Mathematical Geophysics

ABOUT THE COURSE:The primary objective of the course is to describe the physical and mathematical principles of various aspects of geophysical problems ranging from atmospheric sciences, climate dynamics to deep interiors of planets. The numerous applications of geophysics are strongly based on fundamental mathematical and physical principles such as linear algebra, vector calculus leading to potential theory, wave dynamics and turbulence. This course will be focused on such topics with the inclusion of additional insights into novel methods for analyzing geophysical data obtained from observations and field measurements. The content will be useful for learners focusing on fundamental physics applied to Earth sciences and aiming to gain experience in scientific data analysis.INTENDED AUDIENCE: Undergraduate and Post Graduate Students in Geophysics and Earth SciencesPRE REQUISITES: 12th Standard MathematicsINDUSTRY SUPPORT: ONGC, GSI, NTPC, Tata Power and any other company related to geophysical exploration, climate change, wind energy, ocean energy, and atmospheric sciences.

Syllabus

Week 1: Scalars and Vectors, Systems of Coordinates, Solid Angle Conservative geophysical fields, GradientWeek 2:Geometric Model of a Field, Flux, Divergence, Gauss' Theorem, Stokes' Theorem, Green’s Function Week 3:Systems of linear equations, Gravitational Field and Upward Continuation / Downward continuationWeek 4:Systems of linear differential equations, Time-Invariant Electric Field and Potential, Electric Current, Conductivity, and Ohm's LawWeek 5:The Diffusion equation, Geothermal gradient, Magnetic diffusion, Decay of Magnetic fields.Week 6:The Wave equation , Seismic Waves, Inertial waves, Internal gravity waves.Week 7:Laplace’s and Poisson's equations, Convective heat flows in the Earth.Week 8:Geophysical data analysis, Time-series analysis, Principal component analysis