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Wave Propagation and Time Reversal in Randomly Layered Media

  • Textbook
  • © 2007

Overview

Authors:
  1. Jean-Pierre Fouque

    1. Department of Statistics and Applied Probability, University of California, Santa Barbara, USA

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  2. Josselin Garnier

    1. UFR de Mathématiques, Université Paris VII, 2 Place Jussieu, France

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  3. George Papanicolaou

    1. Mathematics Department, Stanford University, Stanford, USA

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  4. Knut Sølna

    1. Department of Mathemathics, University of California at Irvine, Irvine, USA

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  • Sections of notes where the authors give references and additional comments on the various results presented are included at the end of each chapter

Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 56)

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XX
    Download chapter PDF

  2. Introduction and Overview of the Book

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 1-8

  3. Waves in Homogeneous Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 9-31

  4. Waves in Layered Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 33-60

  5. Effective Properties of Randomly Layered Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 61-90

  6. Scaling Limits

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 91-107

  7. Asymptotics for Random Ordinary Differential Equations

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 109-174

  8. Transmission of Energy Through a Slab of Random Medium

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 175-213

  9. Wave-Front Propagation

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 215-248

  10. Statistics of Incoherent Waves

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 249-280

  11. Time Reversal in Reflection and Spectral Estimation

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 281-304

  12. Applications to Detection

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 305-326

  13. Time Reversal in Transmission

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 327-342

  14. Application to Communications

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 343-364

  15. Scattering by a Three-Dimensional Randomly Layered Medium

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 365-391

  16. Time Reversal in a Three-Dimensional Layered Medium

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 393-433

  17. Application to Echo-Mode Time Reversal

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 435-455

  18. Other Layered Media

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 457-486

  19. Other Regimes of Propagation

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 487-517

  20. The Random Schrödinger Model

    • Jean-Pierre Fouque, Josselin Garnier, George Papanicolaou, Knut Sølna
    Pages 519-544
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Keywords

About this book

Our motivation for writing this book is twofold: First, the theory of waves propagating in randomly layered media has been studied extensively during the last thirty years but the results are scattered in many di?erent papers. This theory is now in a mature state, especially in the very interesting regime of separation of scales as introduced by G. Papanicolaou and his coauthors and described in [8], which is a building block for this book. Second, we were motivatedbythe time-reversalexperimentsofM. Finkandhis groupinParis. They were done with ultrasonic waves and have attracted considerable att- tion because of the surprising e?ects of enhanced spatial focusing and time compression in random media. An exposition of this work and its appli- tions is presented in [56]. Time reversal experiments were also carried out with sonar arrays in shallow water by W. Kuperman [113] and his group in San Diego. The enhanced spatial focusing and time compression of signals in time reversal in randommedia have many diverse applications in detection and in focused energy delivery on small targets as, for example, in the - struction of kidney stones. Enhanced spatial focusing is also useful in sonar and wireless communications for reducing interference. Time reversal ideas have played an important role in the development of new methods for array imaging in random media as presented in [19].

Reviews

From the reviews:

"An up-to-date monograph written by highly regarded experts that presents in a modern way the generalities of the physics of randomly layered media and covers a broad range of applications has long been eagerly anticipated by mathematicians, physicists, and engineers. … I strongly recommend the book to graduate students and advanced researchers … . this is an excellent book which will be interesting, informative, and enjoyable for a wide circle of students, researchers, and engineers, demanding a place on their bookshelves." (Valentin Freilikher, Journal of Statistical Physics, Vol. 131, 2008)

"This excellent monograph … provides a masterful presentation of wave propagation in one-dimensional (layered) random media. … This book serve as an indispensable reference to any mathematician and scientist interested in the analysis of partial differential equations with random coefficients." (Guillaume Bal, Mathematical Reviews, Issue 2009 a)

"This book focuses … entirely on the case of classical, linear waves (e.g., acoustics) in randomly layered media. … I recommend this book highly to anyone interested in wave propagation in random media, or just asymptotic methods for stochastic differential equations. … this narrower focus provides necessary clarity to the mathematical presentation. … this book does an admirable job of presenting mathematicians with the fundamental analytical tools needed to study this subject." (Arnold D. Kim, SIAM Review, Vol. 51 (3), 2009)

Authors and Affiliations

  • Department of Statistics and Applied Probability, University of California, Santa Barbara, USA

    Jean-Pierre Fouque

  • UFR de Mathématiques, Université Paris VII, 2 Place Jussieu, France

    Josselin Garnier

  • Mathematics Department, Stanford University, Stanford, USA

    George Papanicolaou

  • Department of Mathemathics, University of California at Irvine, Irvine, USA

    Knut Sølna

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