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The 1-D Fourier transform

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Proceedings Papers

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010
Paper Number: SEG-2010-1892
... is computed followed by a 1-D Fourier transform along the t axis. Since the slant stack sums over the traces in the gather, variability within the gather is averaged. Additional limitations arise from the difficulty in picking the maximum amplitudes in the transform domain because of limited velocity...
Proceedings Papers

Paper presented at the 2008 SEG Annual Meeting, November 9–14, 2008
Paper Number: SEG-2008-2581
... (in 1-D) or plane waves (in 2-D) with the help of the digital Fourier transform (DFT). Some methods of data regularization, such as the anti-leakage Fourier transform of Xu et al. (2005) or the Fourier reconstruction method of Zwartjes and Gisolf (2006, 2007) and Zwartjes and Sacchi (2007), rely...
Proceedings Papers

Paper presented at the 1993 SEG Annual Meeting, September 26–30, 1993
Paper Number: SEG-1993-1322
... (the 1-D Fourier transform from domain) to reject ground roll. Several implementations of f-v filters are used: a surgical filter to suppress low velocity events; a phase difference filter (supposing the ground roll has 90° phase difference in both vertical and radial component data); and a cross...
Proceedings Papers

Paper presented at the 1997 SEG Annual Meeting, November 2–7, 1997
Paper Number: SEG-1997-0035
... and geophone sampling function. Us- ing the Array Theorem used by Optical/Electrical En- gineers, this Fourier transform can be quickly calculated by a concatenation of 1-D analytical functions. Rapid calculation of the recording footprint in migrated sec- tions for different recording arrays can help guide...
Proceedings Papers

Paper presented at the 1991 SEG Annual Meeting, November 10–14, 1991
Paper Number: SEG-1991-1354
...,C? me) and the transformed of the rotated input, F a) = F, @, e - e,) t Fa (7, 0 t 1% -6,) is written as +Lch) @fi-e,) G (Y, 4) = G,(T We) i?t G&t d e- in essence, the 2-D Fourier transform of f(x,y) which is reconverted into polar transformation, is transfor- ned by the 1-D Mellin transform...
Proceedings Papers

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018
Paper Number: SEG-2018-2982574
... of 2-D functions along a path defined by dl. These projections can be related to 2-D Fourier transforms of the desired 2-D function which in the case of CT scans is zx . The projection slice theorem states that a 1-D Fourier transform in the wavenumber domain of the projection defined by (3...
Proceedings Papers

Paper presented at the 1997 SEG Annual Meeting, November 2–7, 1997
Paper Number: SEG-1997-1326
... with the transform between domains. By taking the forward Fourier nonstationary convolution transform of equation can be moved to the domain to give: where In the discrete case, is the 1-D Fourier transform down each column (i.e. along the row coordinate) of the nonstationary impulse response matrices shown...
Proceedings Papers

Paper presented at the 2004 SEG Annual Meeting, October 10–15, 2004
Paper Number: SEG-2004-2144
... is the ray parameter in the t-x plane, and q is the ray parameter in the t-y plane, is intercept time. The 1-D Fourier transformed form of equation (1) is given as: += max min max min x x y y qypxi dxdyeyxdqpm (2) where is angular frequency. The discrete equation (2) is: lk N k T l yqxpi lkij...
Proceedings Papers

Paper presented at the 1997 SEG Annual Meeting, November 2–7, 1997
Paper Number: SEG-1997-1662
...-D Fourier transform of the 3-D Dirac distribution 6(x) is filtered with the wavenumber filter (13) specified in terms of the 1-D fourier transforms of the 1-D Dirac distribution At) and the derivative of the imaging function. Here is the aperture weighting function accounting both for the aperture...
Proceedings Papers

Paper presented at the 2005 SEG Annual Meeting, November 6–11, 2005
Paper Number: SEG-2005-2185
... spectrum is shown on top. The pseudopolar grid system is shown below. The specification of the amplitude spectrum to the pseudopolar grid is shown on the right. The pseudo-Radon transform is implemented using a Discrete Projection Slice Theorem relating it to the pseudopolar Fourier transform: The 1-D...
Proceedings Papers

Paper presented at the 1987 SEG Annual Meeting, October 11–15, 1987
Paper Number: SEG-1987-0479
... a two- data, and inverse Fourier transform. Frequency-domain dimensional Fourier transform and one subtraction noise-adaptive filtering attenuates spatially inco- step are performed; in the double 1-D F-K process herent noise; frequency-wavenumber (F-K) domain two separate one-dimensional Fourier...
Proceedings Papers

Paper presented at the 1988 SEG Annual Meeting, October 30–November 3, 1988
Paper Number: SEG-1988-1081
... acoustic problem relating the 1-D Fourier transform of a k,) with respect to e to a semi- circular slice of the 2-D Fourier transform of U&zJ. For a fixed k,, &, kr) gives fin&) along a semicircle of radius /k,l centered at k,& By letting k, vary, these semicircles span a cone C, which is defined as C={k...
Journal Articles
J Can Pet Technol 38 (07).
Paper Number: PETSOC-99-07-01
Published: 01 July 1999
... efficiency. Only recently do a couple of papers appear to deal with the situation (1–2) . They use the method of images for early time and Fourier Series for late time. Ohaeri and Vo (1) , using Laplace Transform, handle wellbore storage effects, skin and phase redistribution. Thompson et al. (2...
Proceedings Papers

Paper presented at the Annual Technical Meeting, June 11–14, 1994
Paper Number: PETSOC-94-14
... efficiency. Only recently a couple of paper appear to deal with the situation. 1–2 .They use the method of images for early time and Fourier series for late time. Ohaeri and Vo 1 , using Laplace Transform, handle wellbore storage effects, skin and phase redistribution. Thompson et al, 2 on the other hand...
Proceedings Papers

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019
Paper Number: SEG-2019-3199275
.... , Mohammed , 2016 , A faster method to reconstruct seismic data using anti-leakage Fourier transform : Journal of Geophysics and Engineering , 13 , 86 – 95 , doi: 10.1088/1742-2132/13/1/86 . Schonewille , M. , D. , Dishberger , and D. , Kapadia , 2014 , Comparison...
Proceedings Papers

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016
Paper Number: SEG-2016-13960140
... no domínio do tempo: Ph. D. thesis, Universidade Federal da Bahia. Page 4829© 2016 SEG SEG International Exposition and 86th Annual Meeting ABSTRACT Spectral whitening is well known as a good resolution enhancer. Based on Fourier transform, frequency bands are separated with trapezoidal filters...
Proceedings Papers

Paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, March 25–28, 2001
Paper Number: SPE-69482-MS
... analysis using Fast Fourier Transform is performed for a set of wells arranged around a single line along the axis of the reservoir. Lithological geophysical logging (GR, sonic, litho-density and neutron porosity log) were fourier- transformed and their power spectra were analyzed. Observed main...
Proceedings Papers

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010
Paper Number: SEG-2010-1581
... for spectral decomposition of seismic signals by using the deconvolutive short time Fourier transform (DSTFT) spectrogram. The DSTFT spectrogram improves the time and frequency resolution of the short time Fourier transform (STFT) spectrogram by applying a 2-D iterative deconvolution operation on the STFT...
Proceedings Papers

Paper presented at the 1988 SEG Annual Meeting, October 30–November 3, 1988
Paper Number: SEG-1988-0816
...-D Fourier transform over time 1, applied to the momentum and constitutive equations (without source) produces the differential system governing the propagation of displacement and stress with (1) (2) In these expressions u, and u. are the horizontal and ver- tical components of displacements...
Proceedings Papers

Paper presented at the 2007 SEG Annual Meeting, September 23–28, 2007
Paper Number: SEG-2007-0841
... Fourier Transform” (FFT) is applied to transform the data to the frequency domain. The so-called “tuning cube” (i.e. seismic data volume where frequency is represented by the z -direction) typically shows the amplitude of the seismic data at 1 Hz intervals. The bandwidth of the seismic data (typically up...

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