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Galileo was a Migrationist

It is well known that one of the many contributions of Galileo is that he refined the telescope lens to give the first clear view of the four largest moons of Jupiter. In honor of this achievement, we recognize Callisto, Europa, Ganymede and Io as the Galillean moons. However, it not so well known that Galileo also pioneered the use of accurate wavefield migration, eliminating defocussing problems due to statics and migration velocity errors. He even preceeded Claerbout's early development of paraxial migration opera- tors (Claerbout, 1985) by developing the small-angle extrap- olation operator without the use of a VAX 780 computer. In this talk, intended as a bridge between seismic and opti- cal imaging methods, I shed light on how Galileo's optical lens performs Kirchhoff-like migration of light waves in the paraxial approximation. I first review Kirchhoff migration, and then show how focussing by a thin lens performs the same function. For broken lenses (such as the lens in the origi- nal Hubble telescope) that lead to image blurring, decon- volving the point spread function removes artifacts in the blurred image. A similar procedure can be used to deblur images corrupted by broken seismic lenses.

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Department of Mathematics
University of Utah
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