## Geophysics Paper I

**UPSC Combined Geo-Scientist and Geologist Examination 2018 Syllabus for Geophysics**– UPSC GEOL Geology Syllabus | UPSC GEOL Chemistry Syllabus

**Geophysics – Paper I : 200 Marks**

**Part – A : 100 Marks**

**a. Solid Earth Geophysics :** Introduction to Geophysics its branches and relationship with other sciences. Solar system, its origin, characteristics of planetary members, Earth; its rotation and figure. Age of earth & various methods of determination. Tectonics and Geodynamics, Thermal history and its characteristics. Gravity field of earth and Isostasy. Geomagnetism, elements of earth’s magnetism : Internal, External fields and their causes, Paleomagnetism, Polar wandering paths, Seafloor spreading, geophysical evidences. Elastic waves, internal structure of earth, variation of physical properties in the interior of earth.

**b. Earthquake and Engineering Seismology :** Seismology, earthquakes, focal depth, epicenter, great Indian earthquakes, Intensity and Magnitude scales, Energy of earthquakes, foreshocks, aftershocks, Elastic rebound theory, Fault plane solutions, Seismicity and Seismotectonics of India, Frequency-Magnitude relation ( b values ), Velocity structure, Vp / Vs studies. Elastic waves, their propagation characteristics. Seismic ray theory for spherically and horizontally stratified earth, basic principles of Seismic Tomography and receiver function analysis, Seismic network and arrays, telemetry systems, Earthquake prediction; dilatancy theory, short-term, middle-term and long-term predictions, Seismic microzonation studies, application for engineering problems, Seismometry, Principle of electromagnetic seismograph, displacement meters, velocity meter, accelerometer, WWSSN stations, Strong motion seismograph, seismic arrays for detection of nuclear explosions, Broadband seismometry.

**c. Mathematical methods in Geophysics :** Properties of scalars, vectors and tensors, Elements of vector analysis, Gradient, Divergence and Curl, Gauss’s divergence theorem, Stokes theorem, Definition of fields, Gravitational field, Newton’s Law of gravitation, Gravitation potential and fields due to bodies of different geometric shapes, Electrostatic field, Coulomb’s law, Electrical permittivity and dielectric constant, Basic guiding equations, Magneto static field, Origin of Magnetic field, Ampere’s law, Biot and Savart’s law, Geomagnetic fields, Magnetic fields due to different type of structures, Solution of Laplace equation in Cartesian Coordinate,

Cylindrical Polar Coordinate and Spherical Polar Coordinate, Complex Variables in Potential theory, Green’s theorem in Potential Theory. Concept of Image in Potential Theory, Analytical continuation in Potential fields, Numerical Methods in Potential Theory. Electrical fields in geophysics, point source, continuous distribution and double layers, equipotential and line of force. Current and potential in the earth, basic concept and equations of electromagnetic, Maxwell’s equations, boundary conditions, elliptic polarization, electromagnetic potential and waves, radiation from dipoles, retarded potential, near and far fields, radiation resistance, EM field of a loops of wire on half space, multi-layered media, impedance and its application.

**d. Geophysical Inversion :** Fundamental concepts of inverse theory, Basic definition of inversions with application to Geophysics. Probability, Inverses with discrete and continuous models. Forward problems versus Inverse problems. Formulation of inverse problems and their relation to a matrix problem, linear inverse problems, classification of inverse problems, least square solutions and minimum norm solution, concept of norms, concept of ‘a priori’ information, constrained linear least square inversion, review of matrix theory Introduction to finite difference method, forward, backward and central difference method.

Application of finite difference method for solving Helmholtz equation. Introduction to finite element method, various steps, simple examples showing application of finite element method. Models and data spaces, householder transformation, data resolution matrix, model resolution matrix, Eigen values and Eigen vectors, Singular Value Decomposition ( SVD ), generalized inverses, Non-linear inverse problems, Gauss Newton method, steepest descent ( gradient ) method, Marquardt-Levenberg method, Earthquake location problem, tomography problem. Probabilistic approach of inverse problems, maximum likelihood and stochastic inverse methods, Backus-Gilbert method, Global optimization techniques, genetic algorithm, simulated annealing methods, examples of inverting geophysical data.

**Part – B : 100 Marks**

**a. Mathematical Methods of Physics : **Dimensional analysis, Vector algebra and vector calculus, Linear algebra, matrices, Cayley-Hamilton Theorem. Eigen values and eigenvectors. Linear ordinary differential equations of first & second order, Special functions ( Hermite, Bessel, Laguerre and Legendre functions ). Fourier series, Fourier and Laplace transforms. Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues and evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem. Green’s function. Partial differential equations ( Laplace, wave and heat equations in two and three dimensions ). Elements of computational techniques : root of functions, interpolation, and extrapolation, integration by trapezoid and Simpson’s rule, solution of first order differential equation using Runge-Kutta method. Finite difference methods. Tensors. Introductory group theory: SU (2), O (3). Complex Variables, Beta, Gamma functions and special functions, Laplace Transform & Fourier series, Fourier Transforms, Introductory methods of Numerical analysis. Operators and their properties.

**b. Thermodynamics and Statistical Physics :** Laws of thermodynamics and their consequences; Thermodynamic potentials, Maxwell relations; Chemical potential, phase equilibria; Phase space, micro and macrostates; Micro canonical, canonical and grand-canonical ensembles and partition functions; Free Energy and connection with thermodynamic quantities; First and second-order phase transitions; Classical and 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; Introduction to non equilibrium processes; Diffusion equation.

**c. Electrodynamics :** Gauss Theorem, Poison’s equation, Laplace’s equation, solution to Laplace’s equation in Cartesian coordinates, spherical, cylindrical coordinates, use of Laplace’s equation in the solutions of electrostatic problems. Ampere’s circuital law, magnetic vector potential, displacement current, Faraday’s law of electromagnetic induction. Maxwell’s equations, differential and integral forms, physical significance of Maxwell’s equations. Wave equation, plane electromagnetic waves in free space, in non conducting isotropic medium, in conducting medium, electromagnetic vector an scalar potentials, uniqueness of electromagnetic potentials and concept of gauge, Lorentz gauge, Columb gauge, charged particles in electric and magnetic fields, charged particles in uniform electric field, charged particle in homogeneous magnetic fields, charged particles in simultaneous electric and magnetic fields, charged particles in non homogeneous magnetic fields.

Lienard – Wiechert potentials, electromagnetic fields from Lienard – Wiechert potentials of a moving charge, electromagnetic fields of a uniformly moving charge, radiation due to non-relativistic charges, radiation damping, Abrahama-Lorentz formula, Cherenkov radiation, radiation due to oscillatory electric dipole, radiation due to small current element. Condition for plasma existence, occurrence of plasma, magneto hydrodynamics, plasma waves. Transformation of electromagnetic potentials, Lorentz condition in covariant form, invariance or covariance of Maxwell field equations in terms of 4 vectors, electromagnetic field tensor, Lorentz transformation of electric and magnetic fields.

**d. Introductory Atmospheric and Space Physics :** The Neutral atmosphere, atmospheric nomenclature, the 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, fundamentals of EM waves, effects of environment, Antennas-basic considerations, types of antennas. 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 in the ionosphere. Global Positioning Systems ( GPS ) – basic concepts, overview of GPS system, augmentation services, GPS system segment, GPS signal characteristics, GPS errors, multi path effects, GPS performance, satellite navigation system and applications.

## Geophysics Paper II

**Geophysics – Paper II : 200 Marks**

**Part – A : 100 Marks**

**a. Geophysical Potential Fields ( Gravity and Magnetic ) :** Geophysical potential fields, Inverse square law of field, Principles of Gravity and Magnetic methods, Geoid, Spheroid, Nature of gravity and its variation, Properties of Newtonian potential, Laplace’s and Poisons equations, Green’s theorem, Gauss law, Concept of Bouguer gravity anomaly, Rock densities, factors controlling rock densities, determination of density, theory of isostasy, Earth’s main magnetic field, origin, temporal variations, Geomagnetic elements, Columb’s law of magnetic force and fields, intensity of magnetization and induction, magnetic potential and its relation to field, units of measurement, origin of magnetic anomalies, interrelationship between different components of anomalies, Poison’s relation,

Magnetic susceptibility, factors controlling susceptibility ( Bulk chemistry, cooling history, metamorphism. ), magnetic minerals, rock classification, Natural and remnant magnetism, Asiatic and Spinner magnetometers, demagnetization effects. Principles of Gravity and Magnetic instruments, Plan of conducting GM surveys, reduction of gravity and magnetic data, Airborne magnetic surveys and magnetic gradient surveys, Shipborne surveys, Gravity and Magnetic data reduction, IGSN Gravity bases, International Gravity formula, IGRF corrections for magnetic field. Separation of regional and residual anomalies, ambiguity in interpretation, Application of GM surveys for Geodynamic studies, Mineral Exploration, Environmental studies, Data processing and interpretation of anomalies, modeling of anomalies.

**b. Electrical and Electromagnetic Methods :** Electrical properties of rocks and their measurement, concepts and assumptions of horizontally stratified earth, anisotropy and its effects on electrical fields, the geo electric section and geological section, D.O Resistivity method, fundamental laws, concept on natural electric field, electrode configuration, choice of methods, Profiling, Vertical Electrical Sounding, SP Method, Origin of SP, application of SP surveys, Origin of Induced Polarization, Membrane and Electrode potential, time and frequency domains of measurement, IP, chargeability, percent frequency effect and metal factor, dipole theory of IP, Application of IP surveys for mineral exploration ( disseminated sulphides ).

Electromagnetic methods / Telluric / Magneto Telluric methods, Passive and Active source methods, Maxwell’s equations, electromagnetic potential and wave equations, boundary conditions, long wave length approximation, depth of penetration, amplitude and phase relations, real and imaginary components, Principles of EM prospecting, various EM methods, Dip angle method, Turam method, moving source-receiver methods-horizontal loop ( Slingram ) method, AFMAG, and VLF methods, Airborne EM systems – rotary field method, INPUT method, EM Profiling and sounding, Interpretation of EM anomalies, Principles of Ground Penetrating Radar ( GPR ), Origin and characteristics of MT fields, Instrumentation, Field methods and interpretation of MT data and applications.

**c. Seismic Prospecting :** Basic principles of seismic methods, Fermat’s principle, Senell’s law, Reflection, refraction and diffraction from multilayered medium, Reflection and transmission coefficients, propagation model for exploration seismology, Seismic resolution, Seismic absorption and anisotropy, Seismic data acquisition, sources of energy, Geophones, geometry of arrays, Instrumentation, digital recording Seismic Surveys : Principle for multilayer refraction Travel time curves, corrections, Interpretation of data, Reflection principles, CDP, data processing, corrections, NMO correction, Interpretation of data, Fundamental of VSP method, Seismic Tomography. Principles of High Resolution Seismic ( HRS ) for coal exploration.

**d. Borehole Geophysics ( Principles of Well logging ) :** Objectives of well logging, fundamental concepts in 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; Arhcie’s and Humble’s equations; principles, instrumentations, operational procedures and interpretations of various geophysical logs, SP log, resistivity and micro resistivity logs, nuclear / radioactive logs, acoustic impedance and propagation logs, temperature log, caliper log and directional logs; production logging; clean sand and shaly sand interpretations; overlay and cross-plots of well-log data, determination of formation lithology, sub-surface correlation and mapping, delineation of fractures; application of well-logging in hydrocarbon, groundwater, coal, metallic and non-metalic mineral exploration.

**Part – B : 100 Marks**

**a. Atomic and Molecular Physics and Properties 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 & JJ coupling; Zeeman, Paschen Back & Stark effect; X-ray spectroscopy; Electron spin resonance, Nuclear magnetic resonance, chemical shift; Rotational, vibrational, electronic, and Raman spectra of diatomic molecules; Frank – Condon principle and selection rules; Spontaneous and stimulated emission, Einstein A & B coefficients;

Lasers, optical pumping, population inversion, rate equation; Modes of resonators and coherence length. Thermal properties, optical properties, fundamentals of transmission electron microscopy, study of crystal structure using TEM, study of microstructure using SEM. Resonance methods – Spin and an applied field – the nature of spinning particles, interaction between spin and a magnetic field, population on energy levels, the Larmor precession, relaxation times – spin-spin relation, spin-lattice relaxation, Electron spin resonance- Introduction, g factor, experimental methods, Nuclear Magnetic resonance-equations of motion, line width motional narrowing, hyperfine splitting, Nuclear Gamma Resonance : Principles of Mossbauer Spectroscopy, Line width, Resonance absorption, Mossbauer Spectrometer, Isomer Shift, Quadrupole splitting, magnetic field effects, applications.

**b. Nuclear and Particle Physics :** Basic nuclear properties : size, shape, charge distribution, spin and parity; Binding energy, semi-empirical mass formula; Liquid drop model; Fission and fusion; Nature of the nuclear force, form of 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; Rotational spectra; 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,

isospin, 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. 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, Debye theory; Magnetism : dia, para and ferromagnetism; elements of superconductivity; Meissner effect, Josephson junctions and applications; elementary ideas about high temperature superconductivity.

**c. Electromagnetic Theory :** Electrostatics : Gauss’ Law and its applications; Laplace and Poisson equations, boundary value problems; Magnetostatics : Biot-Savart law, Ampere’s theorem, electromagnetic induction; Maxwell’s equations in free space and linear isotropic media; boundary conditions on fields at interfaces; Scalar and vector potentials; Gauge invariance; Electromagnetic waves in free space, dielectrics, and conductors; Reflection and refraction, polarization, Fresnel’s Law, interference, coherence, and diffraction; Dispersion relations in plasma; Lorentz invariance of Maxwell’s equations; Transmission lines and wave guides; Dynamics of charged particles in static and uniform electromagnetic fields; Radiation from moving charges, dipoles and retarded potentials.

**d. Classical Mechanics :** Newton’s laws; Phase space dynamics, stability analysis; Central-force motion; Two body collisions, scattering in laboratory and centre-of-mass frames; Rigid body dynamics, moment of inertia tensor, non-inertial frames and pseudoforces; 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.

## Geophysics Paper III

**Geophysics – Paper III : 200 Marks**

**Part – A : 100 Marks**

**a. Radiometric Exploration / Airborne Geophysical surveys for Geological Mapping :** Principles of radioactivity, radioactivity decay processes, units, radioactivity of rocks and minerals, Instruments, Ionisation chamber, G-M counter, Scintillation meter, Gamma ray spectrometer, Radiometric prospecting for mineral exploration ( Direct / Indirect applications ), Radiometric prospecting for beach placers, titanium, zirconium and rare-earths, portable gamma ray spectrometry and radon studies in seismology, environmental Applications, logging methods, radiometric dating techniques. Airborne geophysical surveys, planning of surveys, sensors, data corrections, flight path recovery methods, applications in geological mapping, interpretation of maps, identification of structural features, altered zones.

**b. Marine Geophysics :** Oceans and Seas, origin of continents and oceans, salinity, temperature and density of sea water. Introduction to Sea-floor features: Physiography, divisions of sea floor, continental shelves, slopes, aprons and abyssal planes, growth and decline of ocean basins, turbidity currents, submarine sedimentation and stratigraphy, occurrence of mineral deposits and hydrocarbons in offshore. Geophysical surveys and instrumentation, Gravity and Magnetic surveys, Instrumentation used in ship borne surveys, towing cable and fish, data collection and survey procedures, corrections and interpretation of data.

Oceanic magnetic anomalies, sea floor spreading, Vine-Mathews hypothesis, geomagnetic time scale and dating sea floor, linear magnetic anomalies, Oceanic heat flow, ocean ridges, basins, marginal basins, rift valleys. Seismic surveys, energy sources, Finger, Boomer, Sparker, Exploder, Air gun, Vapour cook, Hydrophones, processing, data reduction and interpretation. Bathymetry, echo sounding, bathymetric charts, sea bed mapping, seabed sampling, dredging and coring, Navigation methods and Position location methods.

**c. Geophysical Signal Processing :** Various types of signals, sampling theorem, aliasing effect, Fourier series and periodic waveforms, Fourier transform and its properties, Discrete Fourier transform and FFT, Auto and cross correlations, Power spectrum, Delta function, unit step function. Time domain windows, Z transform and properties, Inverse Z transform. Principles of digital filters, types of filters, moving average and recursive and non recursive filters Amplitude and phase response filters low pass, band pass and high pass filters, Processing of Random signals. Signal enhancement for gravity and magnetic maps; regional residual separation, continuations, evaluation of derivatives, pseudo gravity transformations, reduction to poles and equator, Improvement of signal to noise ratio, source and geophone arrays as spatial filters. Earth as low pass filter.

**d. Remote Sensing and GIS Applications :** Fundamental concepts of remote sensing, electromagnetic radiation spectrum, energy-frequency-wavelength relationship, Boltzman Law, Wien Law, electromagnetic energy and its interactions in the atmosphere and with terrain features; elements of photographic systems, reflectance and emittance, false color 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 application. Fundamentals of photogrammetry, satellite remote sensing, multi-spectral scanners, thermal scanners, microwave remote sensing, fundamental of image processing and interpretation for geological applications. Introduction to Geographic Information Systems ( GIS ) spatial data structures, visualization and querying, spatial data analysis.

**Part – B : 100 Marks**

**a. Solid State Physics :** 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, Debye theory; Magnetism : dia, para and ferromagnetism; elements of superconductivity; Meissner effect, Josephson junctions and applications; elementary ideas about high temperature superconductivity.

**b. Laser Systems :** Light amplification and relation between Einstein A and B coeffcients. Rate equations for three level and four level systems. Ruby laser, Nd-YAG laser, CO2 laser, Dye laser, Excimer laser, Semiconductor laser.

**c. Laser Cavity Modes :** Line shape function and full width at half maximum ( FWHM ) for natural broadening, collision broadening, Doppler broadening, saturation hebaviour of broadened transitioins, longitudinal and transverse modes. ABCD matrices and cavity stability criteria for confocal resonators. Quality factor, Q-switching, mode locking in lasers. Expression for intensity for modes oscillating at random and modes locke in phase. Methods of Q-switching and mode locking. Optical fiber waveguides, Fiber characteristics.

**d. Electronics and Devices :** Semiconductor devices ( diodes, junctions, transistors, field effect devices, homo and hetero junction devices ) device structure, device characteristics, frequency dependence and applications. Opto-electronic devices ( solar cells, photo detectors, LEDs ) Operational amplifiers and their applications. Digital techniques and applications ( registers, counters, comparators and similar circuits ). A/D and D/A converters. Microprocessor and microcontroller basics. Data interpretation and analysis. Precision and accuracy. Error analysis, propagation of errors. Least square fitting. Intrinsic extrinsic semiconductors, pn-p and n-p-n transistors; Amplifiers and oscillators; Op-amps; FET, JFET and MOSFET; Digital electronics-Boolean identities, Demorgan’s laws, logic gates and truth tables; simple logic circuits; thermistors, solar cells, fundamentals of microprocessors and digital computers.

**e. Digital Electronics, Radar Systems, Satellite Communications :** Digital circuits, Number systems and codes, Combination logic circuits, sequential logic circuits, microprocessor architecture, functional diagram, Pin description, Timing diagram of read cycle, timing diagram of write cycle. Data transfer techniques-Serial transfer, parallel transfer etc. Radar systems, signal and data processing, satellite communication – Fundamentals Designing a surveillance radar, tracking radar, signal and data processing, radar antenna parameters, satellite systems-communication satellite systems, communication satellites, orbiting satellites, satellite frequency bands, satellite orbit and inclinations. Multiple access techniques, earth station technology.

**f. Quantum Mechanics :** Wave-particle duality; Wave functions in coordinate and momentum representations; Commutators and Heisenberg’s uncertainty principle; Matrix representation; Dirac’s bra and ket notation; Schroedinger equation ( time-dependent and time-independent ); Eigen value problems such as particle-in-a-box, harmonic oscillator, etc.; Tunneling through a barrier; Motion in a central potential; Orbital angular momentum, Angular momentum algebra, spin; Addition of angular momentum; Hydrogen atom, spin-orbit coupling, fine structure; 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.

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