Geophysics : Paper-I

PART-A

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, Paleomagnetism, Polar wandering paths, Continental drift, Seafloor spreading and its geophysical evidences. Elastic Waves, Body Waves and internal structure of earth, variation of physical properties in the interior of earth, Adam-Williamson’s Equation.

A2. Earthquake Seismology:

Seismology, earthquakes, focal depth, epicenter, 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 their 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 network 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 microzonations, Applications for engineering problems.

A3. Mathematical methods in Geophysics:

Elements of vector analysis, Gradient, Divergence and Curl, Gauss's divergence theorem, Stoke’s theorem, Gravitational field, Newton's Law of gravitation, Gravitation 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 and Savart's law, Geomagnetic fields, Magnetic fields due to different type 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 line of force. Current and potential in the earth, basic concept and equations of electromagnetic induction, Maxwell’s Equation, near and far fields, Attenuation of EM waves, EM field of a loops 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 problems versus Inverse problems, direct and model based inversions, Formulation of inverse problems, 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, Eigen values and Eigen vectors, 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

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 & 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: its differential and integral forms, physical significance; Displacement current; Boundary conditions; Wave equation, Plane electromagnetic waves in: free space, non-conducting isotropic medium, conducting medium; Scalar and vector potentials; Reflection; 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, 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 in the ionosphere; Global Positioning Systems (GPS): 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

PART-A

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, factors controlling rock densities, determination of density, Earth's main magnetic field, origin, diurnal and secular variations of the field, Geomagnetic elements, intensity of magnetization and induction, magnetic potential and its relation to field, units of measurement, interrelationship between different components of magnetic fields, Poisson's relation, Magnetic susceptibility, factors controlling susceptibility. Magnetic Mineralogy: Hysteresis, rock magnetism, natural, and remnant magnetization, demagnetization effects. Principles of Gravity and Magnetic instruments, Plan of conducting gravity and magnetic surveys, Gravity and Magnetic data reduction, Gravity bases, International Gravity formula, IGRF corrections. Concept of regional and residual anomalies and various methods of their separation, Edge Enhancement Techniques (Derivatives, Continuation, Analytical Signal, Reduced to Pole and Euler Deconvolution), ambiguity in potential field interpretation, Factors affecting magnetic anomalies, Application of gravity and magnetics in geodynamic, mineral exploration and environmental studies. Qualitative interpretation, Interpretation of gravity and magnetic anomalies due to different geometry shaped bodies and modeling.

A2. Electrical and Electromagnetic methods:

Electrical properties of rocks and minerals, concepts and assumptions of horizontally stratified earth, anisotropy and its effects on electrical fields, geoelectric and geological sections, D.C Resistivity method. Concept of natural electric field, various electrode configurations, Profiling and Sounding (VES). Tpes of Sounding curves, Equivalence and Suppression, Concept of Electrical Resistivity Tomography (ERT). SP Method:, Origin of SP, application of SP surveys. Induced Polarization (IP) Method: Origin of IP, Membrane and Electrode polarization, time and frequency domains of measurement, chargeability, percent frequency effect and metal factor, Application of IP surveys for mineral exploration. Electromagnetic methods, Passive and Active source methods, Diffusion equation, wave equation and damped wave equation used in EM method, boundary conditions, skin depth, depth of investigation and depth of penetration, amplitude and phase relations, real and imaginary components, elliptical polarization, Principles of EM prospecting, various EM methods: Dip angle, Turam, moving source-receiver methods-horizontal loop (Slingram), AFMAG, and VLF.. Principles of Time Domain EM: INPUT method. EM Profiling and sounding, Interpretation of EM anomalies. Principle of EM scale modeling. Magnetotelluric methods: Origin and characteristics of MT fields, Instrumentation, Transverse Electric and Transverse Magnetic Modes, Static Shift. Dimensionality and Directionality analysis. Field Layout and interpretation of MT data and its applications. Principles of Ground Penetrating Radar (GPR).

A3. Seismic Prospecting:

Basic principles of seismic methods, Various factors affecting seismic velocities in rocks, Reflection, refraction and Energy partitioning at an interface, Geometrical spreading, Reflection and refraction of wave phenomena in a layered and dipping media. Seismic absorption and anisotropy, Multi channel seismic (CDP) data acquisition (2D and 3D), sources of energy, Geophones, geometry of arrays, different spread geometry, Instrumentation, 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 Section, 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; Arhcie's and Humble's equations; principles, instrumentations, operational procedures and interpretations of various geophysical logs: SP, resistivity and micro resistivity, gamma ray, neutron, sonic, temperature, caliper and directional logs. Production logging, overlay 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

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; Micro canonical, 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; Frank-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 relaxation, 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 the nuclear forces, Nucleon-nucleon potential; Charge-independence and charge-symmetry of nuclear forces; Isospin; Deuteron problem; Evidence of shell structure, Single-particle shell model and, 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.

Geophysics : Paper-III

PART-A

A1. Radiometric and Airborne Geophysics:

Principles of radioactivity, radioactivity 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. Introduction to 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 ship borne surveys, towing cable and fish, data collection and survey procedures, corrections and interpretation of data. Oceanic magnetic anomalies, Vine-Mathews hypothesis, geomagnetic time scale and dating sea floor, Oceanic heat flow, ocean ridges, basins, marginal basins, rift valleys. Seismic surveys, energy sources, Pinger, Boomer, Sparker, Air gun, Hydrophones and steamer 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 low pass filter.

A4. Remote Sensing and Geohydrology:

Fundamental concepts of remote sensing, electromagnetic radiation spectrum, Interaction of electromagnetic energy and its interactions in atmosphere and surface of the earth, 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. 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

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, photo detectors, 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 behavior 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 fiber waveguides, Fiber characteristics.

B3. Digital electronics, Radar systems, 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. Combination 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; Schrodinger’s wave equation (time-dependent and time-independent); Eigenvalue problems: particle in a box, harmonic oscillator, tunneling 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.