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Published as Geophysics, 78, no. 4, U41U51, (2013)
A fast butterfly algorithm for generalized Radon transforms
Jingwei Hu^{}, Sergey Fomel^{}, Laurent Demanet^{}, and Lexing Ying^{}
^{}Institute for Computational Engineering and Sciences (ICES)
The University of Texas at Austin
201 East 24th St, Stop C0200, Austin, TX 78712, USA
hu@ices.utexas.edu
^{}Bureau of Economic Geology and Department of Geological Sciences
Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X, Austin, TX 78713, USA
sergey.fomel@beg.utexas.edu
^{}Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue, Cambridge, MA 02139, USA
laurent@math.mit.edu
^{}Department of Mathematics and
Institute for Computational and Mathematical Engineering (ICME)
Stanford University
450 Serra Mall, Bldg 380, Stanford, CA 94305, USA
lexing@math.stanford.edu
Abstract:
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 introduce 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 (FIO) butterfly algorithm. For twodimensional data, the algorithm runs in complexity
, where
depends on the maximum frequency and offset in the dataset and the range of parameters (intercept time and slowness) in the model space. Using a series of examples, we show that the proposed algorithm can be significantly more efficient than the conventional timedomain integration.



 A fast butterfly algorithm for generalized Radon transforms  

Next: Introduction
Up: Reproducible Documents
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