GEOL 706 -- Spring 2008
LAB 1 -- Z-Transforms and Spectra

Reading: Claerbout, 1992, Chapter 1 and Chapter 2. (Linked from Stanford.)

The exercises in light gray color are extra credit and are not required.

The first two exercises need not be turned in and will not be graded. However, you should be familiar with this material to do the other exercises. Everyone in the class will have login names on the Seismology Sun systems. The electronic form of Claerbout's 1992 book can only be read on a UNIX workstation. The instructor can loan you the source CD-ROM if you want to try to install your own copy, but it is better to follow the electronic version of PVI at Stanford.

There are Sun workstations available in rooms 320, 207, and 209 LME. You may also be able to read the electronic book through an X-Windows server program running on a PC or Mac, while logged into a Seismology Sun. Feel free to use as much Seismo computer time as you need for your assignments and your project.

1. If you are new to the Seismology Sun system, you should read the Hints and policies for Seismology computers.

   Please change your password to something that no one could guess and cannot be found in any dictionary; use the ``passwd'' command. Notice that the UNIX system distinguishes between upper and lower case letters, so be sure to type commands exactly as you read them.

   To print what you see in one of the applications, try the ``Snapshot'' tool available from the Workspace Programs menu. If you convert a saved snapshot image to GIF or JPEG format, then you will be able to email a plot to the instructor as part of turning in your exercise.

2. Try reading the electronic PVI book on a Sun. You will need to run the commands ``pvi'', ``ed1d'', and ``zplane'' after remotely logging into shake.seismo.unr.edu, viewing the displays on a Seismo Sun. Suppose you are sitting at the machine ``blast'' in LME 320. The commands in a Terminal window would be:

   	xhost +shake
   	rlogin shake
   	setenv DISPLAY blast:0
   	pvi
   

   After a minute you should see a small and a large window. In the large window, click the left mouse button on ``Forward'' to see the next page. Keep going until you reach the table of contents. Note that the page numbers given there are enclosed by red boxes. These are buttons you can activate by clicking the middle mouse button. Try moving around the book by clicking on various sections. You can also move the cursor to the box left of ``Goto'' and enter a page number, then press the ``return'' key, or click ``Goto''. Go to page 3. If you use ``Goto'', you may first go the introductory page ``iii'' in roman numerals. Press ``Goto'' once more for page 3. On page 3 you will notice that the caption for Figure 1.4 also contains a red box. Click the middle mouse button in the box to ``activate'' the figure. A window called ``xtpanel'' appears, including a button labeled ``show figure''. Click ``show figure'' and another window appears showing a large, color version of the figure (this may not work on the machine slip, having a 24-bit color display). You have to click on the ``Quit'' button in the figure's window, and also the ``QUIT'' button on the ``xtpanel'', to go back to reading the book.

   If these instructions do not work for you, see the instructor right away. You can try logging into a Seismo Sun as user ``guest''; the password is related to the class and is the very last word in either volume of Aki and Richards, with the first letter's capitalization changed.

3. Open the electronic book to page 8. The xtpanel you get by clicking on figure 1.6 has a button labeled ``interaction'' that activates the ed1D program. When you are on a Sun you can also type ``ed1d'' at any time to activate the program. It works only on the Suns. Read about the ed1D program in Appendix D of the text (electronic or paper). ed1D comes up in a new window with a column of commands on the left and two panels to show plots. As you move the pointer over the panels, the ``selected'' panel gets an extra box that stays after you move off the panels. Note that the program displays messages for you between the two panels. Among the commands is <TUTOR>. Move the mouse pointer to <TUTOR> and follow the instructions. Go through the complete tutorial, and turn in the answers to the following questions:
   1. The fourier transform of a comb function sampling at is another comb function sampling the frequency domain at . As you increase , how does change?
   2. Why does the square of the spectrum of a boxcar signal yield a triangle?

   If you have enabled Java in your Web browser, you can go the FFT Laboratory within Claerbout's Stanford Exploration Project, or here on the Seismo server to try out a much simplified version of ed1d that runs right in your browser window.

4. Claerbout, 1992, p. 13, exercise 1.

5. Claerbout, 1992, p. 14, exercise 4.

6. Claerbout, 1992, p. 14, exercise 5.

7. Open the electronic book to page 10. The button on Figure 1.7 leads to an ``interaction'' botton on an ``xtpanel'' that activates the Zplane program (again, this may not work if slip is set to 24-bit color). On any of the Suns you can type ``zplane'' at any time. You may prefer to run ``zplane'' directly if you have trouble with the (revised) Zplane activated out of the book disappearing suddenly. Read about the Zplane program in Appendix E of the text. On a monochrome Sun you will not see any data in the bottom panel until you click the left mouse button on the ``Wiggle'' command. Zplane comes up with two data panels and a column of commands at the right. Note that the program displays messages for you between the data panels. Move the mouse pointer to <TUTOR> and follow the instructions. If you get a message like ``You typed p'', click the mouse on the Z-plane panel, and then you will be able to enter a pole or zero. Go through the complete tutorial, and turn in the answers to the following questions:
   1. Why does a pole on the real axis yield a sinusoidal function of time?
   2. Explain how a pole on the imaginary axis yields an exponential in . Why does Zplane not let you put poles or zeros below the real axis?
   3. Explain why, for the approximate second derivative filter, the spectrum is close to the magnitude of .
   4. How do you make the second derivative of the Gaussian?
   5. At what range of time and offset is the lowest frequency of ``ground roll''?

8. Claerbout, 1992, p. 20, exercise 2.

9. Claerbout, 1992, p. 20, exercise 4.