ajmalkoti.github.io

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ajaymalkoti@ngri.res.in
ajmalkoti.github.io

Ajay Malkoti
Seismic Group
CSIR-NGRI

Geophysical Inverse Theory (PHY-NGRI-3-4003 )


Instructor

Dr. Ajay Malkoti,
Room No. 110, Main Building,
CSIR-National Geophysical Research Institute,
Hyderabad-500007, India.

In this course I will discuss fundamental theory underlying the geophysical inversion. It should help students to develop an understanding for the problem and and itutions for the solution/method.
A tentative content/structure for the course is given below and can be changed according to the requirement of audiance.

Prerequisite

A background in physics and mathematics (partiularly, calculus and algebra)

Course Outline

  1. Basic programming in Python (2 lectures + assignment)
  2. Linear algebra and subspace (2 lectures)
  3. Linear inverse theory- LSq, ML, GI, constraints and Examples (2 lecture + assignment)
  4. Nonlinear inverse theory and Iterative (gradient) based procedures
  5. Global optimization methods-SA, GA (2 Lectures + assignment)
  6. Monte carlo methods (2 Lectures + assignment)
  7. Probablistic/baysian inversion (2 lectures + assignment)
  8. Paper presentation

Optional

  1. Continuous inverse theory
  2. Numerical matrix inversion techniques
  3. Neural network

Assignment
See the pdf

Grading Policy

Grade assessment is based upon- Attendance (10%), Assignment (20%), Final exam (70%).
All the assignments must to be handed over before the due dates. Late submission will face a penalty of 20% for each delayed week. If the assignments are found to be copied (among student/from internet) it will be graded as zero.

Lecture Venue

AcSIR lecture Hall, Ist Floor, Ext. Building, CSIR-NGRI, Hyderabad-500007, India

Exam schedule and venue

To be anounced

Reference Material:

Books:
Hill, Christian. Learning scientific programming with Python. Cambridge University Press, 2020.
Lutz, Mark. Programming Python: powerful object-oriented programming. O’Reilly Media, Inc., 2010.
Aster, Richard C., Brian Borchers, and Clifford H. Thurber. Parameter estimation and inverse problems. Elsevier, 2018.
Dimri, Vijay. Deconvolution and inverse theory: application to geophysical problems. Elsevier, 2013.
Menke, William. Geophysical data analysis: Discrete inverse theory. Academic press, 2018.
Sen, M. K., & Stoffa, P. L. Global optimization methods in geophysical inversion. Cambridge University Press, 2013.
Tarantola, Albert. Inverse problem theory and methods for model parameter estimation. Society for Industrial and Applied Mathematics, 2005.
Golub, G., and C. Van Loan, Matrix Computations, Johns Hopkins Press, 1996.
Strang, G., Introduction to Linear Algebra, 5th edition, Wellesley-Cambridge Press, Wellesley, MA, 2016.
Strang, G., Introduction to Applied Mathematics, Wellesley-Cambridge Press, Wellesley, MA, 1986.
Arfken, George B., and Hans J. Weber. “Mathematical methods for physicists.” (1999): 165-169.
Hassani, Sadri. Foundations of mathematical physics. Allyn & Bacon, 1991.
Morse, P.M., and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, 1953.
Riley, Kenneth Franklin, Michael Paul Hobson, and Stephen John Bence. “Mathematical methods for physics and engineering.” (1999): 165-169.

Papers to read:
Weglein et al.(2003) - Inverse scattering series and seismic exploration.
Lines et. al. (1988) Cooperative inversion of geophysical data.
Martin Hanke (1997) A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems.
MK Sen, PL Stoffa (1996) Bayesian inference, Gibbs’ sampler and uncertainty estimation in geophysical inversion.

Application based
Sen and stoff (1993) Nonlinear inversion of resistivity sounding data

Other Material