UPSC GE Geophysics Paper I Syllabus

The syllabus consists of eight sections divided into two parts: A and B. (A1) Solid Earth Geophysics (A2) Earthquake Seismology (A3) Mathematical methods in Geophysics (A4) Geophysical Inversion (B1) Mathematical Methods of Physics (B2) Electrodynamics (B3) Electromagnetic Theory (B4) Introductory Atmospheric and Space Physics.

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.

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.