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Basic Geophysics Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 GEOPHYSICAL MONOGRAPH SERIES NUMBER 22 BASIC GEOPHYSICS Enders A. Robinson Dean Clark with a foreword by managing and volume editor Tijmen Jan Moser SM Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 ISBN 978-0-931830-56-3 (Series) ISBN 978-1-56080-345-4 (Volume) Library of Congress Control Number: 2017952740 Society of Exploration Geophysicists 8801 S. Yale Ave., Ste. 500 Tulsa, OK 74137-3575 # 2017 by Society of Exploration Geophysicists All rights reserved. This book or parts hereof may not be reproduced in any form without written permission from the publisher. Published 2017 Printed in the United States of America Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 This book is dedicated to Gregory W. Randolph, M.D. The Claire and John Bertucci Endowed Chair at Harvard Medical School, Massachusetts Eye and Ear Infirmary, and Massachusetts General Hospital and Giuseppe Barbesino, M.D. Massachusetts General Hospital Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 This page has been intentionally left blank Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 ISCO-front.indd 4 9/21/2016 9:48:29 AM Contents Preface ................................................vii Foreword............................................... xi About the Authors ...................................... xix Chapter 1: Classical Geophysics .............................1 Pythagoras and Archimedes . ........................ 1 Heron and Snell .................................. 12 Descartes as a geophysicist. ....................... 22 Fermat and the principle of least time . ................. 35 Huygens’ principle . ............................. 43 Isaac Newton and the birth of geophysics . ............ 59 Chapter 2: Wave Equation.................................81 Seismic ray direction . ............................. 81 The eikonal equation and Pythagoras . ................. 88 Michael Faraday and the eikonal equation . ............ 92 Pressure and particle velocity . ..................... 100 Chapter 3: Elasticity.....................................131 The wave equation . ............................ 131 A wave at a boundary. ............................ 135 Stress and strain ................................. 146 Hooke’s law . .................................. 155 Cartesian fields of dilatation . ...................... 161 Cartesian fields of rotation . ...................... 175 Equations of motion . ............................ 187 Chapter 4: Rays, Anisotropy, and Maxwell’s Equations.........203 Ray equation . .................................. 203 Discovery of anisotropy ........................... 212 Maxwell’s equations. ............................ 224 v Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 vi Basic Geophysics Chapter 5: Three-dimensional Wave Equation ................227 Wave equation .................................. 227 One-dimensional wave equation ..................... 229 Sinusoidal waves ................................ 231 Plane waves . .................................. 234 Spherical waves ................................. 238 Green’s function................................. 243 Dispersion equation . ............................ 251 Group velocity .................................. 253 Chapter 6: Ray Tracing and Seismic Modeling................261 Hamilton’s equations . ............................ 261 Ray tracing. .................................. 268 Eikonal equation................................. 274 Ray equations. .................................. 277 Reduction of Hamilton’s equations to the ray equations . 279 Numerical ray tracing . ............................ 281 Chapter 7: Reflection, Refraction, and Diffraction .............285 Explanation of terms. ............................ 285 Huygens’ principle . ............................ 287 Reflection and refraction........................... 294 Fermat’s principle. ............................ 295 Resolution and the Fresnel zone ..................... 299 Diffraction . .................................. 302 Diffraction curves................................ 305 Diffractions appearing on seismic sections . .......... 316 Chapter 8: Migration by the WKBJ Method..................321 Geometrical optics and physical optics ................ 321 Exploding reflectors model . ...................... 326 Migration ...................................... 328 Wave depropagation simplified...................... 331 Time migration.................................. 337 WKBJ migration ................................ 343 References.............................................351 Index .................................................355 Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 Preface Come forth into the light of things Let Nature be your teacher. — William Wordsworth (1770 – 1850) Chapters 1 through 4 in this book are composed of articles published by the authors in the journal of the Society of Exploration Geophysicists, The Leading Edge (TLE). Chapters 5 through 8 are taken from their unpublished manuscript, Waves of Discovery. James T. Robertson, member of the TLE Editorial Board, writes, “The intent is to cogently present the body of seismic theory that underlies modern exploration seismology in a format that transfers understanding to the audience. Some readers will be very fam- iliar with many of the topics; others will be expert in only a few. I suspect that most of us ought to know more about these subjects than we really do. If each reader can find an insight or two that were not previously appreci- ated, this book would accomplish its purpose.” An important mode of thinking is visual thinking. Visualization is especially useful in solving problems where shapes, forms, or patterns are concerned. Visual thinking is used constantly by geophysicists, from the layout of a seismic survey to the final interpretation. Geophysicists use visual imagery in the analysis of seismic data and in the synthesis of the structure of the underground earth. They are called upon to exercise an acute sense of visual perception in the production of intricate sequences of images. This process ultimately holds the key to unlocking the secrets of the heterogeneities of the solid earth. Geophysicists also must make use of conceptualization in those instances when the desired results are not at all obvious. Three kinds of visual imagery are necessary for effective visual think- ing: (1) perceptual imagery, (2) mental imagery, and (3) graphic imagery. The first, perceptual imagery, is sensory experience of the physical world. It is what you see with your eyes and record in your brain. You do not record everything you observe. One reason is an over-saturation of input. People tend to see better those things which are more important, or more unusual, or more easily-recorded. The second, mental imagery, is constructed in the mind and utilizes stored information recorded from perceptual imagery. Mental imagery is important when you examine the computer-generated images formed from actual seismic data. The clarity of mental images depends upon several factors. First, it depends on seeing the perceived geological vii Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3996512/frontmatter.pdf by guest on 26 September 2021 viii Basic Geophysics objects. Second, it depends upon the image-reproduction mechanism in the brain. There are individual variations in the ability to imagine things visu- ally, as there is always a range of answers. Try visualizing a series of seismic objects and see if you can determine a pattern in your own imaging ability. Visual images can be consciously enhanced. Are you better at visualizing two-dimensional objects than three-dimensional? Are you better at small structures than large ones? Where do you see the image, in front of your eyes or deep in your mind? Visual imaging ability depends not only on the ability to form images, but also upon the supply of pertinent imagery that is stored in the mind. The third, graphic imagery, is the art of constructing physical images in order to convey specific information. To take advantage of visual thinking ability, this third type of visualization is necessary. Compu- ter graphics allows the recording, storage, manipulation, and communi- cation of images to fill the pictures generated in the imagination. Graphic imagery falls into two categories. One category includes pictures formed to communicate with others, and the other category pictures made for oneself. Leonardo da Vinci was one of the greatest masters of the art of graphic imagery and his mythic stature is well deserved. Some 4000 pages of his drawings and writings survive, which included a vast array of subjects such as anatomy, inventions, landscapes, mythology, and cartography. An essential paradox of his drawings was that they portray nature more closely than had ever been done before, yet every part of them seems to be infused with all of the baffling eccentricities of Leonardo. In contrast
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