Geodesic
Comparison of the Hill's method with the seismic depth migration by the Gaussian beam summation method
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 39, Tome 379 (2010), pp. 88-102

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The mathematical basement of the Hill's method of prestack depth migration is analyzed. It is shown that this method should be classified as the ray based Kirchhoff migration with so called “fat” rays, that is where the rays are substituted by isolated Gaussian beams centered on the rays and associated somehow with the input data on the seismic surface. That makes essential difference with our approach to seismic depth migration based on Gaussian beam summation method. We display on numerical examples the results of implementation of basic Hill's idea in the wave field computations. Bibl. 10 titles. 
@article{ZNSL_2010_379_a4,
     author = {M. M. Popov and P. M. Popov},
     title = {Comparison of the {Hill's} method with the seismic depth migration by the {Gaussian} beam summation method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--102},
     publisher = {mathdoc},
     volume = {379},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_379_a4/}
}
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M. M. Popov; P. M. Popov. Comparison of the Hill's method with the seismic depth migration by the Gaussian beam summation method. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 39, Tome 379 (2010), pp. 88-102. http://geodesic.mathdoc.fr/item/ZNSL_2010_379_a4/