SIO 230 Geophysical Inverse Theory 2009

SIO230 is scheduled to meet on Tuesdays and Thursdays 8:00 AM -- 9:20 AM in the Munk Conference Room in IGPP. The first class is on Tuesday 1/06/09.

There will be homework approximately at weekly intervals and the grade for the class will be based on the homework, although there may also be a final exam. The homework will require a working knowledge of Matlab and access to that program.

The text for the class is my book Geophysical Inverse Theory, Princeton University Press, 1994, which I recommend that you buy. If you don't wish to buy a copy, the book will be on reserve in the SIO Library, and there is a copy in the IGPP Reading Room. Also, generations of geophysics students at SIO have copies they might be willing to lend out. Like any human endeavor GIT is imperfect: there is available a list of known errors in PDF format.

The prolog as been moved to here. A list of potential topics can be found here. We probably will not have the time in one Quarter to cover them all.

Diary

3/17/09: Happy St Patrick's Day!
This is my final post to the class website. Here is the solution to Homework 7. Everyone who submitted a model got reasonably close, although misfits strayed a bit from the requested value. I decided to award full credit to all these hardworking students.

Thank you for your attention and your interest. I hope this material will prove beneficial to you later, although be prepared to argue with your advisor when he/she suggests some scheme like "Most Squares" or Bayesian Inference. I am always available for consultation.

3/11/09: The last class will cover more general optimization techniques, in particular conjugate gradients. Here are notes for this material .

3/5/09: Here is the eagerly anticipated 7th and last homework set and its data set. Solutions are due next Thursday.

3/3/09: The IGPP server has been down all day, and I've only been able to put up my solution to the 6th homework set this evening. On the whole, my solutions to Question 1 are much more elegant than yours, so look at them. Also I discuss some computational aspects of the solutions that are important as systems get larger. I'm still thinking about a final homework set on nonlinear problems.

2/24/09: My apologies for claiming homework was due today, Tuesday: Thursday is the day for Homework 6. Some interest has been expressed concerning the Matlab code for Homework 5. Here is my matlab script for the solution.

2/23/09: I have graded your solutions to the last homework; here is the official solution. It includes a section on how to find the width of the delta-function approximation for arbitrarily large N. Homework 6 is due tomorrow. We will a brief rest from homework, no doubt to universal relief.
We begin tomorrow with our exploration of nonlinear problems, based on GIT.

2/18/09: Tomorrow's class will continue to be from GIT for the most part. We may need a few addition pages of notes about nnls and bvls.
To give you plenty of time I am posting homework number 6 and its table of data. Your solution is due next Thursday.

2/17/09: I have graded homeworkset number 4, and here is my solution.
Today's class will be from GIT.

2/13/09: Here is the 5th homework set, due next Thursday.

2/11/09: Here are a few more pages of notes supplying examples of applications of the theory we covered yesterday.
Next we will move on to Section 4.05 of GIT.

2/9/09: The solution to the 3rd homework is now posted. Some of you may find it helpful in answering one of the parts of the current homework (not due until Thursday). I discovered the problem in Set 3 could be converted into a convolution by using log time. I have included that discussion, for those who may be interested.

After my somewhat uncharitable remarks about the class's inability to display graphical information coherently, here is a positive suggestion: you may like to read (or revisit) Duncan Agnew's essay on the subject. For those with a serious interest, there is Edward Tufte's site and his books.

2/4/09: I have revised the last pages of the current notes once again. When we finish these notes tomorrow, we will turn to GIT for a discussion of resolution.
The 4th set of homework and its data set have been posted. I would like your answers next Thursday.

2/2/09: For tomorrow's class, here are a few notes to complement 3.01 in GIT.
Also there was bug in the code I used to create Fig 13.2 on p 67 of the notes; here is revised picture and some text. The difference may appear slight, but it is important.
Monday afternoon: I have graded the 2nd homework set. My solution.

1/28/09: New notes and new homework; also a table of data values for the homework, which is due, please note, next Tuesday, 2/03/09.

1/26/09: The was an error in equation (9) of Section 8, which had no serious consequence in any of the subsequent calculations; none-the-less, here is a correction.
Also here is the next set of notes.

1/23/09: I have graded the homework, and the official solution can now be revealed.

1/22/09: Two small typos to be fixed: In Question 3 of the new homework, Q in the equation for linearity should be O; on p 47 of the notes just before equation (11), replace "size" with "side".

1/21/09: Here is the next batch of notes for tomorrow's class.
Also I have posted the second homework set. Your answers should be ready next on Thursday 1/29/09.

1/19/09: Tomorrow's class will be centered on generalizing some of the ideas we have reviewed in linear algebra to the more abstract setting of Hilbert space. You may want to look at Chapter 1 of GIT, from which this material comes.
The first homework set is also due.

1/8/09: Today we continue with the notes posted earlier.
As I mentioned in the first class, I will be out of town all of next week. While I am away, I would like you to go over the notes already issued. The material should be largely familiar, although the notation and my perspective may be new to you.
Here is the first homework set, due Tuesday 1/20/09. It is quite long since it covers next week and this; do not wait to the last minute to look at it!

1/6/09: I noticed a few small typos in the notes put up this morning. If you download after 10AM today, they have been fixed. Otherwise here they are:
p 5-6. The vector B₀ should have a hat - it is a unit vector.
p22, after (22), replace "The negative" with "A negative"

1/5/09: Here is the first batch of notes for tomorrow's class in PDF format. These will keep us occupied for some time. I will also be posting a set of homework problems soon.