Syllabus
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Course Code: Elective 4 MMATH21 -408 Course Name: Mathematical Aspects of Seismology |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Introduction to Seismology: Earthquakes, Causes of earthquakes; Elastic rebound theory,
Location of earthquakes, Strength of earthquakes; Earthquake magnitude and intensity,
Observation of earthquakes; Seismograms, Seismometers, Earthquake Focal Mechanisms,
Energy released by earthquakes, Seismic waves as probes of Earth’s interior, Interior of the
earth. General form of progressive waves, Harmonic waves, Plane waves, Wave equation. Principle of superposition, Stationary waves. Special types of solutions: Progressive and Stationary type solutions of wave equation in Cartesian, cylindrical and spherical coordinate systems. |
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| 2 | Equation of telegraphy. Exponential form of harmonic waves. D’Alembert’s formula.
Inhomogeneous wave equation, Boundary conditions and mixed problems, Extension of
solutions by reflection. Doppler Effect, Beats, Amplitude modulation, Dispersion, Group velocity, Relation between phase velocity and group velocity, Motion of wave packets. (Relevant articles from the book “Waves” by Coulson & Jeffrey) Spherical waves. Expansion of a spherical wave into plane waves: Sommerfield’s integral. Kirchoff’s solution of the wave equation, Poissons’s formula, Helmholtz’s formula. |
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| 3 | Seismic waves: Reduction of equation of motion to wave equations. P and S waves and their
characteristics. Polarization of plane P and S waves; Wave potentials. Energy in a plane wave.
Snell’s law of reflection and refraction. Ray parameter and slowness. Reflection of plane P and SV waves at a free surface. Partition of reflected energy. Reflection at critical angles. Reflection and reflection of plane P, SV and SH waves at an interface. Special cases of LiquidLiquid interface, Liquid-Solid interface and Solid-Solid interface. |
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| 4 | Surface waves: Rayleigh waves, Love waves and Stoneley waves. (Relevant articles from the book, “Elastic waves in Layered Media” by Ewing et al). Two dimensional Lamb’s problems in an isotropic elastic solid: Area sources and Line Sources in an unlimited elastic solid. A normal force acts on the surface of a semi-infinite elastic solid, tangential forces acting on the surface of a semi-infinite elastic solid. Three dimensional Lamb’s problems in an isotropic elastic solid: Area sources and Point sources in an unlimited elastic solid, Area source and Point source on the surface of semi-infinite elastic solid. Haskell matrix method for Love waves in multilayered medium |
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