UPSC Combined Geo-Scientist (Geophysics) 2027

1. Solid Earth Geophysics

Introduction to geophysics and its branches; solar system, origin and characteristics of planets; shape and rotation of the Earth; gravity and magnetic fields of the Earth; geomagnetism, rock and mineral magnetism; elastic waves and propagation; internal structure of the Earth; plate tectonics; earthquakes, focal depth, epicentre, intensity and magnitude scales, seismicity.

2. Mathematical Methods in Geophysics

Vector algebra and analysis, gradient, divergence, curl, Gauss divergence and Stokes theorems; matrices, eigenvalues and eigenvectors; Newton's law of gravitation and gravity potential; conservation laws; rigid body motion and moment of inertia; special theory of relativity and Lorentz transformation; inverse theory, forward and inverse problems; probability, binomial, Poisson and normal distributions; linear algebra, ODEs and PDEs (Laplace, wave, heat); numerical techniques — interpolation, Simpson's rule, Runge-Kutta, finite difference and finite element methods.

3. Electromagnetism

Electrostatic and magnetostatic fields, Coulomb's law, permittivity and dielectric constant, Lorentz force; Ampere's law, Biot-Savart law, Gauss theorem, Poisson and Laplace equations; displacement current, Faraday's law; Maxwell's equations and boundary conditions; plane electromagnetic waves in free space, dielectric and conducting media; vector and scalar potentials.

4. Geophysical Prospecting

Principles, data reduction and applications of gravity, magnetic, electrical, electromagnetic and well-logging methods; seismic methods — Fermat's principle, Snell's law, energy partitioning, reflection and transmission coefficients, layered media; signals and systems, sampling theorem, aliasing, Fourier series and transform, Laplace transform, convolution, auto and cross correlation, power spectrum, delta and unit step functions.

5. Remote Sensing and Thermodynamics

Fundamentals of remote sensing, electromagnetic spectrum, energy-frequency-wavelength relationship, Stefan-Boltzmann law, Wien's law, Planck's radiation law, interaction of EM energy with atmosphere and terrain; laws of thermodynamics and thermodynamic potentials.

6. Nuclear Physics and Radiometry

Nuclear size, shape, charge distribution, spin and parity; binding energy and semi-empirical mass formula; fission and fusion; radioactivity, alpha, beta and gamma decay; photoelectric and Compton effect, pair production; decay law; radioactivity of rocks and minerals; radiation detectors — ionization chamber, G-M counter, scintillation counter, gamma-ray spectrometer; matter waves, electron spin, spectra of hydrogen, helium and alkali atoms.

PART A — Geophysics

A1. Solid Earth Geophysics

Introduction to Geophysics and its branches. Solar system: origin, characteristics of planets. Earth: rotation and figure, Geoid, Spheroid and topography. Plate tectonics and geodynamic processes, thermal history and heat flow, temperature variation in the Earth, convection currents. Gravity field of Earth and Isostasy. Geomagnetism, elements of Earth's magnetism: internal and external fields and their causes, palaeomagnetism, polar wandering paths, continental drift, seafloor spreading and its geophysical evidences. Elastic waves, body waves and internal structure of the Earth, variation of physical properties in the interior of the Earth, Adam-Williamson's equation.

A2. Earthquake Seismology

Seismology, earthquakes, focal depth, epicentre, great Indian earthquakes, intensity and magnitude scales, energy of earthquakes, foreshocks, aftershocks, elastic rebound theory, types and nature of faulting, fault plane solutions, seismicity and seismotectonics of India, frequency-magnitude relation (b-values). Bulk and rigidity modulus, Lame's parameter, seismic waves: types and propagation characteristics, absorption, attenuation and dispersion. Seismic ray theory for spherically and horizontally stratified earth, basic principles of seismic tomography and receiver function analysis, velocity structure, Vp/Vs studies, seismic networks and arrays, telemetry systems, principle of electromagnetic seismograph, displacement meters, velocity meters, accelerometers, broadband seismometer, WWSSN stations, seismic arrays for detection of nuclear explosions. Earthquake prediction; dilatancy theory, short-, medium- and long-term predictions, seismic microzonation, applications to engineering problems.

A3. Mathematical Methods in Geophysics

Elements of vector analysis, gradient, divergence and curl, Gauss's divergence theorem, Stokes' theorem, gravitational field, Newton's law of gravitation, gravitational potential and fields due to bodies of different geometric shapes, Coulomb's law, electrical permittivity and dielectric constant, origin of magnetic field, Ampere's law, Biot-Savart law, geomagnetic fields, magnetic fields due to different types of structures, solution of Laplace equation in Cartesian, cylindrical and spherical coordinates, image theory, electrical fields due to charge, point source, continuous charge distribution and double layers, equipotential and lines of force. Current and potential in the earth, basic concept and equations of electromagnetic induction, Maxwell's equations, near and far fields, attenuation of EM waves, EM field of a loop of wire on half space and multi-layered media.

A4. Geophysical Inversion

Fundamental concepts of inverse theory, definition and its application to geophysics. Probability, inversion with discrete and continuous models. Forward versus inverse problems, direct and model-based inversions, formulation and classification of inverse problems, least square solutions and minimum norm solution, concept of norms, Jacobian matrix, condition number, stability, non-uniqueness and resolution of inverse problems, concept of 'a priori' information, constrained linear least squares inversion, review of matrix theory. Models and data spaces, data resolution matrix, model resolution matrix, eigenvalues and eigenvectors, singular value decomposition (SVD), Gauss-Newton method, steepest descent (gradient) method, Marquardt-Levenberg method. Probabilistic approach of inverse problems, maximum likelihood and stochastic inverse methods, random search inversion (Monte Carlo), Backus-Gilbert method, Bayesian theorem and inversion. Global optimization techniques: genetic algorithm and simulated annealing methods.

PART B — Physics

B1. Mathematical Methods of Physics

Dimensional analysis; units and measurement; vector algebra and vector calculus; linear algebra, matrices: eigenvalues and eigenvectors; linear ordinary differential equations of first and second order; special functions (Hermite, Bessel, Laguerre and Legendre); Fourier series, Fourier and Laplace transforms; elementary probability theory, random variables, binomial, Poisson and normal distributions; Green's function; partial differential equations (Laplace, wave and heat equations in two and three dimensions); elements of numerical techniques: root of functions, interpolation and extrapolation, integration by trapezoid and Simpson's rule, solution of first order differential equation using Runge-Kutta method; tensors; complex variables and analysis; analytic functions; Taylor and Laurent series; poles, residues and evaluation of integrals; beta and gamma functions; operators and their properties; least-squares fitting.

B2. Electrodynamics

Electrostatics: Gauss' law and its applications; Laplace and Poisson equations, boundary value problems; magnetostatics: Biot-Savart law, Ampere's theorem, Ampere's circuital law; magnetic vector potential; Faraday's law of electromagnetic induction; electromagnetic vector and scalar potentials; uniqueness of electromagnetic potentials and concept of gauge: Lorentz and Coulomb gauges; Lorentz force; charged particles in uniform and non-uniform electric and magnetic fields; Poynting theorem; electromagnetic fields from Lienard-Wiechert potential of a moving charge; bremsstrahlung radiation; Cerenkov radiation; radiation due to oscillatory electric dipole; condition for plasma existence; occurrence of plasma; magnetohydrodynamics; plasma waves; transformation of electromagnetic potentials; Lorentz condition; invariance or covariance of Maxwell field equations in terms of 4-vectors; electromagnetic field tensor; Lorentz transformation of electric and magnetic fields.

B3. Electromagnetic Theory

Maxwell's equations: differential and integral forms, physical significance; displacement current; boundary conditions; wave equation, plane electromagnetic waves in free space, non-conducting isotropic medium and conducting medium; scalar and vector potentials; reflection and refraction of electromagnetic waves; Fresnel's law; interference; coherence; diffraction and polarization; Lorentz invariance of Maxwell's equations; transmission lines and waveguides.

B4. Introductory Atmospheric and Space Physics

The neutral atmosphere; atmospheric nomenclature; height profile of atmosphere; hydrostatic equation; geopotential height; expansion and contraction; fundamental forces in the atmosphere; apparent forces; atmospheric composition; solar radiation interaction with the neutral atmosphere; climate change; electromagnetic radiation and propagation of waves: EM radiation; effects of environment; antennas: basic considerations and types; propagation of waves: ground wave, sky wave and space wave propagation; troposcatter communication and extra-terrestrial communication; the ionosphere; morphology of ionosphere: the D, E and F regions; chemistry of the ionosphere; ionospheric parameters, E and F region anomalies and irregularities; Global Positioning Systems (GPS): overview of GPS system, augmentation services, GPS system segment, GPS signal characteristics, GPS errors, multipath effects, GPS performance; satellite navigation systems and applications.

PART A — Geophysics

A1. Potential Field (Gravity and Magnetic) Methods

Geophysical potential fields, inverse square law, principles of gravity and magnetic methods, global gravity anomalies, Newtonian and logarithmic potential, Laplace's equations for potential field, Green's function, concept of gravity anomaly, rock densities and factors controlling them, determination of density, Earth's main magnetic field, origin, diurnal and secular variations, geomagnetic elements, intensity of magnetization and induction, magnetic potential and its relation to field, units of measurement, interrelationship between components of magnetic fields, Poisson's relation, magnetic susceptibility and controlling factors. Magnetic mineralogy: hysteresis, rock magnetism, natural and remnant magnetization, demagnetization effects. Principles of gravity and magnetic instruments, plan of conducting surveys, data reduction, gravity bases, International Gravity Formula, IGRF corrections. Regional and residual anomalies and methods of separation, edge enhancement techniques (derivatives, continuation, analytical signal, reduction to pole and Euler deconvolution), ambiguity in potential field interpretation, factors affecting magnetic anomalies, applications in geodynamics, mineral exploration and environmental studies, qualitative interpretation, interpretation of anomalies due to different geometrical bodies and modelling.

A2. Electrical and Electromagnetic Methods

Electrical properties of rocks and minerals, concepts and assumptions of horizontally stratified earth, anisotropy and its effects, geoelectric and geological sections, D.C. resistivity method, natural electric field, various electrode configurations, profiling and sounding (VES), types of sounding curves, equivalence and suppression, Electrical Resistivity Tomography (ERT). SP method: origin of SP and applications. Induced Polarization (IP): origin, membrane and electrode polarization, time and frequency domain measurement, chargeability, percent frequency effect and metal factor, applications in mineral exploration. Electromagnetic methods: passive and active source methods, diffusion equation, wave and damped wave equation, boundary conditions, skin depth, depth of investigation and penetration, amplitude and phase relations, real and imaginary components, elliptical polarization, principles of EM prospecting, dip angle, Turam, moving source-receiver methods — horizontal loop (Slingram), AFMAG and VLF. Time domain EM: INPUT method. EM profiling and sounding, interpretation of EM anomalies, EM scale modelling. Magnetotellurics: origin and characteristics of MT fields, instrumentation, TE and TM modes, static shift, dimensionality and directionality analysis, field layout, interpretation and applications. Principles of Ground Penetrating Radar (GPR).

A3. Seismic Prospecting

Basic principles of seismic methods, factors affecting seismic velocities in rocks, reflection, refraction and energy partitioning at an interface, geometrical spreading, reflection and refraction of waves in layered and dipping media, seismic absorption and anisotropy, multichannel seismic (CDP) data acquisition (2D and 3D), sources of energy, geophones, geometry of arrays, different spread geometries, instrumentation and digital recording. Different types of multiples, travel time curves, corrections, interpretation of data, bright spot, low velocity layer, data processing, static and dynamic (NMO and DMO) corrections, shot-receiver gather, foldage, multiplexing and demultiplexing. Dix's equation, velocities: interval, average and RMS, seismic resolution and Fresnel zone, velocity analysis and migration techniques, seismic interpretation, time and depth sections, fundamentals of VSP method, High Resolution Seismic Surveys (HRSS).

A4. Borehole Geophysics

Objectives of well logging, concepts of borehole geophysics, borehole conditions, properties of reservoir rock formations, formation parameters and their relationships — formation factor, porosity, permeability, formation water resistivity, water saturation, irreducible water saturation, hydrocarbon saturation, residual hydrocarbon saturation; Archie's and Humble's equations; principles, instrumentation, operational procedures and interpretation of various geophysical logs: SP, resistivity and micro-resistivity, gamma ray, neutron, sonic, temperature, caliper and directional logs. Production logging, overlays and cross-plots of well-log data, determination of formation lithology, porosity, permeability and oil-water saturation, sub-surface correlation and mapping, delineation of fractures; application of well logging in hydrocarbon, groundwater, coal, metallic and non-metallic mineral exploration.

PART B — Physics

B1. Classical Mechanics

Inertial and non-inertial frames, Newton's laws; pseudo forces; central force motion; two-body collisions, scattering in laboratory and centre-of-mass frames; rigid body dynamics, moment of inertia, variational principle, Lagrangian and Hamiltonian formalisms and equations of motion; Poisson brackets and canonical transformations; symmetry, invariance and conservation laws, cyclic coordinates; periodic motion, small oscillations and normal modes; special theory of relativity, Lorentz transformations, relativistic kinematics and mass-energy equivalence.

B2. Thermodynamics and Statistical Physics

Laws of thermodynamics and their significance; thermodynamic potentials, Maxwell relations; chemical potential, phase equilibria; phase space, micro- and macro-states; microcanonical, canonical and grand canonical ensembles and partition functions; free energy and connection with thermodynamic quantities; first and second order phase transitions; Maxwell-Boltzmann distribution, quantum statistics, ideal Fermi and Bose gases; principle of detailed balance; blackbody radiation and Planck's distribution law; Bose-Einstein condensation; random walk and Brownian motion; diffusion equation.

B3. Atomic and Molecular Physics and Characterization of Materials

Quantum states of an electron in an atom; electron spin; Stern-Gerlach experiment; spectrum of hydrogen, helium and alkali atoms; relativistic corrections for energy levels of hydrogen; hyperfine structure and isotopic shift; width of spectral lines; LS and JJ coupling; Zeeman, Paschen-Back and Stark effects; rotational, vibrational, electronic and Raman spectra of diatomic molecules; Franck-Condon principle; thermal and optical properties of materials, study of microstructure using SEM, study of crystal structure using TEM; resonance methods: spin and applied magnetic field, Larmor precession, relaxation times — spin-spin and spin-lattice relaxation, electron spin resonance, g factor, nuclear magnetic resonance, line width, motional narrowing, hyperfine splitting; nuclear gamma resonance: principles of Mössbauer spectroscopy, line width, resonance absorption, isomer shift, quadrupole splitting.

B4. Nuclear and Particle Physics

Basic nuclear properties: size, shape, charge distribution, spin and parity; binding energy, packing fraction, semi-empirical mass formula; liquid drop model; fission and fusion, nuclear reactor; line of stability, characteristics of nuclear forces, nucleon-nucleon potential; charge independence and charge symmetry of nuclear forces; isospin; deuteron problem; evidence of shell structure, single-particle shell model, its validity and limitations; elementary ideas of alpha, beta and gamma decays and their selection rules; nuclear reactions, reaction mechanisms, compound nuclei and direct reactions; classification of fundamental forces; elementary particles (quarks, baryons, mesons, leptons); spin and parity assignments, strangeness; Gell-Mann-Nishijima formula; C, P and T invariance and applications of symmetry arguments to particle reactions, parity non-conservation in weak interaction; relativistic kinematics.

PART A — Geophysics

A1. Radiometric and Airborne Geophysics

Principles of radioactivity, radioactive decay processes, units, radioactivity of rocks and minerals, instruments, ionization chamber, G-M counter, scintillation counter, gamma ray spectrometer, radiometric prospecting for mineral exploration (direct/indirect applications), beach placers, titanium, zirconium and rare earths, radon studies in seismology and environmental applications. Airborne geophysical surveys (gravity, magnetic, electromagnetic and radiometric), planning of surveys, flight path recovery methods, applications in geological mapping, identification of structural features and altered zones.

A2. Marine Geophysics

Salinity, temperature and density of sea water. Sea-floor features: physiography, divisions of sea floor, continental shelves, slopes and abyssal plains, growth and decline of ocean basins, turbidity currents, occurrence of mineral deposits and hydrocarbons in offshore. Geophysical surveys and instrumentation: gravity, magnetic and electromagnetic surveys, sonobuoy surveys, instrumentation used in shipborne surveys, towing cable and fish, data collection and survey procedures, corrections and interpretation of data. Oceanic magnetic anomalies, Vine-Matthews hypothesis, geomagnetic time scale and dating of sea floor, oceanic heat flow, ocean ridges, basins, marginal basins, rift valleys. Seismic surveys, energy sources — pinger, boomer, sparker, air gun, hydrophones and streamer cabling, data reduction and interpretation, ocean bottom seismic surveys, bathymetry, echo sounding, bathymetric charts, sea bed mapping, navigation and position fixing methods.

A3. Geophysical Signal Processing

Time series, types of signals, sampling theorem, aliasing effect, Fourier series of periodic waveforms, Fourier transform and its properties, discrete Fourier transform and FFT, Hilbert transform, convolution and deconvolution, auto and cross correlations, power spectrum, delta function, unit step function, time domain windows, Z transform and properties, inverse Z transform, poles and zeroes. Principles of digital filters, types of filters: recursive, non-recursive, time invariant, Chebyshev, Butterworth, moving average, amplitude and phase response of filters, low pass, band pass and high pass filters. Processing of random signals, improvement of signal-to-noise ratio, source and geophone arrays as spatial filters, Earth as a low pass filter.

A4. Remote Sensing and Geohydrology

Fundamental concepts of remote sensing, electromagnetic radiation spectrum, interaction of electromagnetic energy in the atmosphere and at the surface of the Earth, elements of photographic systems, reflectance and emittance, false colour composites, remote sensing platforms, flight planning, geosynchronous and sun synchronous orbits, sensors, resolution, parallax and vertical exaggeration, relief displacement, mosaic, aerial photo interpretation and geological applications. Fundamentals of photogrammetry, satellite remote sensing, multi-spectral scanners, thermal scanners, microwave remote sensing, fundamentals of image processing and interpretation for geological applications. Types of water bearing formations, porosity, permeability, storage coefficient, specific storage, specific retention, specific yield, different types of aquifers, vertical distribution of ground water, general flow equation; steady and unsteady flow of ground water in unconfined and confined aquifers.

PART B — Physics

B1. Solid State Physics and Basic Electronics

Crystalline and amorphous structure of matter; different crystal systems, space groups; methods of determination of crystal structure; X-ray diffraction, scanning and transmission electron microscopes; band theory of solids, conductors, insulators and semiconductors; thermal properties of solids, specific heat: Einstein's and Debye theory; magnetism: dia, para and ferro; elements of superconductivity, Meissner effect, Josephson junctions and applications; elementary ideas about high temperature superconductivity. Semiconductor devices and circuits: intrinsic and extrinsic semiconductors; devices and structures (p-n junctions, diodes, transistors, FET, JFET and MOSFET, homo and hetero junction transistors, thermistors), device characteristics, frequency dependence and applications; opto-electronic devices (solar cells, photodetectors, LEDs); operational amplifiers and their applications.

B2. Laser Systems

Spontaneous and stimulated emission of radiation, coherence, light amplification and relation between Einstein A and B coefficients, rate equations for three and four level systems. Lasers: Ruby, Nd-YAG, CO2, dye, excimer, semiconductor. Laser cavity modes, line shape function and full width at half maximum (FWHM) for natural broadening, collision broadening, Doppler broadening; saturation behaviour of broadened transitions, longitudinal and transverse modes, mode selection, ABCD matrices and cavity stability criteria for confocal resonators, quality factor, expression for intensity for modes oscillating at random and mode-locked in phase, methods of Q-switching and mode locking, optical fibre waveguides and fibre characteristics.

B3. Digital Electronics, Radar Systems and Satellite Communications

Digital techniques and applications: Boolean identities, de Morgan's theorems, logic gates and truth tables; simple logic circuits: registers, counters, comparators and similar circuits; A/D and D/A converters; microprocessor basics and architecture; microcontroller basics; combinational and sequential logic circuits, functional diagram, timing diagram of read and write cycle, data transfer techniques: serial and parallel; fundamentals of digital computers. Radar systems, signal and data processing, surveillance radar, tracking radar, radar antenna parameters. Fundamentals of satellite systems, communication and orbiting satellites, satellite frequency bands, satellite orbit and inclinations, earth station technology.

B4. Quantum Mechanics

Wave-particle duality; wave functions in coordinate and momentum representations; commutators and Heisenberg's uncertainty principle; Schrödinger's wave equation (time-dependent and time-independent); eigenvalue problems: particle in a box, harmonic oscillator, tunnelling through a 1-D barrier; motion in a central potential; orbital angular momentum; addition of angular momentum; hydrogen atom; matrix representation; Dirac's bra and ket notations; time-independent perturbation theory and applications; variational method; WKB approximation; time-dependent perturbation theory and Fermi's Golden Rule; selection rules; semi-classical theory of radiation; elementary theory of scattering, phase shifts, partial waves, Born approximation; identical particles, Pauli's exclusion principle, spin-statistics connection; relativistic quantum mechanics: Klein-Gordon and Dirac equations.