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PREFACE
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This book should provide a good mix of basic principles and current research topics. An introductory course in Monte Carlo simulations can cover most of s 1, 2, 4, 5, 7, and 9.
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Acknowledgments
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We would like to acknowledge the collaboration with our colleagues and graduate students. In particular, we wish to thank Professor Chi Chan of City University of Hong Kong, Professor Joel T. Johnson of Ohio State University, Dr. Robert T. Shin of MIT Lincoln Laboratory, and Dr. Dale Winebrenner of University of Washington. The graduate students who completed their Ph.D. theses from the University of \Vashington on random media scattering include Boheng Wen (1989), Kung-Hau Ding (1989), Shu-Hsiang Lou (1991), Charles E. Mandt (1992), Richard D. West (1994), Zhengxiao Chen (1994), Lisa M. Zurk (1995), Kyung Pak (1996), Guifu Zhang (1998), and Qin Li (2000). Much of their dissertation works are included in this book. Financial supports from the Air Force Office of Scientific Research, Army Research Office, National Aeronautics and Space Administration, National Science Foundation, Office of Naval Research, and Schlumberger-Doll Research Center for research materials included in this book are gratefully acknowledged. We also want to acknowledge the current UW graduate students who have helped to develop the numerical codes used throughout this book. These include Chi-Te Chen, Houfei Chen, Jianjun Guo, Chung-Chi Huang, and Lin Zhou. Special thanks are also due to Tomasz Grzegorczyk for proofreading on parts of the manuscript and Bae-Ian Wu for production assistance. Leung Tsang
Seattle, Washington
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Cambridge, Massachusetts Kung-Hau Ding Hanscom AFB, Massachusetts Chi On Ao Cambridge, Massachusetts February 2001
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SCATTERING OF ELECTROMAGNETIC WAVES
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Scattering of Electromagnetic Waves: Numerical Simulations. Leung Tsang, Jin Au Kong, Kung-Hau Ding, Chi On Ao. Copyright 2001 John Wiley & Sons, Inc. ISBNs: 0-471-38800-9 (Hardback); 0-471-22430-8 (Electronic)
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MONTE CARLO SIMULATIONS OF LAYERED MEDIA
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lOne-Dimensional Layered Media with Permittivity Fluctuations
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1.1 1.2 1.3 Continuous Random Medium Generation of One-Dimensional Continuous Gaussian Random Medium Numerical Results and Applications to Antarctica
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Random Discrete Layering and Applications References and Additional Readings
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1 MONTE CARLO SIMULATIONS OF LAYERED MEDIA
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lOne-Dimensional Layered Media with Permittivity Fluctuations
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We study Monte Carlo simulations of solutions of the Maxwell equations in Volume II. The simplest case of random medium is one where the permittivity is a random function of positions in a one-dimensional problem. In Fig. 1.1.1, we show a stratified medium of many layers. The permittivity fluctuates from layer to layer. The basic theory of waves in layered medium was covered in 5 of Volume 1. Nevertheless, even in this simple case, there can be two distinct kinds of layering. The first kind is a continuous random medium in which the random medium permittivity E(Z) is a random process that is a continuous function of z. The second kind is discrete layering in which there are abrupt changes of permittivity from layer to layer. To further illustrate the difference, we apply both models to thermal emission of a layered medium and make a comparison with observed brightness temperatures of Antarctica. We found that in order to match the observed brightness temperatures, the two models have to use drastically different physical parameters. The results illustrate the difference between a continuous random medium and a discrete random medium.
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1.1 Continuous Random Medium
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Figure 1.1.1 Stratified medium with permittivity fluctuations from layer to layer.
A common approach is to assume a Gaussian random process of the permittivity fluctuations. Figure 1.1.2 illustrates a realization of Gaussian random process as a function of position. The density of snow is used for illustration.
1.1 Continuous Random Medium
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1..----5..1.0---1-01-0---1..1.5-0---2""'00----1 250
Depth (em)
Figure 1.1.2 A single realization of a continuous Gaussian random profile with a mean density of 0.4 gjcm 3 , a correlation length of 2 mm, and a standard deviation in density of 0.0156 gjcm 3 .
For layered random media, one can assume E(Z) as a one-dimensional Gaussian random process with mean Em and variance cr 2 = OE~. The probability density function is
p(E) = ~cr exp ( - (E ~:;n)2)