Difference between revisions of "Dictionary:Delta"

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<math> \delta^* </math> is one of the [[Special:MyLanguage/Dictionary:Thomsen anisotropic parameters|''Thomsen anisotropic parameters'']] (q.v.):  
 
<math> \delta^* </math> is one of the [[Special:MyLanguage/Dictionary:Thomsen anisotropic parameters|''Thomsen anisotropic parameters'']] (q.v.):  
  
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\delta^* = \frac {1} {2 (c_{33})^2}\left[ 2(c_{13}+c_{44})^2-(c_{33}-c_{44})(c_{11}+c_{33}-2c_{44})\right]
 
\delta^* = \frac {1} {2 (c_{33})^2}\left[ 2(c_{13}+c_{44})^2-(c_{33}-c_{44})(c_{11}+c_{33}-2c_{44})\right]
 
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where ''c''<sub>''ij''</sub> indicate elements in the elastic constants matrix <ref name="Thomsen1986">{{cite journal|last1=Thomsen|first1=Leon|title=Weak elastic anisotropy|journal=GEOPHYSICS|volume=51|issue=10|year=1986|pages=1954–1966|doi=10.1190/1.1442051}} [http://www.ime.unicamp.br/~amelia/mt860/thomsen.pdf PDF version.]</ref>.
 
where ''c''<sub>''ij''</sub> indicate elements in the elastic constants matrix <ref name="Thomsen1986">{{cite journal|last1=Thomsen|first1=Leon|title=Weak elastic anisotropy|journal=GEOPHYSICS|volume=51|issue=10|year=1986|pages=1954–1966|doi=10.1190/1.1442051}} [http://www.ime.unicamp.br/~amelia/mt860/thomsen.pdf PDF version.]</ref>.
 
Another Thomsen anisotropic parameter is <math> \varepsilon </math>, and with weak anisotropy, <math> \delta </math>, which is independent of <math> \varepsilon </math>, is generally used instead of <math> \delta^* </math> it is the most critical factor for transverse isotropy<ref name="Thomsen 2002">{{cite book | last=Thomsen | first=Leon | title=Understanding Seismic Anisotropy in Exploration and Exploitation | publisher=Society of Exploration Geophysicists | year=2002 | doi=10.1190/1.9781560801986}}</ref>:
 
Another Thomsen anisotropic parameter is <math> \varepsilon </math>, and with weak anisotropy, <math> \delta </math>, which is independent of <math> \varepsilon </math>, is generally used instead of <math> \delta^* </math> it is the most critical factor for transverse isotropy<ref name="Thomsen 2002">{{cite book | last=Thomsen | first=Leon | title=Understanding Seismic Anisotropy in Exploration and Exploitation | publisher=Society of Exploration Geophysicists | year=2002 | doi=10.1190/1.9781560801986}}</ref>:
  
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\delta = \frac{1}{2} \left[\frac{\varepsilon +\delta^*}{1-\frac{\beta^2}{\alpha^2}}\right] = \frac {1} {2} \frac{(c_{13}+c_{44})^2-(c_{33}-c_{44})^2}{c_{33}(c_{33}-c_{44})}
 
\delta = \frac{1}{2} \left[\frac{\varepsilon +\delta^*}{1-\frac{\beta^2}{\alpha^2}}\right] = \frac {1} {2} \frac{(c_{13}+c_{44})^2-(c_{33}-c_{44})^2}{c_{33}(c_{33}-c_{44})}
 
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Several seismic expressions involve <math> \delta </math>, such as the short-offset moveout correction to the vertical velocity,  
 
Several seismic expressions involve <math> \delta </math>, such as the short-offset moveout correction to the vertical velocity,  
 
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For long offsets, another anisotropy parameter, <math> \eta </math> (eta) captures the deviation of long-offset P-wave moveout from what it would have been for isotropicity <ref name="AlkhalifahTsvankin1995">{{cite journal|last1=Alkhalifah|first1=Tariq|last2=Tsvankin|first2=Ilya|title=Velocity analysis for transversely isotropic media|journal=GEOPHYSICS|volume=60|issue=5|year=1995|pages=1550–1566|doi=10.1190/1.1443888}}[http://home.ustc.edu.cn/~zhouli35/homepage/SeisExp/paper/VelocityAnalysis/AlkhalifahVelocity%20analysis%20for%20transversely%20isotropic%20media.pdf PDF version.]</ref>:  
 
For long offsets, another anisotropy parameter, <math> \eta </math> (eta) captures the deviation of long-offset P-wave moveout from what it would have been for isotropicity <ref name="AlkhalifahTsvankin1995">{{cite journal|last1=Alkhalifah|first1=Tariq|last2=Tsvankin|first2=Ilya|title=Velocity analysis for transversely isotropic media|journal=GEOPHYSICS|volume=60|issue=5|year=1995|pages=1550–1566|doi=10.1190/1.1443888}}[http://home.ustc.edu.cn/~zhouli35/homepage/SeisExp/paper/VelocityAnalysis/AlkhalifahVelocity%20analysis%20for%20transversely%20isotropic%20media.pdf PDF version.]</ref>:  
  
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<center><math>
 
\eta=\frac{\varepsilon-\delta}{1+2\delta}
 
\eta=\frac{\varepsilon-\delta}{1+2\delta}
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== References ==
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Latest revision as of 14:28, 21 November 2018

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is one of the Thomsen anisotropic parameters (q.v.):

where cij indicate elements in the elastic constants matrix [1]. Another Thomsen anisotropic parameter is , and with weak anisotropy, , which is independent of , is generally used instead of it is the most critical factor for transverse isotropy[2]:

Several seismic expressions involve , such as the short-offset moveout correction to the vertical velocity,

For long offsets, another anisotropy parameter, (eta) captures the deviation of long-offset P-wave moveout from what it would have been for isotropicity [3]:


References

  1. Thomsen, Leon (1986). "Weak elastic anisotropy". GEOPHYSICS 51 (10): 1954–1966. doi:10.1190/1.1442051. PDF version.
  2. Thomsen, Leon (2002). Understanding Seismic Anisotropy in Exploration and Exploitation. Society of Exploration Geophysicists. doi:10.1190/1.9781560801986.
  3. Alkhalifah, Tariq; Tsvankin, Ilya (1995). "Velocity analysis for transversely isotropic media". GEOPHYSICS 60 (5): 1550–1566. doi:10.1190/1.1443888.PDF version.