Details of ES4105 (Autumn 2020)

Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
ES4105 Inverse Theory Kajaljyoti Borah

Syllabus
Digital Signal Processing: z-transform, Discrete Fourier Transform, aliasing, filtering, correlation,
deconvolution.
Probability Theory (Random variables, Gaussian distribution, Testing the Assumption of Gaussian
Statistics, Confidence Intervals), Solution of the Linear Gaussian and Non-Gaussian Inverse Problem
(Least Square Problem, The Data and Model resolution matrix, The Unit Covariance matrix, The
Trade-off of resolution and variance, Norm), Non-linear Inverse Problem, Tomography, Numerical
Algorithms (solving Evendetermined, Underdetermined, Overdetermined and Eigen value Problem,
Singular-Value Decomposition), Applications of Inverse Theory to Geophysics.

References
Textbooks:

1. Geophysical Data Analysis: Discrete Inverse Theory, William Menke, Volume 45, Internatonal
Geophysics Series, Academic Press, INC.
2. Inverse Problem Theory and Methods for Model Parameters Estimation, Albert Tarantola, Society
of Industrial and Applied Mathematics, Philadelphia.
3. Time Series Analysis and Inverse Theory for Geophysicists, David Gubins, Cambridge University
Press, 2004.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Elective
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 5 Not Allowed
7 MS 7 Elective
8 MS 9 Not Allowed
9 RS 1 Elective
10 RS 2 Elective