GATE 2025 Question Paper Geology and Geophysics - Geophysics (GG-2)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Is there any good show _______ television tonight?

Select the most appropriate option to complete the above sentence.

(A) in

(B) at

(C) within

(D) on

Q.2 As the police officer was found guilty of embezzlement, he was _______ dismissed
from the service in accordance with the Service Rules.

Select the most appropriate option to complete the above sentence.

(A) sumptuously

(B) brazenly

(C) unintentionally

(D) summarily

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Q.3 The sum of the following infinite series is:

1 1 1 1 1
+ + + + +⋯
1! 2! 3! 4! 5!

(A) 𝜋

(B) 1+𝑒

(C) 𝑒−1

(D) 𝑒

Q.4 A thin wire is used to construct all the edges of a cube of 1 m side by bending,
cutting and soldering the wire. If the wire is 12 m long, what is the minimum number
of cuts required to construct the wire frame to form the cube?

(A) 3

(B) 4

(C) 6

(D) 12

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Q.5 The figures I, II and III are parts of a sequence. Which one of the following options
comes next in the sequence at IV?

?

I II III IV

(A)

(B)

(C)

(D)

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Q.6 – Q.10 Carry TWO marks Each

Q.6 “Why do they pull down and do away with crooked streets, I wonder, which are my
delight, and hurt no man living? Every day the wealthier nations are pulling down
one or another in their capitals and their great towns: they do not know why they do
it; neither do I. It ought to be enough, surely, to drive the great broad ways which
commerce needs and which are the life-channels of a modern city, without
destroying all history and all the humanity in between: the islands of the past.”

(From Hilaire Belloc’s “The Crooked Streets”)

Based only on the information provided in the above passage, which one of the
following statements is true?

(A) The author of the passage takes delight in wondering.

(B) The wealthier nations are pulling down the crooked streets in their capitals.

(C) In the past, crooked streets were only built on islands.

(D) Great broad ways are needed to protect commerce and history.

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Q.7 Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant,
he notices that the hour and minute hands on the wall clock are exactly coinciding.
After about an hour, when he leaves the restaurant, he notices that the clock hands
are again exactly coinciding. How much time (in minutes) did Rohit spend at the
restaurant?

(A) 6
64 11

(B) 5
66 13

(C) 5
65 11

(D) 6
66 13

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Q.8 A color model is shown in the figure with color codes: Yellow (Y), Magenta (M),
Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).

Which one of the following options displays the color codes that are consistent with
the color model?

(A)

(B)

(C)

(D)

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Q.9 A circle with center at (𝑥, 𝑦) = (0.5, 0) and radius = 0.5 intersects with another
circle with center at (𝑥, 𝑦) = (1, 1) and radius = 1 at two points. One of the points
of intersection (𝑥, 𝑦) is:

(A) (0, 0)

(B) (0.2, 0.4)

(C) (0.5, 0.5)

(D) (1, 2)

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Q.10 An object is said to have an 𝑛-fold rotational symmetry if the object, rotated by an
2𝜋
angle of , is identical to the original.
𝑛

Which one of the following objects exhibits 4-fold rotational symmetry about an
axis perpendicular to the plane of the screen?

Note: The figures shown are representative.

(A)

(B)

(C)

(D)

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PART A: COMPULSORY SECTION FOR ALL CANDIDATES
Q.11– Q .17 Carry ONE mark Each

Q.11 The most volcanically active body in our Solar System is

(A) Mars

(B) Io

(C) Moon

(D) Venus

Q.12 A type of fold which is relatively sharp and angular at its synformal and
antiformal hinges is known as

(A) Fan fold

(B) Drag fold

(C) Chevron fold

(D) Dome

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Q.13 Which one of the following geophysical methods can provide information
on deep Earth structures (of the order of 1000 km) with highest resolution?

(A) Seismic methods

(B) Magnetic methods

(C) Electrical methods

(D) Gravity methods

Q.14 The continuous series of Bowen’s reaction series is represented by

(A) the orthoclase - albite feldspar system

(B) the anorthite - albite system

(C) the forsterite - fayalite system

(D) the diopside - anorthite system

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Q.15 Which of the following time boundaries correspond(s) to major mass extinction
events?

(A) Cretaceous - Paleogene

(B) Paleogene - Neogene

(C) Permian - Triassic

(D) Precambrian - Cambrian

Q.16 A watershed has an area of 74 km2. The stream network within this watershed
consists of three different stream orders. The stream lengths in each order are
as follows:

Ist order streams: 3 km, 2.5 km, 4 km, 3 km, 2 km, 5 km

IInd order streams: 10 km, 15 km, 7 km

IIIrd order streams: 30 km

The drainage density of the watershed is __________ km/km2

(Round off to two decimal places)

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Q.17 A sample contains 7 wt% CaO and 5 wt% MgO. The molar ratio of CaO to MgO
in the sample is ___________

(Round off to two decimal places)

Q.18 – Q .26 Carry TWO marks Each

Q.18 Select the option that lists oxide minerals only.

(A) Spinel, Corundum, Rutile

(B) Olivine, Pyroxene, Magnetite

(C) Apatite, Galena, Monazite

(D) Fluorite, Halite, Calcite

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Q.19 Consider two intersecting, north-easterly striking and south-easterly dipping
dikes Y1 and Y2, which are exposed on an east-west trending vertical wall of
a granite (X) quarry as shown below.

The angle that the dikes make with the horizontal on the quarry wall is

(A) true dip

(B) apparent dip

(C) rake

(D) attitude of foliation

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Q.20 The ratio of P-wave to S-wave velocities, Vp/Vs, within the Earth depends on

(A) bulk modulus

(B) shear modulus

(C) density

(D) coefficient of internal friction

Q.21 Three pixels P, Q, and R in an image are characterized by the NDVI values
of + 0.84, + 0.01, and − 0.89, respectively. Which of the following options
is/are correct?

(A) P is from vegetation area and Q is from barren land

(B) Q is from water body and R is from barren land

(C) Q is from barren land and R is from water body

(D) P is from vegetation area and Q is from water body

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Q.22 Which of the following can indicate the presence of significant
sub-surface iron mineralization?

(A) Free air gravity anomaly

(B) Bouguer gravity anomaly

(C) Magnetic anomaly

(D) Electrical resistivity measurements

Q.23 Which of the following statements is/are correct regarding the magnetic
field lines of the Earth, at the magnetic poles and the magnetic equator?

(A) Horizonal at the equator

(B) Vertical at the poles

(C) Horizonal at the poles

(D) Vertical at the equator

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Q.24 If the lowest Digital Number (DN) value in an image of 10-bit radiometric
resolution is 0, then the maximum DN value of that image is _________

(Answer in integer)

Q.25 If one liter of water at pH 7 is mixed with one liter of water at pH 6, the
resulting pH of the mixture is ____________

(Round off to two decimal places)

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Q.26 A hillslope is shown below. If the area over the failure plane is 50 m2 and the
weight of the hillslope material (W) is 2000 tons, the Factor of Safety (FOS)
for this hillslope in dry conditions is ______________

(Cohesion along failure plane = 196 KPa, dip of failure plane = 60, and internal
friction angle = 30).

(Round off to two decimal places)

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PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY
Q.27 – Q.44 Carry ONE mark Each

Q.27 A scalar potential 𝜓 of a vector field, F, satisfies the Laplace equation
(∇2 𝜓 = 0) in free space. 𝜓 can be uniquely determined at any point inside
the closed surface S using

(A) ∇. 𝐅 = 0

(B) ∇×𝐅 =0

(C) 𝜓(𝐱) = constant, 𝐱 ∈ 𝑆

(D) ∇. 𝐅 ≠ 0

Q.28 In resistivity measurements for a double-dipole system, the apparent resistivity
is NOT affected by

(A) the electrode spacing

(B) the resistivity of the subsurface

(C) the distance between the centers of the current and potential dipoles

(D) the telluric current

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Q.29 The working of the proton-precession magnetometer is based on

(A) the magnetic moment of hydrogen-atom nucleus being proportional to the
angular momentum of its spin

(B) the fact that oxygen is diamagnetic

(C) the fact that the lowest energy level of electrons is in the ground state

(D) the Zeeman effect

Q. 30 Which one of these statements is NOT correct for electromagnetic waves
travelling through the subsurface?

(A) They cannot travel without attenuation

(B) They are subject to diffraction

(C) They are analogous to seismic P waves

(D) They can be used to detect highly conductive ore bodies

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Q. 31 Diurnal correction in magnetic survey data accounts for

(A) geomagnetic polarity reversals

(B) charged particles in ionosphere

(C) the westward drift of the Earth’s magnetic field

(D) the lunar magnetic field

Q. 32 Which one of the following options is the primary contributor to the
International Geomagnetic Reference Field?

(A) Ionospheric magnetic field

(B) Magnetic field generated in the outer core

(C) Crustal magnetic field

(D) Solar magnetic field

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Q. 33 If a planet is made of uniform density material and has no topography, then
which one of the following statements is correct?

(A) The geoid surface would be higher than the reference ellipsoid surface

(B) The geoid surface would be lower than the reference ellipsoid surface

(C) The geoid and the reference ellipsoid surfaces would coincide

(D) The geoid surface would be lower in some places, and higher in other places,
with respect to the reference ellipsoid

Q. 34 Which one of the following factors leads to an abrupt increase in density at the
mantle-outer core boundary?

(A) Composition change

(B) Temperature change

(C) Phase change

(D) Viscosity change

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Q. 35 Which one of the options is correct about 𝛽 − decay?

(A) Atomic number increases and mass number remains constant

(B) Atomic weight increases and atomic number remains constant

(C) Number of protons increases and number of neutrons remains constant

(D) Number of neutrons increases and number of protons remains constant

Q. 36 F denotes force, A denotes area, L denotes length, and ∆L is the change in length
due to the applied force. Assuming linear elasticity, select a relationship where
the constant of proportionality is a material property independent of the
dimensions of the body.

(A) F ∝ ∆L

(B) F ∝ ∆L/L

(C) F ∝ A × ∆L/L

(D) F ∝ ∆L × L/ A

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Q. 37 In a gravity survey that is being carried out in the vicinity of a large mountain,
it was observed that the deflection of the plumb line from the vertical is less
than what is calculated using the visible mountain mass. Which one of the
inferences about the mountain is correct?

(A) It has a high-density root

(B) It has no root

(C) It has a low-density root

(D) It has a high-density anti-root

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Q.38 In the schematic, line P shows a 1-D geothermal profile. If the heat
flow at the base of the mantle increases, which line will reflect the new
geothermal profile?

temperature
depth lithosphere

mantle

S R P Q

(A) Line Q

(B) Line R

(C) Line S

(D) Line P

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Q.39 The following figure shows the GPS data at two stations located near each
other at the same latitude. Station A is moving towards the west while
station B is moving towards the east. Which one of the following options
is correct?

A B

(A) A and B are located on two sides of a convergent boundary

(B) A and B are located on two sides of a transform boundary

(C) A and B are located on two sides of a divergent boundary

(D) A and B are parts of the same plate

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Q. 40 The following figure shows a region in which rocks in areas A, B and C
follow Hooke’s law and are subject to the same stress. B exhibits lower
strain than both A and C. What can we infer about the nature of B?

A
B C

(A) B is part of a plate boundary

(B) B has higher heat flow values compared to A and C

(C) B is made up of rocks of lower density compared to A and C

(D) B is made up of rocks that have higher strength compared to A and C

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Q. 41 What is/are the primary effect(s) of applying upward continuation to magnetic
field data?

(A) Decrease in the relative influence of shallow magnetic sources

(B) Increase in the relative influence of deeper magnetic sources

(C) Improvement in the detection of near-surface magnetic sources

(D) Movement of shallow magnetic sources closer to the observation plane

Q. 42 Half-life of 14C is 5730 years. Suppose we start with 1 billon 14C atoms and
after a certain interval of time only 125 million 14C atoms remain, the number
of half-lives that has elapsed is ________

(Answer in integer)

Q.43 When an external magnetic field of strength 1. 5 × 10−3 𝐴/𝑚 is applied to a
rock sample, the measured intensity of magnetization is 0. 5 × 10−3 𝐴/𝑚.
The magnetic susceptibility of this rock is _________

(Round off to two decimal places)

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Q.44 If seismic signals of periods greater than 10 s are of interest, the minimum
sampling frequency should be _________ Hz.

(Round off to one decimal place)

Q.45 – Q .65 Carry TWO marks Each

Q.45 The components 𝑢, 𝑣, 𝑤 of the displacement field along 𝑥, 𝑦, 𝑧 directions,
respectively, are given by

𝑢 = − 𝑠𝑖𝑛( 𝜔𝑡 − 𝑘𝑧)
𝑣 = 𝑠𝑖𝑛( 𝜔𝑡 − 𝑘𝑧)
𝑤=0

where, 𝑡, 𝑘, and 𝜔 are time, wavenumber, and angular frequency, respectively.
Assuming 𝑘 is real, which one of the following options describes the wave?

(A) An S-wave propagating in the 𝑧 direction

(B) A P-wave propagating in the 𝑧 direction

(C) A Rayleigh wave with elliptical motion in the 𝑥𝑦 plane

(D) An S-wave travelling in the 𝑥 direction

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Q.46 Select the correct statement regarding surface waves and upper mantle structure.

(A) Surface waves cannot be used to infer the upper mantle structure as the
amplitudes decay with increasing distance from the surface

(B) Surface waves can be used to infer the upper mantle structure as surface wave
phase velocity varies with frequency

(C) Surface waves can be used to infer the upper mantle structure as the shear-wave
velocity of the medium changes with frequency

(D) Surface waves cannot be used to infer the upper mantle structure as surface
waves travel only along the surface and are not sensitive to the Earth’s internal
structure

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Q.47 A geophysicist is analyzing the elastic-wave radiation to infer the body force
equivalent of a seismic source. She has plotted the horizontal component of
the displacement field, denoted as 𝑢(𝒎, 𝑡), for time 𝑡 and location 𝒎. The
measured field at two locations 𝒎 and 𝒏 is plotted in the figure. Note that S
and P waves have negligible amplitudes at locations 𝒎 and 𝒏, respectively.
Assuming a homogeneous medium, select the most probable direction
(specified by the angle 𝛼) along which the force 𝐹⃗ is applied.

(A) 𝛼 = 0°

(B) 𝛼 = 90°

(C) 𝛼 = 135°

(D) 𝛼 = 315°

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Q.48 For a horizontal liquid-solid interface as shown, which one of the following
ray diagrams with an incident P wave is correct? SH and SV denote
shear-horizontal and shear-vertical waves, respectively.

(A) A

(B) B

(C) C

(D) D

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Q.49 Consider a steady state heat conduction equation for the Earth’s crust where
𝐴 is the heat source and 𝑘 is the thermal conductivity. Given the boundary
conditions:
i) 𝑇 = 0 at the surface and
ii) 𝑄 is the heat flux at the surface,
which one of the following options would be the temperature (𝑇) at depth 𝑧 ?

(A) (𝐴𝑧 + 2𝑄)𝑧
−
2𝑘

(B) (𝐴𝑧 + 2𝑄)𝑧
−
𝑘

(C) (𝐴𝑧 + 𝑄)𝑧
−
2𝑘
(𝐴 + 2𝑄)𝑧 2
(D) −
2𝑘

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Q.50 Consider a ray tomography experiment, where the goal is to estimate the
wave velocity of 9 square cells plotted in each of the cases A and B. The ray
paths for source-receiver pairs for both these cases are shown in the figure.
Select the correct statement.

(A) Both A and B are well-determined problems

(B) Case A has a unique solution, and B is underdetermined

(C) Both A and B are mixed determined problems

(D) Case A is mixed determined, and B is underdetermined

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Q.51 Consider extracting the subsurface medium response by cross-correlating
seismic ambient noise 𝑢(𝑡) and 𝑣(𝑡) measured at two stations. The
cross-correlation 𝑥(𝑡) = ∑𝜏 𝑢(𝜏)𝑣(𝜏 + 𝑡) averaged over a period of one year
is plotted in the figure, with most of the energy in the positive time lags.
In this figure, four probable seismic sources are marked (i), (ii),
(iii) and (iv). Assuming a homogeneous medium, select the source that
is most probably excited.

(A) (i)

(B) (ii)

(C) (iii)

(D) (iv)

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Q.52 Given the following electric field in cartesian coordinates

̂,
𝐄 = 𝑥 2 𝑦 𝒊̂ + 𝑦 2 𝑧 𝒋̂ + 𝑧 2 𝑥 𝒌

which of the following statements is/are correct?

(A) The electric field is not conservative

(B) The electric field is static

(C) Both divergence and curl of the electric field are zero

(D) Electric field is neither conservative nor static

Q.53 What factor(s) determine(s) the magnitude of peak ground acceleration
measured at a particular station due to an earthquake?

(A) Distance from the earthquake

(B) Rupture directivity

(C) Origin time of the earthquake

(D) Type of soil

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Q.54 Consider a geophysical inverse problem of the form 𝒅 = 𝑮𝒎, where 𝑮 is the
forward operator, 𝒎 is the model vector and 𝒅 is the observed data vector.
The Earth model parameters can be estimated using 𝒎𝑒𝑠𝑡 = 𝑯𝒅 , where 𝑯 is
the pseudoinverse of 𝑮. Given 𝑮 = 𝑼𝚺𝑽𝑻 as the singular value decomposition
of 𝑮, and assuming 𝑮 is full rank, which of the following options is/are correct?

(A) 𝑯 = 𝑼𝑻 𝚺 −𝟏 𝐕

(B) 𝑯 = 𝑽𝚺 −𝟏 𝑼𝑻

(C) 𝑯 = 𝑼𝑻 𝚺 −𝟏 𝑽𝑻

(D) 𝑯 = 𝑼𝑼𝑻 𝐕𝚺 −𝟏 𝑼𝑻

Q.55 Consider ray tracing in an isotropic elastic Earth, with travel time function
𝑇(𝑥, 𝑦, 𝑧) in Cartesian coordinates. Select the correct option(s).

(A) The slowness vector is tangential to the wave fronts

(B) The slowness vector is parallel to the gradient of 𝑇(𝑥, 𝑦, 𝑧)

(C) 𝑇(𝑥, 𝑦, 𝑧) is constant on a particular wave front

(D) 𝑇(𝑥, 𝑦, 𝑧) is constant along the rays

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Q.56 Which of the following statements is/are correct regarding the properties of the
oceanic lithosphere?

(A) Older lithosphere cools at a slower rate compared to younger lithosphere

(B) Heat flow increases with lithospheric age

(C) Heat flow in the lithosphere increases with distance from the spreading ridge

(D) Thickness of the lithosphere increases with age

Q.57 For a half space composed of 3 layers with resistivities 𝜌1 , 𝜌2 and 𝜌3 , as shown
in the figure, which of the following statements is/are correct about the variation
of apparent resistivity with electrode spacing?

(A) If 𝜌1 < 𝜌2 < 𝜌3 , the curve of apparent resistivity increases monotonically

(B) If 𝜌1 < 𝜌2 > 𝜌3 , the curve of apparent resistivity decreases monotonically

(C) If 𝜌1 > 𝜌2 < 𝜌3 , the curve of apparent resistivity first decreases and then
increases

(D) If 𝜌1 > 𝜌2 > 𝜌3 , the curve of apparent resistivity increases monotonically

Organizing Institute: IIT Roorkee Page 37 of 42

Q.58 A loop of radius R carries a current I and produces a magnetic field B.
Which of the following statements is/are correct about B?

(A) The magnitude of B is directly proportional to I

(B) The magnitude of B is inversely proportional to the square of radius R

(C) The direction of B is perpendicular to the plane of the loop

(D) The direction of B is parallel to the plane of the loop

Q.59 In seismology, Born approximation of the scattered (perturbed) wavefield is
given by
𝛿𝑢(𝒓, 𝒔 ; 𝑡) ≈ ∫𝑉 𝛿𝑟(𝒙)(𝑢0 (𝒙, 𝒔 ; 𝑡) ∗𝑡 𝑢0 (𝒓, 𝒙 ; 𝑡)) 𝑑𝒙.
Here,
• ∗𝑡 denotes temporal convolution
• 𝛿𝑟(𝒙) is the strength of the scatterer at 𝒙 in volume 𝑉
• 𝛿𝑢(𝒓, 𝒔 ; 𝑡) is the scattered wavefield measured at the receiver 𝒓 from
the source 𝒔
• 𝑢0 (𝒙, 𝒔 ; 𝑡) is the downgoing wavefield (to the scatterer at 𝒙 from the
source 𝒔) in the unperturbed medium
• 𝑢0 (𝒓, 𝒙 ; 𝑡) is the upgoing wavefield (to the receiver 𝒓 from the
scatterer at 𝒙.) in the unperturbed medium

Select the correct statement(s).

(A) The Born approximation can be used to model multiply scattered waves

(B) The Born approximation can model only first-order scattering

(C) The scattered wavefield varies linearly with strength of the scatterers

(D) The Born approximation can be used to model head waves from a horizontal
reflector

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Q.60 A primary electromagnetic field (𝐻𝑃 ) is being generated from current 𝐼𝑃 flowing
in a coil A with negligible capacitance, such that 𝐻𝑃 = 𝐾𝐼𝑃 sin 𝜔𝑡, where 𝜔 is
the angular frequency, 𝐾 is a constant and 𝑡 is time. A secondary
electromagnetic field is being produced by induction in a conducting coil B. The
phase difference between the primary and the secondary electromagnetic fields
depends on which of the following factors?

(A) Inductance of coil B

(B) Resistance of coil B

(C) Frequency of the primary electromagnetic field

(D) Total current (𝐼𝑃 ) flowing through the coil A

Organizing Institute: IIT Roorkee Page 39 of 42

Q.61 Consider a medium of uniform resistivity with a pair of source and sink
electrodes separated by a distance 𝐿 , as shown in the figure. The fraction of
the input current (𝐼) that flows horizontally (𝐼𝑥 ) across the median plane
𝐿 𝐿 √3 𝐼 𝐿 𝑍2 𝑑𝑧
between depths 𝑧1 = and 𝑧2 = , is given by 𝑥 = ∫ 2 .
2 2 𝐼 𝜋 𝑍 1 (𝐿 +𝑧 2 )
4

𝐼𝑥
The value of is equal to __________
𝐼

(round off to two decimal places)

(Figure not to scale)

Organizing Institute: IIT Roorkee Page 40 of 42

Q.62 Suppose a mountain at location A is in isostatic equilibrium with a column
at location B, which is at sea-level, as shown in the figure. The height of the
mountain is 4 km and the thickness of the crust at B is 1 km. Given the
densities of crust and mantle are 2700 kg/m3 and 3300 kg/m3, respectively,
the thickness of the mountain root (r1) is ________km.

(Answer in integer)

A

4 km
B

Crust 1 km

r1
Mantle

(Figure not to scale)

Q.63 While doing Bayesian inference, consider estimating the posterior distribution
of the model parameter (m), given data (d). Assume that Prior and Likelihood
are proportional to Gaussian functions given by

Prior ∝ 𝑒𝑥𝑝( − 0.5(𝑚 − 1)2 )
Likelihood ∝ 𝑒𝑥𝑝( − 0.5(𝑚 − 3)2 )

The mean of the posterior distribution is ______

(Answer in integer)

Organizing Institute: IIT Roorkee Page 41 of 42

Q.64 Consider a two-dimensional reflection experiment, where a horizontal
boundary between two layers is at a depth of 500 m below the free surface.
A source and geophone are placed on the free surface with an offset of
2000 m. The P wave velocity of the top layer is 3000 m/s. The travel time
of a recorded free-surface reflection multiple, which got reflected twice at
the free surface, is __________ s.

(Round off to two decimal places)

Q. 65 Consider the acceleration due to gravity (g ) at an altitude (h) of 50 km above
the Earth’s surface. If R is the radius of the Earth, and the acceleration due to
gravity measured at the surface is g, the ratio of g to g, is ________

(Assume h<<R, R = 6370 km, and round off to two decimal places)

Organizing Institute: IIT Roorkee Page 42 of 42

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