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Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Classical and Modern Diffraction Theory Edited by Kamill Klem-Musatov Henning C. Hoeber Tijmen Jan Moser Michael A. Pelissier SEG Geophysics Reprint Series No. 29 Sergey Fomel, managing editor Evgeny Landa, volume editor Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Society of Exploration Geophysicists 8801 S. Yale, Ste. 500 Tulsa, OK 74137-3575 U.S.A. # 2016 by Society of Exploration Geophysicists All rights reserved. This book or parts hereof may not be reproduced in any form without permission in writing from the publisher. Published 2016 Printed in the United States of America ISBN 978-1-931830-00-6 (Series) ISBN 978-1-56080-322-5 (Volume) Library of Congress Control Number: 2015951229 Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Dedication We dedicate this volume to the memory Dr. Kamill Klem-Musatov. In reading this volume, you will find that the history of diffraction We worked with Kamill over a period of several years to compile theory was filled with many controversies and feuds as new theories this volume. This volume was virtually ready for publication when came to displace or revise previous ones. Kamill Klem-Musatov’s Kamill passed away. He is greatly missed. new theory also met opposition; he paid a great personal price in Kamill’s role in Classical and Modern Diffraction Theory goes putting forth his theory for the seismic diffraction forward problem. far beyond that of co-editor. He was a pioneer of the extension of To model diffractions in the subsurface, he extended the diffraction modern diffraction theory of edge and tip waves to the seismic theory to take semi-transparent edges into account. For a number of method. His formulation of the seismic diffraction forward and years, this approach, a departure from the theory based on non-trans- inverse problems brought a new discipline to geophysics, one we parent edges, met strong opposition and criticism. might call the seismic diffraction method. In many ways, the Working with Kamill was a great honor and privilege for us. In purpose of Classical and Modern Diffraction Theory is to communi- remembering Kamill, a quote from Newton comes to mind “If I cate the theoretical foundations and their historical context to the geo- have seen further, it is by standing on the shoulders of giants.” physical community, for it is upon this foundation that Kamill based the seismic diffraction method. H. Hoeber, T. J. Moser, M. Pelissier Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 This page has been intentionally left blank Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Table of Contents About the Editors ......................................................................................... vii Preface .................................................................................................... ix Acknowledgments .......................................................................................... xi Chapter 1: Overview . 1 The Fresnel diffraction phenomena ........................................................................ 3 W. Arkadiew The geometrical theory of diffraction ..................................................................... 13 J. B. Keller Diffraction theory ........................................................................................ 17 C. J. Bouwkamp Developments in our concepts of diffraction phenomena (on the 130th anniversary of the death of Thomas Young) ................................................................................... 57 G. D. Malyuzhinets Rays, waves and asymptotics ............................................................................. 67 J. B. Keller Rubinowicz and the modern theory of diffracted rays .................................................... 81 P. Ya. Ufimtsev Chapter 2: Early Developments in Diffraction Theory . 89 Translation editor’s introduction ........................................................................ 107 K. Helbig A physico-mathematical treatise on light, colors and the rainbow, Proposition 1 ........................... 108 F. M. Grimaldi Treatise on light, Chapter 1: On the rectilinear propagation of rays ...................................... 117 C. Huygens The Bakerian lecture: Experiments and calculations relative to physical optics ............................ 123 T. Young Chapter 3: The Classical Mathematical Theory of Diffraction . 129 Memoir on the diffraction of light ....................................................................... 147 A. Fresnel An essay on the application of mathematical analysis to the theories of electricity and magnetism ........................................................................... 177 G. Green Theory of air vibration in pipes with open ends .......................................................... 187 H. Helmholtz Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 vi Classical and Modern Diffraction Theory On the ray theory of light ............................................................................... 191 G. Kirchhoff On the passage of waves through apertures in plane screens, and allied problems ......................... 205 Lord Rayleigh (J. W. Strutt) Chapter 4: Foundations of Modern Diffraction Theory . 213 Reciprocal diffraction relations between circular and elliptical plates ..................................... 217 J. Coulson and G. G. Becknell An extension of the principle of the diffraction evolute, and some of its structural detail ................... 223 G. G. Becknell and J. Coulson An asymptotic treatment of diffraction problems ......................................................... 227 N. G. Van Kampen Boundary layer problems in diffraction theory ........................................................... 235 R. N. Buchal and J. B. Keller Geometrical theory of diffraction ........................................................................ 251 J. B. Keller A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface ................. 267 R. G. Kouyoumjian and P. H. Pathak The ray method and the theory of edge waves ............................................................ 283 K. D. Klem-Musatov and A. M. Aizenberg Resolution and super-resolution in inverse diffraction ................................................... 293 M. Bertero, P. Boccacci, and M. Piana Appendix A: The Cornu Spiral ........................................................................ 303 New method for the discussion of diffraction problems in the case of a cylindrical wave ............... 305 M. A. Cornu Appendix B: Babinet’s Principle ....................................................................... 315 Memoirs on meteorological optics ................................................................... 317 M. Babinet The London and Edinburgh Philosophical Magazine and Journal of Science .......................... 319 A. Necker References: Reprinted Technical Papers ................................................................. 323 References: General ..................................................................................... 325 Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 About the Editors After the defense of his candidate dissertation on mathemat- ical physics (Ph.D. equivalent), Kamill joined the Institute of Pet- roleum Geology and Geophysics (Novosibirsk Scientific Centre, Siberian Branch, Russian Academy of Sciences, Russian Federa- tion) in 1968 and worked there for 47 academic years, until his last working day. For the first 12 academic years, Kamill’s scientific interests were devoted to a 2D canonical forward problem: wave diffraction in a sec- torial acoustic/elastic medium with one common sharp edge and several plane interfaces. He was one of the first scientists who obtained a rigorous solution of the difficult forward problem using the Sommer- feld-Malyuzhinets technique improved by him to semitransparent interfaces. He published a series of articles on this topic in Russian scientific journals. Among them, three results were the most valuable. The first of these is a justification of the edge-diffraction law: “amplitude of acoustic, elastic, electromagnetic and other edge Kamill D. Klem-Musatov, 1930–2015 waves inside the boundary layer (vicinity of shadow boundary) can be described by the universal special function W(w).” The second “All unknown and complex is hidden in the well-known and simple.” result is verification of this law by physical (laboratory) modeling. Using the above two results, Kamill and his pupil Evgeny Landa — Kamill D. Klem-Musatov introduced a theoretical criterion of detecting small-throw faults. Kamill summarized this period in his first monograph, Theory of On the morning of 18 June 2015, Professor Kamill D. Klem-Musatov, Edge Waves and its Application in Seismic (1980, in Russian). In doctor of science in mathematical physics, passed away at the age of 1980, he defended his doctoral dissertation based on the monograph 85
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