A fast butterfly algorithm for generalized Radon transforms
Author(s)Hu, Jingwei; Fomel, Sergey; Demanet, Laurent; Ying, Lexing
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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 low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N[superscript 2] 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Society of Exploration Geophysicists
Hu, Jingwei, Sergey Fomel, Laurent Demanet, and Lexing Ying. “A fast butterfly algorithm for generalized Radon transforms.” GEOPHYSICS 78, no. 4 (June 21, 2013): U41-U51. © 2013 Society of Exploration Geophysicists
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