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 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 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 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.

- Examination I - 17%
- Examination II - 17%
- Examination III - 17%
- Journal - 25 %
- Final Examination - 24%

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

- A typewritten discussion (a few pages) of the theory behind the problem, and how the computer program solves the problem. The discussion of your computer program should make it clear that you understand how the FORTRAN code is used to implement the theory. Where appropriate, include references to outside reading material in your discussion. Please! Do your own programming; however, discussion of the problems and comparison of results with your colleagues (preferably those who are now taking the course. Those who took it in previous years are now pretty busy doing other things) is encouraged.
- Complete computer listings of all programs and subroutines used to solve each problem.
- Use SCRIPT on the mainframe or KEDIT on your PC. Print the reports on the 3812 page printer. Do not piece together parts of programs that worked with parts that did not. Each listing should be complete and correct, showing the program and output as received from a single run.
- Answers in the form of computer output listings and/or Page segment plots from the 3812 page printer.
- It is not necessary to include class notes or handouts in the Journal.

Your grade for the laboratory will have for its basis:

- The quality of the Journal, including the accuracy of your answers and the organization and completeness of your discussions.
- Spelling. Check your spelling on the computer using PROOF SPELL while in XEDIT mode.One point will be deducted for each spelling error. Please note that Fourier is capitalized.
- Punctuality. For each Journal problem that is handed in late, points will be deducted at a rate of one (1) point/hour. Journals should be handed in to me at the beginning of the regular lecture period on the day they are due. If you turn in a problem late, please give it to me.

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. | |

1a | Plot of roots in the z-plane | Friday, January 26, 1996 |

1b | Frequency response of dipoles | Friday, February 2, 1996 |

1c | Generation of seismic wavelets | Friday, February 9, 1996 |

1d | Finding roots of seismic wavelets | Friday, February 16, 1996 |

1e | Inverse filtering of dipoles | Friday, February 23, 1996 |

1f | Inverse filtering
of wavelets and seismic trace using z-transforms | Friday, March 1, 1996 |

1g | Inverse filtering
of the same wavelets and the same seismic trace using Fourier theory | Friday, March 8, 1996 |

1h | Wavelet shaping with z-transforms and Fourier theory | Friday, March 29, 1996 |

2 | The 2- and 3-point water-layer filter | |

3 | An Introduction to Subroutine EUREKA | Friday, April 5, 1996 |

4 | Predictive Deconvolution | Friday, April 12, 1996 |

5 | Predictive Deconvolution of the Maine Seismic Data | Friday, April 19, 1996 |

6 | Hilbert transforms | Friday, April 26, 1996 |