Syllabus of Combined Geo-Scientist (Main) Examination

Stage-II (Descriptive Type)

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 (bvalues).
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; Leastsquares
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.