This is my masters thesis from the University of
Southern California. If you are really going to read it,
please remember that when I was in graduate school (1981 to 1984)
there were no such things as PCs or graphics workstations. The
VAX 11/780 was the big thing in computers.
At Purdue, where I got my undergraduate degree, the professors in
Geophysics were big on computer-aided processing of data. At USC, my
advisor knew little of computers, nor of computer processing with
Fast Fourier Transforms.
I turned in my thesis in June of 1984, right before USC shut down
for the Los Angeles Summer Olympics. (USC was the location of the Olympic
village and the swim stadium. Next to USC is Exposition Park. This was the
location of all track and field events, as well as boxing.)
I spent the remainder of the summer working as a volunteer driver for the
LAOOC, driving atheletes and dignitaries around town. Then in the fall,
I started work for the International division of Union Oil. By this time,
my advisors had read my thesis. Dr Henyey was willing to sign it off, but
the other two felt that it read like a highschool term paper and really
didn't say anything. So I spent the next six months rewriting it. Finally,
in the spring of 1985, I turned it in and graduated.
WAVENUMBER FILTERING OF GRAVITY DATA
AND ITS
APPLICATION TO INTERPRETING STRUCTURE
IN THE WESTERN TRANSVERSE RANGES
OF SOUTHERN CALIFORNIA
Timothy M. Fogarty
1985
unpublished Masters thesis
University of Southern California.
- Title Page
- ACKNOWLEDGEMENTS
- ABSTRACT
- TABLE OF CONTENTS
- LIST OF FIGURES
- Chapter 1, INTRODUCTION
- Chapter 2, METHOD OF WAVENUMBER FILTERING
- Chapter 3, APPLICATION OF FILTERING
METHODS TO GRAVITY OF SOUTHERN CALIFORNIA
- Chapter 4, INTERPRETATION OF THE GRAVITY FIELD
- BIBLIOGRAPHY
- APPENDIX A. COMPUTER PROGRAMS
- APPENDIX B. GRAVITY ANOMALY CONTOUR MAPS
- B1 Original data
- B2 Low-pass, 0 to 1/2 Nyquist
- B3 Low-pass, 0 to 1/4 Nyquist
- B4 Low-pass, 0 to 1/8 Nyquist
- B5 Low-pass, 0 to 1/16 Nyquist
- B6 Band-pass, 1/16 to 1/2 Nyquist
- B7 Band-pass, 1/16 to 1/4 Nyquist
- B8 Band-pass, 1/8 to 1/2 Nyquist
- B9 Upward continuation to 2.5 km
- B10 Upward Continuation to 5 km
- B11 Upward continuation to 10 km
- B12 Upward continuation to 25 km
- B13 Downward continuation 2.5 km of Band-pass
low-pass 0 to 1/2 Nyquist
- B14 Downward continuation 5 km of Band-pass
low-pass 0 to 1/2 Nyquist
- B15 Downward continuation 2.5 km of Band-pass
low-pass 0 to 1/4 Nyquist
- B16 Downward continuation 5 km of Band-pass
low-pass 0 to 1/4 Nyquist
- B17 Downward continuation 10 km of Band-pass
low-pass 0 to 1/4 Nyquist
- B18 Downward continuation 5 km of Band-pass
1/16 to 1/2 Nyquist
- B19 First horizontal derivative in X direction
- B20 First vertical derivative of Upward
continuation 2.5 km
- B21 Second vertical derivative of Upward
continuation 2.5 km
- B22 First vertical derivative of Band-pass
0 to 1/2 Nyquist
- B23 Second vertical derivative of Band-pass
0 to 1/2 Nyquist
- B24 First horizontal derivative in X direction
of Upward continuation 2.5 km
- B25 First horizontal derivative in Y direction
of Upward continuation 2.5 km
- B26 First horizontal derivative in X direction
of Band-pass 0 to 1/2 Nyquist
- B27 First horizontal derivative in Y direction
of Band-pass 0 to 1/2 Nyquist
- B28 Second horizontal derivative in X direction
of Upward continuation 2.5 km
- B29 Second horizontal derivative in Y direction
of Upward continuation 2.5 km
- B30 Second horizontal derivative in X direction
of Band-pass 0 to 1/2 Nyquist
- B31 Second horizontal derivative in Y direction
of Band-pass 0 to 1/2 Nyquist
- B32 Horizontal derivative in the X and Y dirction
of Upward continuation 2.5 km
- B33 Horizontal derivative in the X and Y dirction
of Band-pass 0 to 1/2 Nyquist
- B34 Strike-pass, 80 to 110 degrees
- B35 Strike-pass, 125 to 145 degrees
- LIST OF FIGURES
- 1) Flow chart of the wavenumber filtering method.
- 2)Profile of various two-dimensional bodies used to
analyze error due to leakage and Gibb's phenomenon,
anomaly calculated at elevation z=0 (+), and
anomaly calculated at elevation z=2 (X)
- 3) Input data for comparison of methods to limit edge effects and leakage.
- a) Original data set.
- b) Data set tapered by cosine window.
- c) Data set extened with its end values.
- d) Data set extended with its reflection.
- 4) Results of upward continuation filtering for comparison
of methods to limit edge effects and leakage.
- a) Original data set.
- b) Data set tapered by cosine window.
- c) Data set extened with its end values.
- d) Data set extended with its reflection.
- 5) Error for comparison of methods to limit edge effects and leakage.
- a) Original data set.
- b) Data set tapered by cosine window.
- c) Data set extened with its end values.
- d) Data set extended with its reflection.
- 6) Band-pass filters.
- a) Ideal band-pass filter.
- b) Band-pass filter transformed to spacial domain,
tapered with a cosine taper and then transformed
back to wavenumber domain.
- c) Band-pass filter with intermediate value of 0.5. 49
- 7)
a) Method of storage of a two-dimensional array
for the Fast Fourier Transform. Modified from
Reed (1980).
b) Relationship between wavelengths, wavenumbers
and frequencies in the Fast Fourier Transform.
- 8) Example of two-dimensional filters:
- a) First vertical derivative.
- b) Second vertical derivative.
- c) First horizontal derivative in X direction.
- d) First horizontal derivative in Y direction.
- e) Upward continuation.
- f) Downward continuation.
- g) Band-pass 1/4 to 1/2 Nyquist.
- h) Strike-pass, 80 to 110 degrees.
- 9) Region of study in southern California showing
selected geological features.
- 10) Location of all gravity station in region of study.
- 11) Color contour map of original data as gridded by
the program POLYMAP and contoured by COLCON
- 12) Boundaries determined from the analysis of the
filtered gravity maps overlain various contour maps.
- a) Original gravity map B1.
- b) Downward continuation filtered map B22.
- c) First vertical derivative filtered map B30.
- d) First horizontal derivative in X direction filtered map B34.
- 13) Locations of profiles for 2-D modeling.
- 14) Two-dimensional gravity modeling.
- a) Column 40 of grid, Santa Monica basin to Santa Ynez Mountains.
- b) Column 40 of grid, alternate model, Santa
Monica basin to Santa Ynez Mountains.
- c) Western half of row 12, Santa Rosa Cortez ridge
to Los Angeles basin.
- d) Western half of row 12, alternate model, Santa
Rosa Cortez ridge to Los Angeles basin.
