A fast butterfly algorithm for the hyperbolic Radon transform

Hu, Jingwei; Fomel, Sergey; Demanet, Laurent; Ying, Lexing

doi:10.1190/segam2012-0462.1

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2014

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“…Following our previous work on 2D hyperbolic Radon transform (Hu et al . , ), we formulate the time‐domain summation as a discrete oscillatory integral in the frequency domain and apply the 3D version of the Fourier integral operator buttery algorithm (Candès, Demanet, and Ying, ). As a result, computational complexity of the velocity scan reduces to roughly

O (N^{3} log N)

, where N is the representative of the number of points in either dimension of data space or model space.…”

Section: Introductionmentioning

confidence: 99%

A fast algorithm for 3D azimuthally anisotropic velocity scan

Fomel

Ying

2014

Geophysical Prospecting

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The conventional velocity scan can be computationally expensive for large‐scale seismic data sets, particularly when the presence of anisotropy requires multiparameter scanning. We introduce a fast algorithm for 3D azimuthally anisotropic velocity scan by generalizing the previously proposed 2D butterfly algorithm for hyperbolic Radon transforms. To compute semblance in a two‐parameter residual moveout domain, the numerical complexity of our algorithm is roughly O(N3logN) as opposed to O(N5) of the straightforward velocity scan, with N being the representative of the number of points in a particular dimension of either data space or parameter space. Synthetic and field data examples demonstrate the superior efficiency of the proposed algorithm.

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