Wigner distribution and reduced distribution functions

1973 ◽  
Vol 58 (11) ◽  
pp. 5120-5124 ◽  
Author(s):  
D. Shalitin
Keyword(s):  
Wigner Distribution ◽  
Distribution Functions ◽  
Reduced Distribution Functions

Interferometric imaging condition for wave-equation migration

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S47-S61 ◽  
Author(s):  
Paul Sava ◽  
Oleg Poliannikov
Keyword(s):  
Large Scale ◽  
Wigner Distribution ◽  
Random Noise ◽  
Velocity Model ◽  
Distribution Functions ◽  
Small Scale ◽  
Interferometric Imaging ◽  
Imaging Data ◽  
Imaging Condition ◽  
Velocity Models

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components, corresponding to large-scale and small-scale variations. In practice, the large-scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small-scale component cannot. When the earth has significant small-scale velocity components, wavefield reconstruction does not completely describe the recorded data, and migrated images are perturbed by artifacts. There are two possible ways to address this problem: (1) improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g., wavefield crosscorrelation) or (2) reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction. Wedescribe the unknown component of the velocity model as a random function with local spatial correlations. Imaging data perturbed by such random variations is characterized by statistical instability, i.e., various wavefield components image at wrong locations that depend on the actual realization of the random model. Statistical stability can be achieved by preprocessing the reconstructed wavefields prior to the imaging condition. We use Wigner distribution functions to attenuate the random noise present in the reconstructed wavefields, parameterized as a function of image coordinates. Wavefield filtering using Wigner distribution functions and conventional imaging can be lumped together into a new form of imaging condition that we call an interferometric imaging condition because of its similarity to concepts from recent work on interferometry. The interferometric imaging condition can be formulated both for zero-offset and for multioffset data, leading to robust, efficient imaging procedures that effectively attenuate imaging artifacts caused by unknown velocity models.

scholarly journals Wigner Distributions of Quark

2016 ◽  
Vol 40 ◽  
pp. 1660055
Author(s):  
Asmita Mukherjee ◽  
Sreeraj Nair ◽  
Vikash Kumar Ojha
Keyword(s):  
Phase Space ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Space Distribution ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Phase Space Distribution ◽  
Generalized Parton Distributions ◽  
Wigner Distributions ◽  
Classical Phase Space

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

Wigner distribution functions for a relativistic linear oscillator

1998 ◽  
Vol 114 (3) ◽  
pp. 322-334 ◽  
Author(s):  
N. M. Atakishiyev ◽  
Sh. M. Nagiyev ◽  
K. B. Wolf
Keyword(s):  
Wigner Distribution ◽  
Distribution Functions ◽  
Linear Oscillator

scholarly journals Contact interaction analysis of pion GTMDs

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Jin-Li Zhang ◽  
Zhu-Fang Cui ◽  
Jia-Lun Ping ◽  
Craig D. Roberts
Keyword(s):  
Form Factor ◽  
Contact Interaction ◽  
Wigner Distribution ◽  
Interaction Analysis ◽  
Valence Quark ◽  
Distribution Functions ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Distribution Form ◽  
Negative Support

AbstractA contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction’s simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions, it is found that the pion’s mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion’s core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions, their magnitude and domain of material support decrease with increasing twist. The simplest Wigner distribution associated with the pion’s twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.

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