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Inversion of the seismic parabolic Radon transform and the seismic hyperbolic Radon transform

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Title
Inversion of the seismic parabolic Radon transform and the seismic hyperbolic Radon transform
Author
Moon, Sunghwan
Issue Date
2016-02
Publisher
TAYLOR & FRANCIS LTD
Citation
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, v.24, no.2, pp.317 - 327
Abstract
Reflection seismology is a method of exploration of the hidden structure of the earth subsurface by processing received seismograms. For a long time, this processing utilizes the so-called slant stack transform, or line Radon transform. More recently, two generalizations of the slant stack transform have been introduced to extract new features of the seismic data and to improve their treatment. These transforms are the parabolic and hyperbolic seismic Radon transforms. The first transform maps a given function to its integrals over parabolas with a fixed axis direction, whereas the second one maps a function to its integrals over hyperbolas (more generally also over ellipses and circles) of fixed axis directions. We show how they can be converted to a line Radon transform, and thereby obtain their inversion formulas. Numerical simulations for each transform were performed and commented to illustrate the suggested algorithms.
URI
https://scholarworks.unist.ac.kr/handle/201301/11261
URL
http://www.tandfonline.com/doi/abs/10.1080/17415977.2015.1025071#.VSc29dysUcg
DOI
10.1080/17415977.2015.1025071
ISSN
1741-5977
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PHY_Journal Papers
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