UPSC Previous Year Question Paper 2026-Combined Geo-Scientist (Main) Examination,-GEO-PHYSICS paper II

Physical Constants :

Electron rest mass, meme​ = 9.109x10- 31 kg

Proton rest mass, mpmp​ = 1.672x10- 27 kg

Neutron rest mass, mnmn​ = 1.675x10- 27 kg

Atomic mass unit (C12 = 12 a.m.u.) = 1.661x10- 27 kg

Bohr magneton, μBμB​ = 9.27x10- 24 J/tesla

Nuclear magneton, μNμN​ = 5.05x10- 27 J/tesla

Boltzmann constant, kBkB​ = 1.381x10- 23 J/K

Universal gravitational constant, GG = 6.67x10- 11 N- m2/kg2

Magnetic permeability of free space, μ0μ0​ = 4πx10- 7 Wb/(A- m)

Permittivity of free space, ϵ0ϵ0​ = 8.85x10- 12 F/m

1. (a) Consider a stack of five horizontally stratified isotropic layers. Each layer has a thickness of 1m1m and the resistivity from top to bottom is alternate 10ohm⋅m10ohm⋅m and 100ohm⋅m100ohm⋅m . Find the thickness and resistivity of the equivalent isotropic layer. 8

(b) Draw a dip angle profile over a thin vertical conductor assuming a fixed horizontal loop transmitter. The current is flowing anticlockwise in the transmitter. Give justification for the profile plot. 8

(c) (i) What will be the ratio of reflected energy to incident energy for compressional wave incident normally over horizontal interface between shale and sandstone having velocity as 1.5km/s1.5km/s and 2.5km/s2.5km/s , and density as 2.2g/cc2.2g/cc and 2.7g/cc2.7g/cc respectively? 4

(ii) Arrange direct, reflected and refracted waves in order of their arrival times at a geophone located—

(1) between critical and crossover distances;
(2) beyond crossover distance over a horizontally stratified two-layer structure.

(d) How are current and potential electrodes placed in a borehole in normal resistivity logging? Derive a simplified mathematical relation to compute apparent resistivity in terms of electrode spacing. Differentiate between short and long normal resistivity logs. 8

(e) Explain the concept of free-air correction in gravity prospecting. Derive the mathematical relation for computation of free-air correction and give its numerical value. 8

UPSC Previous year question paper Geo scientist exam

1. (a) What are bright spot, flat spot and dim spot in seismic data recording? Draw a seismic reflection trace for a shot and geophone closely located over the following geological settings:

Shale as caprock followed by a gas sand layer, followed by an oil sand layer, followed by a water sand layer

Justify the amplitude and phase drawing in the trace for each geological unit. 4+6=10

(b) Using a three-layer resistivity model, explain the concept of equivalence as observed in resistivity data interpretation. 10

1. (a) In which geophysical method, 'reduction to pole' transformation is applied and why? Draw the anomaly profile taken at various latitudes (say, 0∘0∘ , 30∘30∘ , 45∘45∘ , 60∘60∘ ) over the same structure (say, spherical body) and explain how all profiles look after 'reduction to pole' transformation. 10

(b) (i) What is static shift in magnetotelluric data? 2

(ii) Consider a two-layer Earth model. The thickness of the first layer is 5km5km . The resistivities of the first and second layer are 10ohm−m10ohm−m and 1000ohm−m1000ohm−m respectively. Draw the plots showing variation of apparent resistivity and phase versus time period. Assume that the plane EM waves are travelling vertically downwards and the period range is 0⋅010⋅01 s to 100 s 100 s  . 5

(iii) Show how the plots in part (ii) will change in case of static shift. Mention suitable numerical values on all the plots. 3

(c) A formation is evaluated using density and neutron logs, and the following readings were obtained:

Bulk density from density log as 2⋅35 g/cc2⋅35 g/cc Matrix density as 2⋅65 g/cc2⋅65 g/cc Fluid density as 1⋅00 g/cc1⋅00 g/cc Neutron porosity reading as 0⋅300⋅30

Assuming that the formation is clean and water- filled, calculate the porosity from density log. Compare neutron porosity with density porosity, and write your observation about the nature of reservoir and its hydrocarbon potential. 10

1. (a) (i) Using travel time versus offset, explain how the unmigrated section will look like for a synclinal and an anticlinal feature. 6

(ii) What is the effect of migration on a dipping reflector? Draw a suitable diagram. 4

(b) What are the different methods for regional-residual anomaly separation in gravity method? Explain mathematically the polynomial fitting method (1st and 2nd order) in regional-residual separation and its efficacy and limitations. 10

4

(ii) Draw the potential difference and potential gradient anomaly profile over two closely spaced thin vertical sheet- type structures located at the same depth in the subsurface. Explain the significance and limitations of both measurements over each other.

1. (a) Total magnetic field is measured along a 1000 m1000 m long profile over a vertically polarized monopole- type structure. Peak anomaly along the profile is observed at 500 m500 m location and half- peak anomalies are observed at 400 m400 m and 600 m600 m locations.

(i) What is the depth of the monopole?

(ii) If downward continuation is applied on the recorded data at a depth level equal to half of the depth of the monopole, then at what distances along the profile, half of the peak anomaly will be observed on the computed downward continued data?

(iii) Draw the representative figure for the downward continued data over original recorded data with respect to amplitude and wavelength of the anomaly along the profile.

(b) Consider a seismic survey as shown in the figure below. Source (S) and geophones (R1…RN)(R1​…RN​) are placed at 50 m50 m interval:

(i) Find the geophone number closest to the source at which refracted wave will be recorded.

(ii) If the recorded seismic data for this survey was given to you, then group the recorded traces into two parts (R1…Rx)(R1​…Rx​) and (Rx+1…RN)(Rx+1​…RN​) to estimate the velocities of two layers. (Give the value of geophone number RxRx​ )

(c) What are the applications of SP logging in various (shallow, intermediate, larger depths) geophysical applications? Draw SP logs related with each application by making suitable geological units in the borehole. Justify the nature (positive or negative) of SP logs.

UPSC Previous year question paper Geo scientist exam

1. (a) A particle of unit mass moves along the xx -axis under the influence of a potential V(x)=x(x−2)2V(x)=x(x−2)2 . Find the time period of small oscillation around the stable equilibrium. 8

(b) A drunk starts out from a lamppost in the middle of a street, taking steps of equal length either to the right or to the left with equal probability. What is the probability that the drunk will again be at the lamppost after taking NN steps, if (i) NN is even and (ii) NN is odd? 8

(c) In a Stern-Gerlach experiment, the magnetic field is varied in the zz -direction according to dBz/dz=1.5T/mmdBz​/dz=1.5T/mm . Silver atoms travel a distance of 4cm4cm through the magnet. The speed of atoms coming out of the oven is 700m/s700m/s . Calculate the separation of the two beams as they leave the magnet. (Given : Mass of silver atom =1.8×10−25kg=1.8×10−25kg and its magnetic moment is 1 Bohr magneton) 8

(d) What is isomer shift? Why does it take place? What information do you obtain by measuring this parameter? 2+3+3=8

(e) Define critical energy of fissionable nucleus. Obtain the rate of fission for 235U235U required to produce 10 watts. 4+4=8

1. (a) If F(qi,pi,t)F(qi​,pi​,t) and G(qi,pi,t)G(qi​,pi​,t) are two constants of motion for a particular theory, then show that the Poisson bracket {F(qi,pi,t),G(qi,pi,t)}{F(qi​,pi​,t),G(qi​,pi​,t)} is also a constant of motion for that theory. 10

(b) An electron moves in a uniform electromagnetic field given by

B⃗=B0i^,E⃗=E0k^B=B0​i^,E=E0​k^

Write down the Lagrangian and Hamiltonian of the system. Find the canonical equations of motion for the electron. 10

(c) (i) Write down Wien's law and Rayleigh-Jeans law of spectral distribution of energy. 4

(ii) What is ultraviolet catastrophe? 2

(iii) Show that Planck's law of radiation reduces to Wien's law and Rayleigh- Jeans law at certain conditions. 4

UPSC Previous year question paper Geo scientist exam

1. (a) Consider a collection of NN , 1- D quantum simple harmonic oscillators with angular frequency ωω in a thermal bath of temperature TT . Construct the partition function of this system assuming that the oscillators are non- interacting. Calculate the entropy of the system. 7+3=10

(b) Compare microcanonical, canonical and grand canonical ensemble theories. Explain where these are applicable. 10

(c) (i) Write down the selection rules governing the transitions which take place in normal and anomalous Zeeman effects. 4

(ii) How does Landé gg - factor help us to explain the anomalous Zeeman effect? 6

1. (a) (i) Why is analysis of microstructure of a material important for geological applications? 5

(ii) How is SEM used to study the microstructures of porous and geomaterials? 5

(b) (i) What are hot bands? Why are they called so? 6

(ii) The fundamental and first overtone transitions of 14N14N and 16O16O are centred at 1876 cm−11876 cm−1 and 3724 cm−13724 cm−1 respectively. Calculate the values of equilibrium vibration frequency, anharmonicity constant and zeropoint energy of the molecule.

(Given : Mass of 14N=23.25×10−27kg14N=23.25×10−27kg ; Mass of 16O=26.56×10−27kg16O=26.56×10−27kg ) 4

(c) What do you mean by parity conservation in particle physics? Explain parity violation in nuclear ββ -decay process. 10

1. (a) (i) What are the important findings from the plot of binding energy per nucleon with mass number? 5

(ii) Briefly discuss the complementarity of the above plot and packing fraction plot. 5

10

(b) Calculate the threshold kinetic energy of the incident proton to hit another proton at rest to produce proton- antiproton pair through the process

p+p→p+p+p+p‾(10)p+p→p+p+p+p​(10)

(c) The Lagrangian of a relativistic free particle of rest mass m0m0​ with velocity v⃗v is given by

L(v⃗)=−m0c21−v⃗2c2L(v)=−m0​c21−c2v2​​

Find the Hamiltonian of the system.

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UPSC Previous year question paper Geo scientist exam

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