Gabor deconvolution revisited

Margrave, Gary F.; Henley, David C.; Lamoureux, Michael P.; Iliescu, Victor; Grossman, J. P.

doi:10.1190/1.1818033

Cited by 31 publications

(15 citation statements)

References 2 publications

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“…For other windows, it is not usually the case that the STFT factor V g γ factors as a product of two functions h(x) and k(ξ), although the smoothness 15 The symplectic Fourier transform puts one plus, and one minus, in the exponential, sô…”

Section: Short Time Fourier Transforms and Their Multipliersmentioning

confidence: 99%

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An Introduction to Numerical Methods of Pseudodifferential Operators

Lamoureux

Margrave

2008

Pseudo-Differential Operators

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Pseudodifferential operators were introduced in the mid 1900s as a powerful new tool in the development of the theory of partial differential equations. More recently, it has been observed that these operators may form the basis for novel numerical techniques used in the analysis and simulation of physical systems including wave propagation and medical imaging, as well as for advances in signal processing. This course will focus on the numerical implementations of pseudodifferential operators and practical applications. Of particular interest are: the variety of ways to implement these operators, including via fast transforms, decomposition into product-convolution operators, Gabor multipliers, and wavelet transform; speed of implementations; relation to asymptotic expansions; real experience with numerical implementations including in geophysical applications.

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Section: Short Time Fourier Transforms and Their Multipliersmentioning

confidence: 99%

“…Closely related to these ideas is the technique of wavefield extrapolation using Gabor multipliers (see [11]) as well as Gabor deconvolution (see [12], [16], [15], [13], [17]) which is a nonstationary generalization of Wiener deconvolution. Computer code based on these ideas have been implemented and are used competitively in the seismic industry.…”

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confidence: 99%

An Introduction to Numerical Methods of Pseudodifferential Operators

Lamoureux

Margrave

2008

Pseudo-Differential Operators

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“…This leaves only the estimated reflectivity in its output making it suitable to apply in a case where seismic energy loss clouding the real amplitude response commonly found in deeper level of seismic data. [3] in general sense.…”

Section: Methodsmentioning

confidence: 99%

“…al. [3] and now using Lamoureux window to decompose trace into Gabor Wave Packet. The Lamoureux window provides a more localized signal due to its zero condition on each end point whereas the Gaussian window only decays to each end point; never touches zero condition.…”

Section: Methodsmentioning

confidence: 99%

Gabor Deconvolution as Preliminary Method to Reduce Pitfall in Deeper Target Seismic Data

Oktariena

Triyoso

2018

IOP Conf. Ser.: Earth Environ. Sci.

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Abstract. Anelastic attenuation process during seismic wave propagation is the trigger of seismic non-stationary characteristic. An absorption and a scattering of energy are causing the seismic energy loss as the depth increasing. A series of thin reservoir layers found in the study area is located within Talang Akar Fm. Level, showing an indication of interpretation pitfall due to attenuation effect commonly occurred in deeper level seismic data. Attenuation effect greatly influences the seismic images of deeper target level, creating pitfalls in several aspect. Seismic amplitude in deeper target level often could not represent its real subsurface character due to a low amplitude value or a chaotic event nearing the Basement. Frequency wise, the decaying could be seen as the frequency content diminishing in deeper target. Meanwhile, seismic amplitude is the simple tool to point out Direct Hydrocarbon Indicator (DHI) in preliminary Geophysical study before a further advanced interpretation method applied. A quick-look of Post-Stack Seismic Data shows the reservoir associated with a bright spot DHI while another bigger bright spot body detected in the North East area near the field edge. A horizon slice confirms a possibility that the other bright spot zone has smaller delineation; an interpretation pitfall commonly occurs in deeper level of seismic. We evaluates this pitfall by applying Gabor Deconvolution to address the attenuation problem. Gabor Deconvolution forms a Partition of Unity to factorize the trace into smaller convolution window that could be processed as stationary packets. Gabor Deconvolution estimates both the magnitudes of source signature alongside its attenuation function. The enhanced seismic shows a better imaging in the pitfall area that previously detected as a vast bright spot zone. When the enhanced seismic is used for further advanced reprocessing process, the Seismic Impedance and Vp/Vs Ratio slices show a better reservoir delineation, in which the pitfall area is reduced and some morphed as background lithology. Gabor Deconvolution removes the attenuation by performing Gabor Domain spectral division, which in extension also reduces interpretation pitfall in deeper target seismic.

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“…Equation 1 is used to calculate the Gabor spectrum of s(xT ); in order to recover the original signal s(xT ) from its Gabor spectrum Vgs(x ′ T , kT ), analysis and synthesis windows must satisfy (Margrave and Lamoureux, 2001), which is called a partition of unity (POU). The analysis windows could be any kind of mathematical function.…”

Section: Gabor Wavefield Extrapolation Theory the Gabor Transformmentioning

confidence: 99%

Seismic depth imaging with the Gabor transform

Margrave

2008

GEOPHYSICS

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SummaryWavefield extrapolation by spatially variable phase shift is currently a migration tool of importance. In this paper, we present a new prestack seismic migration algorithm using the Gabor transform with application to the Marmousi acoustic dataset. The imaging results show a very promising depth imaging algorithm, which is competitive with the best depth imaging algorithms. The Gabor depth imaging algorithm approximates generalized phase shift plus interpolation (GPSPI) wavefield extrapolation using the Gabor, or windowed Fourier, transform to localize the wavefield. The key to an efficient algorithm is to develop an adaptive windowing scheme that only localizes the wavefield as required by the lateral velocity variation. If there is no lateral velocity variation then no localization (windowing) is required. When velocity varies rapidly, then many, relatively narrow, windows are required for accurate wavefield extrapolation. We present the details of an adaptive windowing method that has a controlled phase error. Programs have been coded with the adaptive windowing algorithm, which substantially reduces the computational burden in wavefield extrapolation when compared to the full GPSPI integral. We will illustrate the performance of this algorithm with images from prestack depth migration of the Marmousi dataset.

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Gabor deconvolution revisited

Cited by 31 publications

References 2 publications

An Introduction to Numerical Methods of Pseudodifferential Operators

An Introduction to Numerical Methods of Pseudodifferential Operators

Gabor Deconvolution as Preliminary Method to Reduce Pitfall in Deeper Target Seismic Data

Seismic depth imaging with the Gabor transform

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