scholarly journals Exchange potential from the common energy denominator approximation for the Kohn–Sham Green’s function: Application to (hyper)polarizabilities of molecular chains

2002 ◽  
Vol 116 (15) ◽  
pp. 6435-6442 ◽  
Author(s):  
M. Grüning ◽  
O. V. Gritsenko ◽  
E. J. Baerends
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Exchange Potential ◽  
The Common ◽  
Energy Denominator

Retrieving reflections by source-receiver wavefield interferometry

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. SA1-SA8 ◽  
Author(s):  
Oleg V. Poliannikov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Boundary Data ◽  
Ray Theory ◽  
Geometric Description ◽  
Virtual Source ◽  
Classical Correlation ◽  
Common Path ◽  
The Common ◽  
Stationary Sources

Source-receiver wavefield interferometry has been proposed recently as an extension of classical correlation-based interferometry. Under idealized assumptions, it allows the Green’s function between a source and a receiver to be reconstructed from boundary data that are collected using two closed contours of sources and receivers, respectively. An intuitive geometric description of this method, based on ray theory, can be used to design a method for reconstructing virtual-gather events that typically are lost when conventional interferometry is employed. In classical interferometry, events in the Green’s function between two receiver locations are reconstructed by automatically finding a ray that emanates from a stationary source, passes through the virtual source, reflects off the structure, and finally is recorded by the second receiver. The common path to both receivers is then canceled by a suitable crosscorrelation. If illumination of the structure is not ideal, such a ray may not exist and the reflection is not reconstructed. Source-receiver wave interferometry can be given a similar geometric description. The reflection off the structure can be constructed using not one but multiple rays produced simultaneously by two stationary sources. This new redatuming technique proves successful in geometries in which classical interferometry fails. Extensive numerical simulations support these theoretical conclusions.

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method

THE EMPIRICAL GREEN’S FUNCTION TECHNIQUE MODIFICATION FOR ACCELEROGRAM SYNTHESIS IN LOWSEISMICITY REGIONS

2018 ◽  
Vol 12 (5-6) ◽  
pp. 72-80
Author(s):  
A. A. Krylov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Main Shock ◽  
Amplitude Spectrum ◽  
Strong Motion ◽  
Function Technique ◽  
Focal Region ◽  
Empirical Green’S Function ◽  
Epicentral Zone ◽  
Empirical Green's Function

In the absence of strong motion records at the future construction sites, different theoretical and semi-empirical approaches are used to estimate the initial seismic vibrations of the soil. If there are records of weak earthquakes on the site and the parameters of the fault that generates the calculated earthquake are known, then the empirical Green’s function can be used. Initially, the empirical Green’s function method in the formulation of Irikura was applied for main shock record modelling using its aftershocks under the following conditions: the magnitude of the weak event is only 1–2 units smaller than the magnitude of the main shock; the focus of the weak event is localized in the focal region of a strong event, hearth, and it should be the same for both events. However, short-termed local instrumental seismological investigation, especially on seafloor, results usually with weak microearthquakes recordings. The magnitude of the observed micro-earthquakes is much lower than of the modeling event (more than 2). To test whether the method of the empirical Green’s function can be applied under these conditions, the accelerograms of the main shock of the earthquake in L'Aquila (6.04.09) with a magnitude Mw = 6.3 were modelled. The microearthquake with ML = 3,3 (21.05.2011) and unknown origin mechanism located in mainshock’s epicentral zone was used as the empirical Green’s function. It was concluded that the empirical Green’s function is to be preprocessed. The complex Fourier spectrum smoothing by moving average was suggested. After the smoothing the inverses Fourier transform results with new Green’s function. Thus, not only the amplitude spectrum is smoothed out, but also the phase spectrum. After such preliminary processing, the spectra of the calculated accelerograms and recorded correspond to each other much better. The modelling demonstrate good results within frequency range 0,1–10 Hz, considered usually for engineering seismological studies.

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