GEOPHYSICS 5104 - Seismic Deconvolution

Course Outline, Lecture and Laboratory Notes, Index No. 2685, Quarter equivalent: GEOL 5140 Exploration Geophysics

Derring 4052 11:00-11:50 M W F

4 credit hours

Instructor: John K. Costain, Professor Emeritus of Geophysics

Regional Geophysics Laboratory, Department of Geological Sciences, Virginia Tech

1050 Derring Hall

(703) 231-5096

Notes are Version 1996.1

January 18, 1996

Office hours: Any mutually convenient time by appointment

Textbook : Geophysical Signal Analysis by E. A. Robinson and S. Treitel, Prentice-Hall, 466 pp., 1980. Out of print, but a good reference if you can find a copy somewhere. I will hand out my class notes. This senior-graduate level course assumes familiarity with convolution, Fourier transforms, frequency- and time-domain aliasing, description of a filter by amplitude and phase, and other elementary concepts as introduced in Geophysics 4136 (Exploration Geophysics) or elsewhere.

Chapter 1 of Robinson and Treitel (1980, Geophysical Signal Analysis, E. A. Robinson and S. Treitel, Prentice-Hall, 466 pp., 1980 is a summary of seismic data acquisition and general objectives of reflection seismology; all of this is covered in Geophysics 4136 or 3104 (Elementary Geophysics) and will not be repeated in this course. They are not a prerequisite for this course if an appropriate background has been obtained elsewhere.

For those in the class not familiar with geophysical data, I will introduce real seismic data into the course at every opportunity. Reflection seismology appears to be the best geophysical technique to examine the internal geometry of the Earth's crust and upper mantle to depths of at least 50 km. It is therefore essential to complement tectonic studies. High resolution reflection seismology can be effectively used to map and evaluate the extent of coal resources. We will discuss these topics as case histories.

This course is mostly about the mathematical properties of the seismic wavelet and the process of inverse filtering ("deconvolution") that leads to increased seismic resolution in the time domain.Migration is also a deconvolution, but in the space domain as well as the time domain. Migration is covered in detail in Geophysics 5134 taught by Dr. Çoruh.

One of the major problems in reflection seismology is to determine the shape of the reflected seismic wavelet so that its time duration can be shortened. This will result in increased resolution and therefore a better geologic interpretation. Obviously, this concept has application in fields other than geology and geophysics such as the detection of cracks within materials of various sorts, seismic and medical tomography, foundation design in engineering applications, evaluation of the thicknesses of aquifers, etc.

Much information can be learned about the physical properties of the Earth by studying the shape of the seismic wavelet. The conventional stacking procedure for common-depth-point seismic data would be considerably improved if the shape of the wavelet as recorded on near-offset traces were the same as that recorded on far-offset traces. It is not, and one of the reasons is intrinsic damping and the attenuation of the higher seismic frequencies with respect to the lower frequencies. Results of one of my former Ph.D. students, Berkan Ecevitoglu, on the effect of intrinsic damping on the shape of the seismic wavelet will be shown. We will examine absorption-dispersion pairs and Ecevitoglu's results showing the time-domain consequences of attenuation that is linear or proportional to some arbitrary power of the frequency. The Hilbert transform plays a critical role in this regard. Much of the literature appears to handle this controversial problem in a perhaps overly complicated way; we will attempt to reduce it to essential concepts.

The laboratory deals primarily with the implementation on the digital computer of the theory covered in class; it is therefore essential that you have a good background in FORTRAN programming before enrolling in this course. Some of the FORTRAN programs used in this course will be given to you; others you will write yourself.

All FORTRAN programs and/or subroutines that you won't have to write yourself are on Userid G5140 on VM1. No read password is necessary. You can examine these at any time (LDISK G5140). Each member of the class will have his/her own Userid and password.

The general philosophy of the course is to understand better the geophysical applications of filter theory by using computer programs, some of which you write yourself, to analyze real and synthetic geophysical seismic data.

The course will be useful to all geologists, geophysicists, electrical engineers and groundwater hydrologists who must make geologic interpretations of reflection seismic data, and who need to know what effects mathematical analyses of the data might have on a geologic interpretation of data from the Earth's crust, from an oil field, or from an engineering application where reflection seismic data might have been used in a foundation study, for example.



A Journal will be required for the homework problems that are done on the computer. The Journal should contain:

Your grade for the laboratory will have for its basis:

Walk in and see me any time, even if the door is closed. It is not locked if I am in my office. My office is in room 1050 Derring Hall., telephone: 231-8912.

Schedule of Due-dates for Journal Problems
Problem Problem name Due date
0 Introduction to Virginia Tech computing facilities.
Assignment of computer account numbers.
How to log on. How to run a Fortran program.
SLFTEACH (Editing, etc.). Spelling checker.
CMS EXEC programs. BATCH mode.
1aPlot of roots in the z-planeFriday, January 26, 1996
1b Frequency response of dipolesFriday, February 2, 1996
1c Generation of seismic waveletsFriday, February 9, 1996
1d Finding roots of seismic waveletsFriday, February 16, 1996
1eInverse filtering of dipolesFriday, February 23, 1996
1fInverse filtering of wavelets and seismic trace
using z-transforms
Friday, March 1, 1996
1gInverse filtering of the same wavelets and
the same seismic trace
using Fourier theory
Friday, March 8, 1996
1hWavelet shaping with z-transforms and Fourier theoryFriday, March 29, 1996
2The 2- and 3-point water-layer filter
3An Introduction to Subroutine EUREKAFriday, April 5, 1996
4Predictive DeconvolutionFriday, April 12, 1996
5Predictive Deconvolution of the Maine Seismic DataFriday, April 19, 1996
6Hilbert transforms Friday, April 26, 1996