scholarly journals An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

2008 ◽  
Vol 56 (12) ◽  
pp. 3733-3742 ◽  
Author(s):  
Ana L. Fructos ◽  
Rafael R. Boix ◽  
Francisco Mesa ◽  
Francisco Medina
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Efficient Approach ◽  
Homogeneous Media

Sensitivity kernels for seismic Fresnel volume tomography

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. U35-U46 ◽  
Author(s):  
Yuzhu Liu ◽  
Liangguo Dong ◽  
Yuwei Wang ◽  
Jinping Zhu ◽  
Zaitian Ma
Keyword(s):  
Green's Functions ◽  
Heterogeneous Media ◽  
Green’S Functions ◽  
Dominant Frequency ◽  
Sensitivity Kernel ◽  
Distribution Ranges ◽  
Band Limited ◽  
Homogeneous Media ◽  
Limited Sensitivity ◽  
Fresnel Volume Tomography

Fresnel volume tomography (FVT) offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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