GEOL 706 - Geophysical Series, Filtering, and Introduction to Imaging

Course Outline

Instructor: J. Louie, 217 LME, 784-4219

louie@seismo.unr.edu

Fall, 2012

Learning Objectives: This course gives the fundamentals of time-series analysis for physical scientists, and then goes on with acoustic imaging examples to give the student practical experience in implementing these fundamentals. This is the first course of two at the graduate level in seismic imaging at the University of Nevada. The second course is Geol 757 Advanced Seismic Imaging and Tomography. Further objectives from Claerbout (1985):
``As it happens, waves are marvelously geometrical objects, and much can be learned with little mathematical analysis. But you should begin the book having previous familiarity with calculus, complex exponentials, and Fourier transformation.

``Your knowledge won't be complete if you don't know some opinions as well as the facts. You will be getting opinions as well as facts when I explain the discrepancies between theory and industrial practice, and when I explain what should work but doesn't seem to.

``Prospecting for oil begins with seismic soundings. The echoes are processed by computer into images that reveal much geological history. Worldwide, echo sounding and image making constitute about a four-billion-dollar-per-year activity.

``... the skills developed in this book, computer implementations of concepts from physics, will always be of general utility.''
Lectures Mondays, Wednesdays, and Fridays from 11:00 to 11:50 in room 415 of the Laxalt Mineral Engineering (LME) building. Lecture notes are on-line in PDF at:
http://crack.seismo.unr.edu/ftp/pub/louie/class/706/lectures/
Recorded lectures are on-line in M4V format at:
http://crack.seismo.unr.edu/ftp/pub/louie/class/706/recordings/

Lab solution sets are available as encrypted PDF files at http://crack.seismo.unr.edu/ftp/pub/louie/class/706/solutions/. When you turn in a lab, I will give you the password that unlocks the solution set.

Grading: Labs and Discussions 100%.
I encourage any student needing to request accommodations for a specific disability to please meet with me at your earliest convenience to ensure timely and appropriate accommodations.

Part I: Geophysical Time Series Analysis

Introduction and Review Time Series Domains, Models Sampling, Z Transform Fourier Sums, Spectra Correlations Discrete Fourier Transform Nyquist, Comb Function Slow FT, Symmetries Fast FT, Doubling Lab 1 Z-transforms and spectra
Quasi-Analytic Analyses The Z Plane Integration, Smoothing Causality, Oscillation Rational Filters, Instability Minimum Phase, Classification Lab 2 Spectra and the Z-plane Filter Design Hilbert Transform, Analytic Signal Instantaneous Attributes Spectral Factorization, Causality Butterworth Filters Phase and Group Delay Lab 3 Minimum phase Resolution and Variance Uncertainty Principles Expectation, Tradeoffs Crosscorrelation, Coherence Central Limit Theorem Lab 4 Resolution and noise

Part II: Introduction to Seismic Imaging

Introduction

Background of seismic imaging

Geophysical Exploration for Geothermal Resources: Advanced Seismic Technology Sept. 2007 workshop presentation for the Geothermal Resources Council conference.
PDFs of examples of imaging research to 2001
A national seismic imaging project - Earthscope and USArray
What is Seismic Migration?

Reproducibility of "noise"
Simplifying assumptions
Lab 5: Java applications

Zero-Offset Methods

Multiplicity and stacking
Exploding reflector model
Extrapolation and imaging
Migration

Impulse response and superposition
Hand migration
Dispersion relation for acoustic WE
Downward continuation (image of 3-d examp.)
2-d Fourier transforms
Phase-shift (Gazdag) migration
F-K (Stolt) migration
Lab 6: 2-d FFTs and migration

Physical and geological factors

Accuracy of seismic experiments
Property variation and the acoustic WE
Evanescent energy

Paraxial wave equation

Fourier derivation
Planewave derivation
Parabolic WE
15, 45, and 60 degree extrapolators
Retarded coordinates
Thin lens term, time & depth migrations

Finite differencing

Explicit methods
Implicit methods
Tridiagonal systems
Stability
Lab 7: Finite differencing
Time-domain extrapolation
Absorbing boundaries

Perspective on extrapolation
Lab 8: Monochrome wave extrapolation
Dip filters
Splitting and full separation

3-d migration
Thin-lens term

Lab 9: Time-domain downward continuation

Texts:

Jon Claerbout, 1992, Earth Soundings Analysis: Processing versus Inversion (PVI), Blackwell, ISBN #0-86542-210-9, out of print. Available from the instructor and in the DeLaMare Library. Read the text on-line at Stanford. Here is a 4 Mb PDF version built by the author in 2006.
Jon Claerbout, 1985, Imaging the Earth's Interior (IEI), Blackwell, ISBN #0-86542-304-0, out of print. Available from the instructor and in the DeLaMare Library. Read it on-line at Stanford; or download your own copy in PDF format, in parts through pages: 50; 100; 150; 200; 250; 300; 350; 400 (up to 1.7 Mb each).
Jon Claerbout, 1999, Geophysical Estimation By Example (GEE), Free. Available only on-line from Stanford; some sections in in a directory of PDF files on the Seismo server.

The lecture notes will be available prior to each lecture for you to copy.

The course will give 9 lab assignments of one or two weeks duration each, during the semester. The Labs will include both take-home problem sets and exercises with applications that will help you understand the transforms and domains. You will receive a class account for the Seismology server system for lab and project use; but exercises can be completed at home if you obtain Java compilers. All students are encouraged to work together on the lab exercises, but each student must turn in his or her own work.

All of the codes presented in the texts are accessible on-line from the Stanford Exploration Project. We also have local copies of: codes from PVI; codes from GEE; and HTML documentation on SEPlib.

Here is a list of and access to the 9 Lab assignments:

Lab 1 Z-transforms and spectra

Lab 2 Spectra and the Z-plane

Lab 3 Minimum phase

Lab 4 Resolution and noise

Lab 5 Java applications

Lab 6 2-d FFTs and migration

Lab 7 Finite differencing

Lab 8 Monochrome wave extrapolation

Lab 9 Time-domain downward continuation

No project is required for 706; Geol 757 Advanced Seismic Imaging and Tomography will require two term projects.

Course Schedule

We ought to have 45, 50-minute-long leture sessions during the semester. What with holidays and all the technical meetings we will be going to, only 31 of our regular MWF lecture periods are available. So we are scheduling lecture on every Mon., Tues., Weds., and Thurs. available (not Fridays due to Wesnousky's class), for 43 sessions total.

Monday		August 27	Organization and first lecture
				(regular time and room: 11:00-11:50 in LME 415; unless noted below)
Tuesday		August 28	Lecture 11:00-11:50 in LMR 415
Wednesday	August 29	Lecture 11:00-11:50 in LMR 415
Thursday	August 30	Lecture 11:00-11:50 in LMR 415
Monday		September 3	No lecture (Labor Day)
Tuesday		September 4	Lecture 11:00-11:50 in LMR 415
Wednesday	September 5	Lecture 11:00-11:50 in LMR 415
Thursday	September 6	Lecture 11:00-11:50 in LMR 415
Mon.-Weds.	Sept. 10-12	No lecture (SCEC Meeting)
Thursday	September 13	Lecture 11:00-11:50 in LMR 415
Monday		September 17	No lecture (Instructor's Holiday)
Tuesday		September 18	Lecture 11:00-11:50 in LMR 415
Wednesday	September 19	Lecture 11:00-11:50 in LMR 415; Lab 1 DUE (2 weeks effort)
Thursday	September 20	Lecture 11:00-11:50 in LMR 415
Monday		September 24	Lecture 11:00-11:50 in LMR 415
Tuesday		September 25	Lecture 11:00-11:50 in LMR 415
Wednesday	September 26	No lecture (Instructor's Holiday)
Thursday	September 27	Lecture 11:00-11:50 in LMR 415
Monday		October 1	Lecture 11:00-11:50 in LMR 415
Tuesday		October 2	Lecture 11:00-11:50 in LMR 415
Wednesday	October 3	Lecture 11:00-11:50 in LMR 415
Thursday	October 4	Lecture 11:00-11:50 in LMR 415
Monday		October 8	Lecture 11:00-11:50 in LMR 415; Lab 2 DUE (2 weeks effort)
Tuesday		October 9	Lecture 11:00-11:50 in LMR 415
Wednesday	October 10	Lecture 11:00-11:50 in LMR 415
Thursday	October 11	Lecture 11:00-11:50 in LMR 415
Monday		October 15	Lecture 11:00-11:50 in LMR 415
Tuesday		October 16	Lecture 11:00-11:50 in LMR 415
Wednesday	October 17	Lecture 11:00-11:50 in LMR 415
Thursday	October 18	Lecture 11:00-11:50 in LMR 415
Mon.-Tues.	Oct. 22-23	ExxonMobil recruiter John Foudy's visit: please sign up to interview
Monday		October 22	Lecture 11:00-11:50 in LMR 415; Lab 3 DUE (2 weeks effort)
Tuesday		October 23	Lecture 11:00-11:50 in LMR 415
Wednesday	October 24	Lecture 11:00-11:50 in LMR 415
Thursday	October 25	Lecture 11:00-11:50 in LMR 415
Friday		October 26	No lecture (Nevada Day)
Monday		October 29	No lecture (Instructor at NSF workshop)
Tuesday		October 30	No lecture (Instructor at NSF workshop)
Wednesday	October 31	Lecture 11:00-11:50 in LMR 415
Thursday	November 1	Lecture 11:00-11:50 in LMR 415; Lab 4 DUE (1 week effort); Complete Lab 5 (not graded)
Mon.-Fri.	November 4-9	No lecture (SEG Meeting). Each student chooses a session to attend and report on.
Monday		November 12	No lecture (Veterans Day)
Tuesday		November 13	Lecture 11:00-11:50 in LMR 415
Wednesday	November 14	Lecture 11:00-11:50 in LMR 415
Thursday	November 15	Lecture 11:00-11:50 in LMR 415; Lab 6 DUE (2 weeks effort)
Monday		November 19	Lecture 11:00-11:50 in LMR 415
Tuesday		November 20	Lecture 11:00-11:50 in LMR 415
Wednesday	November 21	Lecture 11:00-11:50 in LMR 415
Thurs.-Fri.	Nov. 22-23	No lecture (Thanksgiving Holiday)
Monday		November 26	Lecture 11:00-11:50 in LMR 415; Lab 7 DUE (1 week effort)
Tuesday		November 27	Lecture 11:00-11:50 in LMR 415
Wednesday	November 28	Lecture 11:00-11:50 in LMR 415
Thursday	November 29	Lecture 11:00-11:50 in LMR 415; Lab 6 DUE (2 weeks effort)
Mon.-Fri.	December 3-7	No lecture (AGU Meeting)
Monday		December 10	Lecture 11:00-11:50 in LMR 415
Tuesday		December 11	Lecture 11:00-11:50 in LMR 415; Lab 8 DUE (2 weeks effort); last lecture period.
Wednesday	December 19	Lab 9 DUE (1 week effort)

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