TY - JOUR

T1 - A fast butterfly algorithm for generalized Radon transforms

AU - Hu, Jingwei

AU - Fomel, Sergey

AU - Demanet, Laurent

AU - Ying, Lexing

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We are grateful to Tariq Alkhalifah, Anatoly Baumstein, Ian Moore, Daniel Trad, and the anonymous reviewer for their valuable comments and suggestions. We thank Alexander Klokov for preprocessing the field data. We thank KAUST and sponsors of the Texas Consortium for Computational Seismology (TCCS) for financial support.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/6/21

Y1 - 2013/6/21

N2 - Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise lowrank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N2 log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration. © 2013 Society of Exploration Geophysicists.

AB - Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise lowrank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N2 log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration. © 2013 Society of Exploration Geophysicists.

UR - http://hdl.handle.net/10754/597264

UR - http://mr.crossref.org/iPage?doi=10.1190%2Fgeo2012-0240.1

UR - http://www.scopus.com/inward/record.url?scp=84894445454&partnerID=8YFLogxK

U2 - 10.1190/GEO2012-0240.1

DO - 10.1190/GEO2012-0240.1

M3 - Article

SN - 0016-8033

VL - 78

SP - U41-U51

JO - GEOPHYSICS

JF - GEOPHYSICS

IS - 4

ER -