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Geol 335.3 LAB 9: Fourier transforms and Filtering |
This lab has two parts dealing with Fourier analysis, and the relations between the time and frequency domains.
This exercise is designed to familiarize you with Fourier transforms. You will need to make sure you are using a browser with Java enabled - you can run this part of the lab on any system. If you are using Netscape on a Unix box, look under "Options" for "Network preferences", then click on "Languages" and make sure the box for Java is checked.
Use the Fourier transform tool :
Set the checkbox “origin centered”. Zero all the coefficients. The top two panels are the real and imaginary parts of the time domain. The bottom two panels are the real and imaginary parts of the signal in frequency domain.
Zero time is shown as the open circle in the top panels, zero frequency is shown as the open circle in the bottom. Make plots of your work. To plot, it is usually sufficient to click File->Print in your browser.
1) (5%) Put in a “boxcar” function (square wave) 5 units wide (a box of 5 samples of equal values) centered on the origin. What is the Fourier transform of this? How wide is the main lobe? Print the plot out and mark it up.
2) (5%) Double the width of the square wave function. How wide is the transform? What property of the Fourier transform does this illustrate?
3) (5%) Move the boxcar function so that its rightmost sample is at the origin. What does the transform look like? What property of the Fourier transform does this illustrate?
4) (5%) Put a single impulse at the origin. What does its transform look like?
5) (5%) Move the impulse 2-4 time samples away from the zero grid point. What happens to the transform?
6) (5%) Put in two impulses equally spaced around the origin two units away from the origin. This is called an even impulse pair. What is the transform?
7) (5%) Make one of the impulses negative. This is called the odd impulse pair. What does the transform look like?
8) (5%) Put the even impulse pair two units away from the origin on the real part of the frequency domain. What is the time domain signal look like? What property of the Fourier transform do questions 6 and 8 together illustrate?
9) (5%) Perform step (8) using an odd impulse pair, but put it on the imaginary part of the Fourier transform. What does the transform look like?
10) (5%) In the origin centered mode, the first sample in the frequency domain is the Nyquist frequency. Put a single spike there. What is the time domain signal?
Play around with the transform tool.
The most common use of bandpass filtering on real
seismic data is to try to remove noise when the signal and noise don’t overlap
too much in frequency. In this exercise, you will use the seismic processing
package
To obtain the initial Vista data, you will need to copy file Vista_335.zip from directory http://seisweb.usask.ca/classes/GEOL335/ to your Windows computer. Uncompress this file and save the resulting directory. The web directory above also contains subdirectory Vista_335; if you can figure out how to copy it to your computer, you will not need to decompress it. This directory will contain all of your Vista projects. At present, you will only find one project (subdirectory) there, named 'Vista335'.
You should have a
1) (5%) What is the Nyquist frequency for this dataset?
Click on the second column (a tiny icon next to the number ‘1’ of the dataset). This will open the seismic data display.
On the “MAIN SEISMIC TOOLBAR” on the left, locate the button “Sort Display Order”, click it, and select “Shot Order”. You will see the data now being displayed one shot at a time. Click on the display; this will make a box with the number of the shot appear on the lower-left of the plot panel. Double-click on this box, and in the resulting pop-up window, select “11: LINE 1 SHOT 163”. We will work with this shot.
2) (20%) Make a hardcopy plot of the data (use File->Print), label the main phases, and sketch the areas that you think are mostly signal and those where there is a lot of noise. How did you decide between them?
3) (5%) What periods/frequencies can you see in the noisy area?
Now you will test 2 series of filters with 1-octave slopes at each end and a 1-octave bandpass (i.e., four numbers with frequency doubling each time; for example: 2-4-8-16). The two series need to overlap: often a series similar to the following is used
2-4-8-16
3-6-12-24
4-8-16-32
6-12-24-48
8-16-32-64
12-24-48-96
You need to choose series that start below the lowest frequencies you can see in the data (typically seismic sources don't have much energy below ~6Hz), and extend up to the Nyquist frequency. This means that we can choose corner frequencies to within half an octave anywhere in the frequency range of our data.
To apply the filters, on the “MAIN SEISMIC TOOLBAR”, click the “Seismic Data Plot Parameter” button (the leftmost one). In the popup, choose “Process” tab, check the “Apply Ormsby Filter” box, and set its frequency parameters in the F1, F2, F3, F4 fields as specified above. Then click Apply or OK to apply the filter.
4) (0%) Make hardcopies of the resulting panels - this is a set of filter test panels.
5) (5%) Which of these panels are mostly noise and which are mostly signal?
6) (10%) Now mix the filter panel ranges to choose a single bandpass filter that includes the range of the signal but excludes the noise. What are the four corner frequencies? Note that lower-frequency contains information about the deeper reflections yet more ground roll - you have to balance between these two criteria.
7) (5%) Make a hardcopy plot the data with this bandpass filter and compare to the original and to the filter panels. Did this bandpass remove anything you think was significant in the data?
Answers to the questions and the plots in a binder.