Esmersoy, Cengiz; Oristaglio, Michael L.; Levy, Bernard C. Multidimensional Born velocity inversion: Single wideband point source. (English) Zbl 0585.73038 J. Acoust. Soc. Am. 78, 1052-1057 (1985). Summary: The inverse scattering problem for an acoustic medium is considered within the approximate direct inversion framework. As opposed to iterative methods, the direct inversion approach gives an estimate of the medium velocities by operating on the observed scattered field without repeated solutions of the forward problem. Previous solutions to the multidimensional Born velocity inversion problem require either coincident source and receiver arrays or plane-wave sources. In both cases an array of point sources is required to collect the proper data for inversion. In this paper, the solution to the single point source problem is derived. It is shown that by extrapolating and imaging the observed scattered field appropriately, the projections of the velocity function at all angles can be obtained. The velocities are, then, reconstructed by the inverse Radon transform method of tomography. Cited in 1 Document MSC: 74J25 Inverse problems for waves in solid mechanics 74J99 Waves in solid mechanics 74J20 Wave scattering in solid mechanics Keywords:arbitrary Green functions; volume integral representation of; extrapolated field in terms of medium velocities; Lippmann-Schwinger equation; Born approximation; sound waves; velocity varies in all directions; constant density; nondispersive; medium; inverse scattering problem; acoustic medium; approximate direct inversion framework; estimate of the medium velocities; single point source problem; extrapolating; imaging; projections of the velocity function at all angles; inverse Radon transform method of tomography PDFBibTeX XMLCite \textit{C. Esmersoy} et al., J. Acoust. Soc. Am. 78, 1052--1057 (1985; Zbl 0585.73038) Full Text: DOI Link