Abstract
Throughout this text we have treated the seismic imaging problem as an inverse problem. To realize the goal of creating inversion formulas, we began with a simple idea. We created approximate forward modeling formulas, which we wrote as Fourier-like integrals. We then deduced their inverses, relying on the invertibility property of the Fourier transform. The inversion formulas that we obtained were also Fourier-like integrals owing to this procedure, with many of the classical Fourier-based migration techniques “falling out” as special cases of these more general formulas.
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© 2001 Springer Science+Business Media New York
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Bleistein, N., Stockwell, J.W., Cohen, J.K. (2001). The General Theory of Data Mapping. In: Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion. Interdisciplinary Applied Mathematics, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0001-4_7
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DOI: https://doi.org/10.1007/978-1-4613-0001-4_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6514-6
Online ISBN: 978-1-4613-0001-4
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