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The three-dimensional inverse-scattering and inverse-source problems with a planar aperture
1. The source can also be generated by a random wave field incident on a spatially-varying scattering potential characteristic of the medium (such as density of compressibility variations), so that .
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6. S. J. Norton and M. Linzer, “ Backprojection reconstruction of random source distributions,” J. Acoust. Soc. Am. 81, 977–985 (1987).
8. S. J. Norton, B. J. Carr, and A. J. Witten, “ Passive imaging of underground acoustic sources,” J. Acoust. Soc. Am. 119, 2840–2847 (2006).
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When signals are recorded on a planar aperture with point emitters/detectors, from either a three-dimensional
scattering potential or from a 3D spatially-incoherent source distribution, an integral equation arises containing the product of two Green's functions in the weak scattering limit (the Born approximation). This fundamental imaging equation for scatterers or sources is derived and solved analytically.
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