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Marine Acoustics: Direct and Inverse Problems

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‘This book is a very thorough mathematical treatise on direct and inverse problems in marine acoustics. Waveguide inversion problems have not received the attention they deserve in the literature and this book may correct some of this inattention.’ John A. DeSanto, Mathematical Reviews

This book presents current research trends in the field of underwater acoustic wave direct and inverse problems. The ocean-seabed system is an acoustic waveguide, and this is the only book that treats inverse problems in a waveguide. The propagation of acoustic waves in this system is treated for various types of seabeds and the direct and inverse problems are considered in realistic ocean environments. The inverse problem is to determine the shape of an impenetrable or penetrable object, or to determine the coefficients describing the seabed, achieved by acoustically illuminating the seabed and investigating the scattered field. The book emphasizes computation of Green's Functions with new material added for elastic and poro-elastic seabeds. It addresses many areas of practical interest related to underwater acoustical imaging, including ecological survey and cleanup, protection of open water harbors, maintenance of offshore petroleum and gas enterprises, and other areas of environmental and military concern.

Marine Acoustics: Direct and Inverse Problems presents current research trends in the field of underwater acoustic wave direct and inverse problems. It is the first to investigate inverse problems in an ocean environment, with heavy emphasis on the description and resolution of the forward scattering problem.

About the Author

James L. Buchanan is Professor of Mathematics at the United States Naval Academy. He has published two books and over 30 articles in function theoretic methods, elasticity, ocean acoustics, inverse problems, and numerical analysis.

Robert P. Gilbert is Unidel Chair of Applied Analysis at the University of Delaware. He is primarily known for his treatises on function theoretic methods applied to partial differential equations and his work in elasticity. He has published 13 books and over 260 articles and is founding editor of two mathematics journals, Complex Variables and Applicable Analysis.

Armand Wirgin is Directeur de Recherche at the Laboratoire de Mécanique et d’Acoustique of the Centre National de la Recherche Scientifique. He has published over 170 articles, book chapters, and books on direct and inverse scattering of electromagnetic and elastic waves.

Yongzhi S. Xu is a University of Chattanooga Foundation Professor of Mathematics at the University of Tennessee at Chattanooga. He has published over 60 papers in direct and inverse problems in ocean acoustics, function theoretic methods, mathematical study of carcinoma and osteoporosis, and other applied partial differential equation problems.

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