Ge 193: An introduction to Geophysical Inverse Problems

Description

The purpose of the course is to introduce students to the principles and techniques of inversion and data inference. To give them an understanding of the underlying theory and an ability to recognize and tackle inverse problems in the geosciences or more generally. Areas to be covered include: The theory behind Linear, Linearized and Nonlinear inverse problems; Techniques for fitting models to data; Ill-posed inverse problems and methods of solution; Making sense of a solution: resolution, error propagation and goodness of fit. Nonlinear optimization and algorithms; Probabilistic inference theory and techniques; Fully nonlinear inversion: Monte Carlo based approaches to exploring parameter spaces.

The lectures will be supported by numerous examples and most likely MATLAB based exercises. Prerequisites: The course is aimed primarily at students with background in Physics and Mathematics, although some background mathematical material will be covered where necessary. Exposure to university level mathematics, particularly linear algebra and vector calculus will be an advantage.

Units: 3-0-6 (first term)
Regular class time: Tuesday and Thursday 1 PM – 2:30 PM, 162 S. Mudd
Grading policy: 3-4 homeworks (60%), 2-3 tutorials (30%), Class participation (i.e. discussion, answering and asking questions) (10%). No final exam.

Topics

Background material for this class is available HERE.

COMPLETE LECTURE NOTES for this class are available HERE [42 MB PPT File!].

Practicals

Practicals will be held two or three times during the quarter, on dates that will be decided in class. Additional software and tutorials useful for the practicals are HERE.

Homework

Late homeworks will be penalized 10% per day, unless there is a clear problem with any given assignment or there is some kind of real emergency. Discussing homeworks with fellow students is fine, but what is turned in should represent your work, not a group effort. Please do not request extensions on the same day the homework is due. Software and tutorials useful for completing your homeworks are HERE.

*BOC = beginning of class

Reading assignments

As part of this class, we will read selected important papers/textbook chapters. The reading material will be handed out during the class or available as PDFs from the class website.

Your paper summaries/comparisons should be two pages long, max - UNLESS OTHERWISE STATED BELOW. In general, please treat this assignment like any other scientific writing (i.e., papers, reviews, and proposals) and conform to a format with single or double-spaced lines, 1 inch margins, and 12 pt font. Use a concise style of prose (but do not slip into outline form). Choose an active style over a passive style, avoid chatty colloquialisms (this is not a diary), watch that you have some kind of logical order of presentation, and be precise with your language.

*BOC = beginning of class

Bibliography

All textbooks below should be available in the Geology Library Reference by October 8th.

• Inverse Theory:

  • Parameter Estimation and Inverse Problems, by Richard Aster, Brian Borchers, and Clifford Thurber, Academic Press (Elsivier) 2004. [Book Details]

  • Inverse Problem Theory, by Albert Tarantola, SIAM, 2005. [FREE Download]

  • Geophysical Inverse Theory, by Robert Parker, Princeton University Press, 1994. [Book Details]

  • Geophysical Data Analysis, by William Menke, Academic Press (Elsivier) 1989. [Book Details]

  • Data Analysis: A Bayesian Tutorial, by Devinderjit Sivia and John Skilling, Oxford University Press, 2006. [Book Details]

  • Numerical Recipes in Fortran 77, by Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Cambridge University Press, 1992: Chapter 15 [FREE Download]

  
  

• Introductory Material from a Seismological Perspective:

  • An Introduction to Seismology, Earthquakes, and Earth Structure, by Seth Stein and Michael Wysession, Blackwell Publishing, 2002: Chapter 7. [Book Details]

  • Introduction to Seismology, by Peter Shearer, Cambridge University Press, 1999: Chapter 5. [Book Details]

  
  

• Papers:

  • Understanding inverse theory, Parker, R. L. (1977), Ann. Rev. Earth Planet. Sci., 5, 35-64. [PDF]

  • Interpretation of inaccurate, insufficient and inconsistent data, Jackson, D. D. (1972), Geophys. J. Roy. astr. Soc., 28, 97-109. [PDF]

  • Monte Carlo sampling of solutions to inverse problems, Mosegaard, K. and A. Tarantola (1995), J. Geophys. Res., 100, 12,431–12,447. [PDF]

  • Monte Carlo methods in geophysical inverse problems, Sambridge, M. and K. Mosegaard (2002), Rev. of Geophys., 40, 3.1-3.29. [PDF]

  • Seismic traveltime tomography of the crust and lithosphere, Rawlinson, N. and M. Sambridge (2003), Advances in Geophysics, 46, 81-198. [PDF]

  
  

• Other Online Sources:

  • Inverse Problem Courses at several U.S. Universities
    (NOTE: You have to scroll down that page to see the list)

Instructor

• Malcolm Sambridge, 252F South Mudd, Malcolm.Sambridge@anu.edu.au, x3429

Teaching Assistant

• Ravi Kanda, 358 South Mudd, rkanda@gps.caltech.edu, x6971

Ombudsperson

• Laura Alisic, 362 South Mudd, alisic@gps.caltech.edu, x6974

Last updated by Ravi Kanda in December, 2007