GEOL 706 -- Spring 2008
LAB 2 -- Spectra and the Z-Plane

DUE Fri. 29 February

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

Reading: Claerbout, 1992, Chapter 2 and Chapter 3.

1. Claerbout, 1992, p. 37, exercise 2.

2. Claerbout, 1992, p. 43, exercise 2.

3. Claerbout, 1992, p. 43, exercise 3.

4. Claerbout, 1992, p. 50, exercise 3.

5. Claerbout, 1992, p. 60, exercise 1.

6. Claerbout, 1992, p. 64, exercise 1.

7. Claerbout, 1992, p. 65, exercise 1.

8. Claerbout, 1992, p. 72, exercise 2.

9. Claerbout, 1992, p. 73, exercise 1. Develop the filter empirically using the Zplane program.

Some Possible Projects

These are listed to make you aware of possible applications of the ideas covered by this lab. Although 706 does not require a term project, you could use these for one of the two projects required in 757.

Deconvolve a single-channel seismic-reflection data set recorded in Lake Washington, that crosses the Seattle fault several times. Use both recorded source wavelets and spectral whitening in your trials.

Invert single-channel reflection data from Lake Washington for the reflectivity sequence, given data sets recorded at different ranges of frequency over the same location. Develop a transfer function between the reflectivity and other geophysical measurements of the profile.

Construct a minimum-phase multiple-notch filter for a data set contaminated by 60 Hz noise and harmonics. Filter the data set, and describe artifacts, confidence in the content of the filtered spectrum, and any phase changes in the data.

Implement a flexible time-varying, minimum-phase Butterworth filter that will accomplish band pass or reject operations on aritrarily-sized seismic data. Test it on a real data set.

Investigate the use of the slant-stack operator for estimating missing data. Implement a moving-window routine for computing local slantstacks, and test it by filling gaps in stacks, migrations, shot records, and images.

Investigate the properties of a tree-ring data set. Put quantitative bounds on the confidence of cross-correlations between overlapping data, and on the periodicities of climatic cycles.

Develop a method for computing a spectrum from unequally-spaced data. Explore the advantages and disadvantages of linear and spline interpolation, integrations, and model fitting. Speculate on 2-d spectra from randomly-spaced 2-d data.