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Waves generated by opportunistic or ambient noise sources and recorded by passive sensor arrays can be used to image the medium through which they travel. Spectacular results have been obtained in seismic interferometry, which open up new perspectives in acoustics, electromagnetics, and optics. The authors present, for the first time in book form, a self-contained and unified account of correlation-based and ambient noise imaging. In order to facilitate understanding of the core material, they also address a number of related topics in conventional sensor array imaging, wave propagation in random media, and high-frequency asymptotics for wave propagation. Taking a multidisciplinary approach, the book uses mathematical tools from probability, partial differential equations and asymptotic analysis, combined with the physics of wave propagation and modelling of imaging modalities. Suitable for applied mathematicians and geophysicists, it is also accessible to graduate students in applied mathematics, physics, and engineering.
List of contents
Preface; 1. Introduction and overview of the book; 2. Green's function estimation from noise cross correlations; 3. Travel time estimation from noise cross correlations using stationary phase; 4. Overview of conventional sensor array imaging; 5. Passive array imaging of reflectors using ambient noise illumination; 6. Resolution analysis for passive array imaging using ambient noise illumination; 7. Travel time estimation using ambient noise in weakly scattering media; 8. Correlation-based reflector imaging using ambient noise in weakly scattering media; 9. Virtual source imaging in homogeneous media; 10. Virtual source imaging in scattering media; 11. Imaging with intensity cross correlations; 12. A review of wave propagation in random media; Appendix. Basic facts from analysis and probability; References; Index.
About the author
Josselin Garnier is a professor in the Mathematics Department at the Université Paris Diderot, France. His background is in applied probability and he has many years of research experience in the field of wave propagation and imaging in random media. He received the Blaise Pascal Prize from the French Academy of Sciences in 2007 and the Felix Klein Prize from the European Mathematical Society in 2008.George Papanicolaou is the Robert Grimmett Professor in Mathematics at Stanford University, California. He specializes in applied and computational mathematics, partial differential equations, and stochastic processes. He received the John von Neumann Prize from the Society for Industrial and Applied Mathematics in 2006 and the William Benter Prize in Applied Mathematics in 2010. He was elected to the National Academy of Sciences in 2000 and he became a fellow of the American Mathematical Society in 2012.
Summary
This multidisciplinary book, for researchers and graduate students, presents the mathematical underpinnings in the analysis of passive sensor array imaging using ambient noise sources. It also covers a range of related topics, including conventional sensor array imaging, wave propagation in random media, and high frequency wave propagation.
