Mathematical Geophysics

By Prof.Swarandeep Sahoo | IIT(ISM) Dhanbad

Learners enrolled: 418 | Exam registration: 35

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 Sciences

PRE REQUISITES: 12th Standard Mathematics

INDUSTRY SUPPORT: ONGC, GSI, NTPC, Tata Power and any other company related to geophysical exploration, climate change, wind energy, ocean energy, and atmospheric sciences.

Summary

Course Status :	Ongoing
Course Type :	Core
Language for course content :	English
Duration :	8 weeks
Category :	Earth Sciences
Credit Points :	2
Level :	Undergraduate
Start Date :	17 Feb 2025
End Date :	11 Apr 2025
Enrollment Ends :	17 Feb 2025
Exam Registration Ends :	28 Feb 2025
Exam Date :	26 Apr 2025 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Scalars and Vectors, Systems of Coordinates, Solid Angle Conservative geophysical fields, Gradient

Week 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 continuation

Week 4: Systems of linear differential equations, Time-Invariant Electric Field and Potential, Electric Current, Conductivity, and Ohm's Law

Week 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

Books and references

References:

1. Boas, Mary L. Mathematical methods in the physical sciences. John Wiley & Sons, 2006.

2. Arfken, George B., Hans J. Weber, and Frank E. Harris. Mathematical methods for physicists: a

comprehensive guide. Academic press, 2011.

3. Gubbins, David. Time series analysis and inverse theory for geophysicists. Cambridge university press,

2004.

4. Barman, Tirtharaj, and Swarandeep Sahoo. "Role of partial stable stratification on fluid flow and heat

transfer in rotating thermal convection." Physics of Fluids 36.4 (2024).

5. Mukherjee, Priyabrata, and Swarandeep Sahoo. "Coherent flow structures and magnetic field patterns

in rotating spherical shell convective dynamos: A data-driven approach." Physics of Fluids 36.11 (2024).

6. Sharma, Dheeraj Kumar, and Swarandeep Sahoo. "On the onset of thermal convection in a rotating

spherical shell with spatially heterogeneous heat source distribution." Physics of Fluids 36.12 (2024).

7. Kaufman, Alexander A. Geophysical Field Theory and Method, Part A: Gravitational, Electric, and

Magnetic Fields. Academic Press, 1992.

8. Riley, Kenneth Franklin, Michael Paul Hobson, and Stephen John Bence. Mathematical methods for

physics and engineering: a comprehensive guide. Cambridge university press, 2006.

9. Agnew, D. C., and R. L. Parker. "Geophysical Data Analysis: Time Series." SIO 223B CLASS NOTES,

http://igppweb. ucsd. edu/~ agnew/Courses/Sio223b/sio223bnotes. html.(Last accessed Feb

2015) (2011).

Instructor bio

Prof.Swarandeep Sahoo

IIT(ISM) Dhanbad

Prof. Swarandeep Sahoo is an Assistant Professor at the Department of Applied Geophysics, Indian Institute of Technology (ISM), Dhanbad, India. His research interests include Planetary Fluid Dynamics, Rotating Convection, Planetary Magnetism, Geomagnetic Reversals, Vortex Dynamics. An aerospace engineer with expertise in planetary sciences, he has a broad coverage of research areas and teaching subjects. He has co-authored more than 30 contributions in international journals and conferences.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: EXAM DATE : April 26, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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