Wave Propagation and Time Reversal in Randomly Layered Media / Edition 1

by Jean-Pierre Fouque, Josselin Garnier, G. Papanicolaou, Knut Solna

Overview

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 different 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 effects 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].

Product Details

ISBN-13:	9781441921628
Publisher:	Springer New York
Publication date:	11/24/2010
Series:	Stochastic Modelling and Applied Probability , #56
Edition description:	Softcover reprint of hardcover 1st ed. 2007
Pages:	612
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

and Overview of the Book.- Waves in Homogeneous Media.- Waves in Layered Media.- Effective Properties of Randomly Layered Media.- Scaling Limits.- Asymptotics for Random Ordinary Differential Equations.- Transmission of Energy Through a Slab of Random Medium.- Wave-Front Propagation.- Statistics of Incoherent Waves.- Time Reversal in Reflection and Spectral Estimation.- Applications to Detection.- Time Reversal in Transmission.- Application to Communications.- Scattering by a Three-Dimensional Randomly Layered Medium.- Time Reversal in a Three-Dimensional Layered Medium.- Application to Echo-Mode Time Reversal.- Other Layered Media.- Other Regimes of Propagation.- The Random Schrödinger Model.- Propagation in Random Waveguides.

Editorial 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 shastic 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)

From the Publisher