layer below. The true
thickness of the shale bed is ________ m. [in integer]

Q.17 The mass and volume of a fully dried soil sample are 2200 gm and 1100
cm3, respectively. If the specific gravity of the soil particles is 2.5 and water
density is 1 gm/cm3, the void ratio of the soil is ________. [round off to 2
decimal places]

Q.18 A constant-head permeability test was performed on a vertical sand
column of height 40 cm and cross-sectional area of 25 cm2. During the test,
when the loss of head was 50 cm, the volume of water collected in 2 minutes
was 300 cm3. Applying Darcy’s law, the calculated coefficient of
permeability of the sand column is ________ cm/sec. [round off to 2
decimal places]

Q.19 The radius (r) of the oblate spheroid at 45° latitude with ellipticity of polar
flattening of 1/298.25 and equatorial radius of 6378140 m is ________ km.
[round off to 2 decimal places]

Q.20 Light passes through two media with refractive indices of 1.75 and 1.55,
respectively. The thickness of both the media is 30 m. The resultant path
difference of the yellow light component ( = 589 nm) is ________ m.
(Take  = 3.141) [round off to one decimal places]

Q.21 The water table in an unconfined aquifer at a place near the coast is 1 m
above the Mean Sea Level. Given the densities of fresh and saline water as
1.001 and 1.025 g/cc, respectively, the fresh-saline water interface at the
same location should be at a depth of _______ m from the water table.
[round off to one decimal place]

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Q.22 The volume percentage of galena and quartz in an ore body of Pb are 90
and 10, respectively. The densities of galena and quartz are 7.6 and 2.65
g/cc, respectively. The grade of the ore body in terms of weight percent of
Pb is _____. (Atomic weights of Pb = 206 and S = 32) [round off to 2 decimal
places]

Q.23 Normal moveout (NMO) for reflected phase of seismic data is 2
milliseconds. Consider the diffraction source at the edge of the same
reflector, where the shot point is directly above diffraction source. In this
case, the NMO due to diffraction is ______ milliseconds [in integer].

Q.24 In a 2D seismic survey, first receiver location is at (1000 m, 4000 m), second
receiver location is at (2000 m, 4000 m) and the source location is at
(2000 m, 1000 m). Consider P-wave velocity as 5000 m/sec. The difference
in first arrival time of P-wave phase for the two receivers is ________
seconds. [round off to 2 decimal places].

Q.25 The potential difference measured between potential electrodes using
Wenner array is 500 mV when a current of 2 A is passed through the
subsurface between current electrodes. If the computed apparent
resistivity is 100 m then the distance between the current electrodes will
be ________ m. [round off to 2 decimal places] (Use  = 3.141)

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Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q.26 In a horizontally stratified cuboid rock sample (stratified in vertical z
direction with various layers of different resistivity), bulk resistivity is
measured in three perpendicular directions. If 1, 2, and 3 are the bulk
resistivities measured perpendicular to xy, xz and yz planes, respectively,
then

(A) 1 < 2 = 3

(B) 1 > 2 = 3

(C) 1 = 2 ≠ 3

(D) 1 ≠ 2 ≠ 3

Q.27 Which one is the CORRECT sequence of electromagnetic methods in terms
of depth of investigation?
P – AFMAG method
Q – VLF method
R – GPR method
S – Magnetotelluric method

(A) P > Q > S > R

(B) P > S > R > Q

(C) S > P > Q > R

(D) S > Q > R > P

Q.28 Which Norm gives the maximum weight to the data points having
maximum deviation/outlier from the smoothly fitted curve during
linearized inversion?

(A) L1-Norm

(B) L2-Norm

(C) Lp-Norm

(D) L∞-Norm

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Q.29 Which one of the following statements is CORRECT for the Quenching
agent used in the tube of Geiger-Muller counter?

(A) It enhances the emission of secondary electrons from the cathode.

(B) It reduces the emission of secondary electrons from the cathode.

(C) It enhances the emission of secondary electrons from the anode.

(D) It reduces the emission of secondary electrons from the anode.

Q.30 Which one of the following statements is CORRECT regarding the
property of Laplacian operator for vector/scalar fields?

(A) Laplacian of a vector field is zero if the Laplacian of each of its components are
zero.

(B) Laplacian of a vector field is zero if the Laplacian of any one of its component
is zero.

(C) If the Laplacian of a scalar field is zero then the scalar field is not harmonic.

(D) If the Laplacian of a scalar field is finite (non-zero) then the scalar field is
harmonic.

Q.31 The most desirable interaction of -ray with matter for -ray spectroscopy
is

(A) Photoelectric effect only

(B) Both Photoelectric effect and Compton scattering

(C) Both Compton Scattering and Pair production

(D) Photoelectric effect, Compton scattering and Pair production

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Q.32 Which one of the following is the CORRECT sequence for a 2D seismic
reflection data processing prior to Time-depth conversion?

(A) Migration → Deconvolution → Filtering → Equalization → Coherency

(B) Deconvolution → Migration → Filtering → Coherency → Equalization

(C) Filtering → Deconvolution → Migration → Equalization → Coherency

(D) Deconvolution → Filtering → Equalization → Migration → Coherency

Q.33 Choose the CORRECT procedure to avoid the area of cracked, altered
formation in Sonic log.

(A) Measure interval transit times using long-spacing sonic tools.

(B) Use more number of sets of sources.

(C) Measure interval transit times using short-spacing sonic tools.

(D) Use more number of sets of detectors.

Q.34 The factor that DOES NOT influence measurement of Nuclear Magnetic
Resonance log is

(A) mineral composition of the rock.

(B) bound water (irreducible water).

(C) free water.

(D) pore fluid pressure.

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Q.35 Consider a time-invariant geophysical filter with the given input as:
𝒙(𝒕) = 𝒆−𝜶𝒕 𝒘𝒉𝒆𝒏 𝒕 ≥ 𝟎 ; 𝒙(𝒕) = 𝟎 𝒘𝒉𝒆𝒏 𝒕 < 𝟎 and output
𝒚(𝒕) = 𝒆−𝒕 𝒘𝒉𝒆𝒏 𝒕 ≥ 𝟎 ; 𝒚(𝒕) = 𝟎 𝒘𝒉𝒆𝒏 𝒕 < 𝟎. The transfer function for
the given input and output of time-invariant filter will be:

(A) 𝛼 + 𝑖𝜔
𝛽 − 𝑖𝜔

(B) 𝛼 + 𝑖𝜔
𝛽 + 𝑖𝜔

(C) 𝛼 − 𝑖𝜔
𝛽 + 𝑖𝜔

(D) 𝛼 − 𝑖𝜔
𝛽 − 𝑖𝜔

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Q.36 Which of the given figures is the Hilbert transform of the Dirac delta
function 𝜹(𝝃) :

(A) Figure 1

(B) Figure 2

(C) Figure 3

(D) Figure 4

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Q.37 If a mountain range is 100% isostatically compensated (Airy’s type), what
would be the expected nature of the Bouguer anomaly and free air
anomaly?

(A) Bouguer anomaly is very large and negative; free air anomaly is small and
positive.

(B) Bouguer anomaly is very large and negative; free air anomaly is large and
positive.

(C) Bouguer anomaly is exactly zero; free air anomaly is very large and positive.

(D) Bouguer anomaly is very large and negative; free air anomaly is large and
negative.

Q.38 Which of the following is INCORRECT for a recorded nuclear explosion
event?

(A) The first P-wave from an explosion to arrive at any seismic station, irrespective
of Azimuth, should be compressional.

(B) Nuclear explosions are not as good as earthquakes at generating surface waves
or S-waves.

(C) In general, earthquakes have Mb values same those for nuclear explosions with
same Ms values.

(D) Nuclear explosions have all been shallower than 2 km depth.

Q.39 Focal depth can be determined from measurement of the difference in the
travel time between:

(A) pP and P

(B) PP and P

(C) PcP and P

(D) PPP and P

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Q.40 Of the following options, at which discontinuity both P-wave and S-wave
have maximum velocity drop?

(A) Conard

(B) Mohorovicic

(C) Gutenberg

(D) Lehman

Q.41 In data enhancement techniques, what is the advantage of magnetic
anomaly being ‘Reduced to the pole’?

(A) Enhances the signal to noise ratio.

(B) Estimates the depth to the basement.

(C) Takes care of variation of the magnetic anomaly with latitude.

(D) Helps in pseudo-gravity transformation.

Q.42 Match the source in Group – I with their half-width (X1/2) / 𝛅𝒈𝐦𝐚𝐱 𝐚𝐧𝐝 depth
(d) relation in Group –II
Group - I Group - II
P. Sphere 1. 𝒅 = 𝟎. 𝟕𝑿𝟏/𝟐

𝛅𝒈
Q. Horizontal Cylinder 2. 𝐝 ≤ 𝟎. 𝟖𝟔 × { 𝐦𝐚𝐱⁄ 𝒅𝒈 }
( 𝒅𝒙 )
𝒎𝒂𝒙

R. Steeply dipping sheet 3. 𝒅 = 𝟏. 𝟑𝑿𝟏/𝟐
S. Irregular body 4. d= 𝑿𝟏/𝟐

(A) P-1, Q-2, R-4, S-3

(B) P-1, Q-4, R-3, S-2

(C) P-3, Q-4, R-1, S-2

(D) P-3, Q-1, R-4, S-2

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Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Q.43 If a gravity determination is made at an elevation of 150 m above mean sea
level, the Bouguer correction required for a density contrast of 250 kg m-3 with
the surroundings is________ mgal. [round off to 2 decimal places]

Q.44 An infinite horizontal cylinder of radius 40 km is buried at a depth of 100 km
and yields the same maximum gravity anomaly as that of an infinite horizontal
cylinder of radius 1 km, buried at a depth of 1 km having density contrast with
the surroundings of 200 kgm-3. The density contrast of the deeper cylinder with
respect to the surrounding is ________ kg/m3. [round off to one decimal place]

Q.45 An earthquake causes an average of 25 m strike slip displacement over a 50
km long, 25 km deep portion of a transform fault. Assuming that the rock
rigidity is 3  1010 Nm-2, the moment magnitude (Mw) of the earthquake is
______ . [round off to 2 decimal places]

Q.46 Lithological unit X is sandwiched between Y1 above and Y2 below it. Now
consider a log across lithology X, where Gamma ray (GR) reading is given by
100API; Y1 lithology, where minimum GR reading is 10API; and Y2 lithology
of shale, where GR reading is 200API. Then the shale-free fractional volume
in the X lithology will be________. [round off to 2 decimal places]

Q.47 In a 2D seismic survey, 25 receivers are placed in a group and 25 sources are
placed in another group, where random noise is present. The signal to noise
ratio for this arrangement will be_______. [in integer]

Q.48 In a VSP survey, the tube wave passage through borehole causes cross-
section area change from 0.79 m2 to 1.13 m2. The transmission coefficient will
be ______. [round off to 2 decimal places]

Q.49 In a cratonic region, radioactive heat generation decreases exponentially with
depth. Assuming characteristic depth as 10 km and surface heat generation
as 3 Wm-3 and neglecting mantle heat flow, the heat production per unit
volume for a 30 km thick layer will be_______ Wm-3. [round off to 2 decimal
places]

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Q.50 In an Induced Polarization survey, 50 milliseconds chargeability was
measured for steady state voltage (full saturation reached) of 200 V between
potential electrodes. When the current was switched off, the voltage across
potential electrodes drops instantaneously (time t = 0 s) to a level Va and
thereafter decays linearly with time and becomes zero in 10 seconds. The
magnitude of instantaneous voltage Va (at time t = 0 s) will be________ mV.
[in integer]

Q.51 Apparent resistivity sounding data for Schlumberger array is theoretically
generated by the teacher for the following 4-layer model as: 1 = 100 m,
2 = 20 m, 3 = 500 m, 4 = 10 m and layer thicknesses h1 = 50 m,
h2 = 20 m and h3 = 50 m. If the student interprets this theoretical sounding
data for 3 as 750 m, then according to the Principle of Equivalence, the
thickness h3 would be ________ m. [round off to 2 decimal places]

Q.52 A 3D conducting body is located at a depth of 50 m in a homogeneous
medium of resistivity 500 m. A frequency of f1 Hz is appropriate to detect
this conducting body in a plane wave EM survey. When the same conducting
body is located in a host medium of resistivity 100 m at the same depth then
𝒇
a frequency of f2 Hz is found to be appropriate. Then the value of 𝒇𝟐 will be
𝟏
_____________. [round off to 2 decimal places]

Q.53 The apparent resistivity and phase computed for MT measurement at 10-3 Hz
frequency is 500 m and 30, respectively. Ratio of Imaginary to Real
component of the Impedance tensor is ______. [round off to 2 decimal
places]

Q.54 The diagonal elements of a covariance matrix computed for a linearized
inverse problem having model parameters m1, m2, m3, m4, m5 are 49, 15, 3,
200, 40, respectively. The standard deviation (uncertainty) in the estimation
of model parameters m4 is ________. [round off to 2 decimal places]

Q.55 Electric current density incident at an angle 40 from vertical at the
horizontal interface between two layers with resistivity 1 = 100 m and
2 = 500 m (from layer 1 to layer 2). The current density will enter into the
second layer at an angle ________ degrees from vertical. [round off to 2
decimal places]

END OF THE QUESTION PAPER

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