Course: GPGN 605 Inverse Theory

Instructor: John Scales (jscales@mines.edu, 273-3408)

Wednesday 6:00 - 9:00 PM (i.e., 18:00 - 21:00)

Green Center (room 295)

Fall 1998

Here is the latest snapshot of the book: main.pdf

Here is a link to Per Christian Hansen's Matlab regularization package

Link to Kasper
Van Wijk's page containing the Matlab code for the VRP problem.

*News: 15 August 2000*

- an expanded treatment of frequentist methods of inference (click here for a tutorial with Luis Tenorio to appear in Geophysics).
- a discussion of imaging and migration versus inversion ( click here for a paper on this subject to appear next year.
- all new exercises and demos in Matlab. During the first class we will go over a toy tomography problem.

Chapters 1 - 12: 1.5
Mb gzipped postscript. 10/20/98.
This include lots of recent bug fixes and has the table of contents and
bibliography. **Note** that this file uncompresses to about 6
Mb of postscript. On some Unix systems there is a default limit to
the size of files you can print. This can usually be fixed by giving
lpr a command line argument, such as -s. If you run into this problem
read the man page for lpr. Of course, you can always use ghostview or gv
to print only selected pages. *I also fixed the labeling problem with
the lemmas in chapter 10.*

Software
Resources (emacs, xlisp-stat, etc)
*Some toy software*

- A Mathematica code for doing linear, limited angle tomography via SVD.10/14/98
- Quadratic forms Mathematica notebook.10/14/98
- An Xlisp-Stat package for VSP inversion. Same idea as the Mathematica code, but written using Luke Tierney's wonderful (and free!) Xlisp-Stat package. Click here for my Surfer's Guide to Xlisp-Stat and OO programming.
- A Mathematica notebook resolution matrix calculations.
- A Mathematica notebook for the vsp calculation 10/7/98Here is the jacobian
- A Mathematica notebook for the Monte Carlo risk calculation in the MGSS paper.
- A Mathematica notebook implementing the IRLS algorithm.

- Wences Gouveia's package of codes for parallel reflectivity-based Bayesian inversion of elastic seismograms.
- Philip Stark's bounded variable least square code and much more

*Additional background material, lecture notes, software
and links*

*Three recent papers*

A new approach to incorporating geologic and geophysical inforamtion
into inverse calculations (**Geophysical Joural International**, 141,
713-723, 2000). Click
here for the postscript.

A case study of Bayesian inversion applied to
full-waveform seismic data (J**ournal of Geophysical Research**, 103
2759-2779, 1998). Treats the practical problems of how
compute a priori distributions and data uncertainties for field data.Click
here for the postscript.

Comparison of Bayesian methods with Tikhonov regularization.
(**Inverse Problems**. 13, 323-349, 1997.) Computes resolution
and bias in these two different schemes. Regularization methods bear
a superficial similarity to Bayesian formulae, but the goals and conclusions
are completely different. Click
here for the postscript. Both of these papers were co-written
with Wences Gouveia.

Annotated Reference List (books, papers, etc.)

Residual statics example. Start with the Readme file.

Here are the
data files for the example in Chapter 11.