Combined Geo-Scientist Preliminary Exam Geophysics Syllabus

The syllabus consists of six units: (1) Solid Earth Geophysics (2) Mathematical Methods in Geophysics (3) Electromagnetism (4) Geophysical Prospecting (5) Remote Sensing and Thermodynamics (6) Nuclear Physics and Radiometry.

1. Solid Earth Geophysics

Introduction to Geophysics and its branches. Solar system: origin, formation and characteristics of planets, Earth: shape and rotation. Gravity and magnetic fields of earth. Geomagnetism, elements of earth's magnetism, Rock and mineral magnetism, Elastic waves, types and their propagation characteristics, internal structure of earth, variation of physical properties in the interior of earth. Plate tectonics, Earthquakes and their causes, focal depth, epicenter, Intensity and Magnitude scales, Energy of earthquakes, Seismicity.

2. Mathematical Methods in Geophysics

Elements of vector analysis, Vector algebra, Properties of scalars, vectors and tensors, Gradient, Divergence and Curl, Gauss's divergence theorem, Stoke’s theorem. Matrices, Eigen values and Eigen vectors and their applications in geophysics.

Newton's Law of gravitation, Gravity potential and gravity fields due to bodies of different geometric shapes. Basic Forces of Nature and their strength: Gravitational, Electromagnetic, Strong and Weak forces. Conservation Laws in Physics: Energy, Linear and angular momentum. Rigid body motion and moment of inertia. Basics of special theory of relativity and Lorentz transformation.

Fundamental concepts of inverse theory, Definition of inversion and application to Geophysics. Forward and Inverse problems. Probability theory, Random variables, binomial, Poisson and normal distributions. Linear algebra, Linear ordinary differential equations of first and second order. 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, Introduction to finite difference and finite elements methods.

3. Electromagnetism

Electrostatic and magneto-static fields, Coulomb's law, Electrical permittivity and dielectric constant, Lorentz force and their applications. Ampere's law, Biot and Savart's law, Gauss’s Theorem, Poisson's equation. Laplace's equation: solution of Laplace's equation in Cartesian coordinates, use of Laplace's equation in the solutions of geophysical and electrostatic problems.

Displacement current, Faraday's law of electromagnetic induction. Maxwell's equations. Boundary conditions. Wave equation, plane electromagnetic waves in free space, dielectric and conducting media, electromagnetic vector and scalar potentials.

4. Geophysical Prospecting

Elements of geophysical methods: Principles, data reduction and applications of gravity, magnetic, electrical, electromagnetic and well logging methods. Fundamentals of seismic methods: Fermat’s Principle, Snell’s Law, Energy portioning, Reflection and transmission coefficients, Reflection and Refraction from layered media.

Signals and systems, sampling theorem, aliasing effect, Fourier series and periodic waveforms, Fourier transform and its application, Laplace transforms, Convolution, Auto and cross correlations, Power spectrum, Delta function, unit step function.

5. Remote Sensing and Thermodynamics

Fundamentals of remote sensing, electromagnetic spectrum, energy frequency-wavelength relationship, Stefan-Boltzmann Law, Wien’s Law, electromagnetic energy and its interactions in the atmosphere and with terrain features. Planck’s Radiation Law. Laws of thermodynamics and thermodynamic potential.

6. Nuclear Physics and Radiometry

Basic nuclear properties: size, shape, charge distribution, spin and parity; Binding energy, semi-empirical mass formula; Fission and fusion. Principles of radioactivity, Alpha, beta and gamma decays, Photoelectric and Compton Effect, Pair Production, radioactivity decay law, radioactivity of rocks and minerals, Radiation Detectors: Ionization chamber, G-M counter, Scintillation counter and Gamma ray spectrometer. Matter Waves and wave particle duality, Electron spin, Spectrum of Hydrogen, helium and alkali atoms.