Difference between revisions of "Dictionary:Thomsen anisotropic parameters"

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The relationship between the stress <math>\sigma</math> and strain <math>\varepsilon</math> vectors for polar anisotropic (transversely isotropic) media can be expressed as <math>\sigma=\textbf{C}\varepsilon</math>, where <b>C</b> is the stiffness tensor as shown in Figure [[Special:MyLanguage/Dictionary:Fig_H-7|H-7]]. With the ''z''-axes as the symmetry axis, we have <ref> Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966. </ref>
 
The relationship between the stress <math>\sigma</math> and strain <math>\varepsilon</math> vectors for polar anisotropic (transversely isotropic) media can be expressed as <math>\sigma=\textbf{C}\varepsilon</math>, where <b>C</b> is the stiffness tensor as shown in Figure [[Special:MyLanguage/Dictionary:Fig_H-7|H-7]]. With the ''z''-axes as the symmetry axis, we have <ref> Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966. </ref>
  
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See [[Special:MyLanguage/Dictionary:polar_anisotropy|''polar anisotropy'']] (transverse isotropy).
 
See [[Special:MyLanguage/Dictionary:polar_anisotropy|''polar anisotropy'']] (transverse isotropy).
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Revision as of 01:43, 14 April 2019

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The relationship between the stress and strain vectors for polar anisotropic (transversely isotropic) media can be expressed as , where C is the stiffness tensor as shown in Figure H-7. With the z-axes as the symmetry axis, we have [1]

The five independent constants, c11, c13, c33, c44, c66, for weak anisotropy have been combined into the Thomsen parameters that relate more directly to seismic data:

P-wave velocity parallel to the symmetry axis

S-wave velocity parallel to the symmetry axis

Half fractional change in the P-wave velocity

Half fractional change in the S-wave velocity



where indicate elements in the stiffness matrix. Note that , and are dimensionless and have values smaller than 0.5, frequently much smaller. For longer offsets another parameter, (eta), captures the deviation of the long-offset P-wave moveout from what it would have been for an isotropic medium[2]:


For weak polar anisotropy, the velocities of P- and S-waves at the angle θ with the symmetry axis are [3]:

See polar anisotropy (transverse isotropy).


References

  1. Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966.
  2. Alkhalifah, T. and Tsvankin, I., 1995, Velocity analysis for transversely isotropic media: Geophysics, 60, 1550–1566.
  3. Thomsen, L., 2002, Understanding seismic anisotropy in exploration and exploitation: SEG-EAGE Distinguished Instructor Series #5: Soc. Expl. Geophys.


External links

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Thomsen anisotropic parameters
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