Volume 7, No. 8 August 1996

CREWES News

The Consortium for Research in Elastic Wave Exploration Seismology

Fall Course in Seismic Data Processing

This course is offered as Geophysics 557/657 (undergrad or grad) through the Department of Geology and Geophysics at the University of Calgary. Subjects to be covered include: statics, filtering in various domains (f-k, t-p, etc.), deconvolution, velocity analysis, NMO correction, AVO analysis,wavelet processing, migration, inversion, seismic attributes, and 3-C analysis. All subjects will be considered for both 2-D and 3-D geometries. Assignments will emphasize real data processing problems and lab exercises will involve processing real 2-D and 3-D datasets with ProMAX. For more information on this and other geophysics courses at the U of C, see the last part of this newsletter.


1996 Sponsors Meeting - November 3 to 5

We will be holding our Annual Sponsors Meeting at the Lodge at Kananaskis again this year. The Lodge is located 90 kms west of Calgary in the spectacular Rocky Mountains. There are excellent recreational facilities to enjoy in the evenings. The format for the meeting will be similar to that of previous years, with registration on the Sunday evening (Nov. 3) and presentations on the Monday and Tuesday. Additional information will be included in a future newsletter. We look forward to seeing you!


Personel

Cheers to Helen Isaac, who successfully defended her Ph.D. in Geophysics this summer. Helen, under the supervision of Dr. Don Lawton, studied seismic methods for heavy oil reservoir monitoring using time-lapse 3-D and 3C-2D seismic data sets. Helen will be working with the Foothills Research Project as a Research Geophysicist starting in September.

The Fall semester is about to begin and we are looking forward to welcoming 11 new students into the graduate program in Geophysics this year. Many of the new students will be working in the CREWES Project and we'll be letting you know more about them in September.


Theory of nonstationary linear filtering in the Fourier domain

by Gary F. Margrave

I have developed a general linear theory which describes the extension of the convolutional method to nonstationary processes and then have recast the theory in the Fourier domain. The result is a mathematical method which can apply an arbitrary nonstationary filter (i.e. any amplitude and phase spectra with any temporal variation) in the time domain, the Fourier domain, or either of two possible mixed time-frequency domains. The key to the theory is the reformulation of the convolution integral such that it still corresponds to a scaled superposition but allows the filter waveform to change arbitrarily with time.

Box A in the figure shows the matrix form of stationary convolution for the case of a minimum phase wavelet being convolved with a reflectivity to produce a seismogram. The convolution matrix is built by placing the wavelet in each column, delayed such that its start time is on the main matrix diagonal. Convolutional processes are said to be stationary because the wavelet is the same in all columns.

In Box B is the matrix representation of the nonstationary generalization of convolution for the case of a forward Q filter being applied to a reflectivity to produce an attenuated seismogram. The nonstationary convolution matrix shows a wavelet in each column which changes systematically with time.

Stationary filters can be applied in the Fourier transform domain by simply multiplying their spectra. This is shown in box C for the case of the wavelet in box A. When the nonstationary formalism is moved into the Fourier domain, the result is also a matrix multiplication as shown in box D. The nonstationary spectral matrix is formed from the 2-D Fourier transform of the nonstationary convolution matrix in B. It operates on the spectrum of the input trace to produce the spectrum of the output trace. The strength of the off-diagonal energy is directly related to the degree of nonstationarity. As the waveform becomes stationary, the matrix in D becomes a diagonal matrix with the filter spectrum along the diagonal and the result is the simple multiplication of wavelet and reflectivity spectra, as was the case for box C. The nonstationary filter can be applied efficiently in the Fourier domain by keeping only the significant off-diagonal terms.

There are many potential applications of this theory including seismic modeling, time variant filtering, time variant deconvolution, and depth migration. I will present the complete theory at the 1996 annual CREWES meeting and will continue to explore its applications in the coming year. Anyone desiring more information can contact me via email at: gary@geo.ucalgary.ca or phone (403)-220-4606.

For these matrices, black represents a large positive number, white a large negative, and medium gray is zero.

StationaryNonstationary

Above figure for browsers which don't support tables
View close-up versions of box A | box B | box C | box D


Geophysics Courses at the U of C

Keep your mind sharp and your knowledge up to date by enrolling in a geophysics course at the U of C. These are credit courses which can be applied towards the course-based M.Sc. degree in Geophysics. For registration information, please contact Ms. Marg Graham, Department of Geology and Geophysics (220-5841). Graduate courses have 600 or 700 number.
*These courses have a 3 hour per week laboratory component.

FALL 1996:

CourseTitleTimeProfessor(s)
GOPH 355Exploration GeophysicsLEC MWF 15:00*J.C. Bancroft
GOPH 365Environmental GeophysicsLEC MW 16:00*Duckworth, Krebes
GOPH 453Mining Geophysics ILEC MWF 10:00*K. Duckworth
GOPH 553Mining Geophysics IILEC MWF 14:00*K. Duckworth
GOPH 557/657Geophysical Data ProcessingLEC T 17:00*G.F. Margrave
GOPH 645Seismic Wave PropagationLEC MWF TBAE.S. Krebes
GOPH 653Electromagnetics & Potential Field MethodsLEC MWF 14:00K. Duckworth
GOPH 701Advanced Independent StudyD.C. Lawton
GOPH 703Readings in GeophysicsD.C. Lawton

WINTER 1997:

CourseTitle Time Professor(s)
GOPH 359 Global Geophysics LEC MWF 15:00* E.S. Krebes
GOPH 375 Natural Disasters LEC MWF 10:00 R.R. Stewart
GOPH 457 Physical Properties of Rocks LEC MWF 14:00* P.P.C. Wu
GOPH 547 Gravity and Magnetics LEC MWF 13:00* P.P.C. Wu
GOPH 551 Seismic Theory & Methods LEC MWF 10:00* P.P.C. Wu
GOPH 559 Geophysical Interpretation LEC MWF 15:00* Cook, Lawton
GOPH 647 Advanced Digital Signal Processing
(Advanced Applied Geophysics)
TBA * G.F. Margrave

Making Contact...

The CREWES Project
Dept. of Geology & Geophysics
University of Calgary
2500 University Dr. N.W.
Calgary, Alberta
T2N 1N4 CANADA

Fax: (403)284-0074
Email: crewes@geo.ucalgary.ca
WWW (World Wide Web):
http://www.crewes.ucalgary.ca/

Administrative Secretary:
Louise Forgues: 220-8279
Editor: Sue Miller

Directors:
Dr. Robert Stewart: 220-3265
Dr. Don Lawton: 220-5718

Research Staff:
Dr. John Bancroft: 220-5026
Malcolm Bertram: 220-3267
Henry Bland: 220-8461
Darren Foltinek: 220-6137
Eric Gallant: 220-3259
Dr. Gary Margrave: 220-4606
Sue Miller: 220-7462
Colin Potter: 220-8012
Vladan Simin: 220-4292
Grace Yang: 220-8969
Qi Zhang: 220-3264

Graduate Students
Jill Belisle:220-3271
Siriporn Chaisri: 220-3083
Wai-Kin Chan: 220-8093
Maria Donati: 220-6444
Jocelyn Dufour: 220-8266
Ken Fang: 220-8093
Robert Ferguson: 220-3271
Helen Isaac: 220-8396
Glenn Larson: 220-3458
Xinxiang Li: 220-6749
Nicolas Martin: 220-3083
Darryl Parry: 220-3032
Chanpen Silawongsawat: 220-3083
Zandong Sun: 220-6444
Dan Vetrici: 220-3269
Shaowu Wang: 220-5027
Hans Westbroek: 220-6596