User:Ageary/Sheriff

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Derivation of Poisson's ratio

Figure E-5. Elastic constants for isotropic media expressed in terms of each other and P- and S-wave velocities ( and ) and density .

Figure E-5 in Sheriff’s Encyclopedic Dictionary of Applied Geophysics contains basic information on elastic constants in isotropic media expressed in terms of each other and compressional and shear wave velocities and , respectively. The following are derivations of in terms of and Poisson’s ratio s, in terms of and s, and s in terms of / where and are initially defined in terms of density , shear modulus and Lame’s constant . [1]

Equations

By definition, Poisson's ratio:











(1)


By definition:






(2)


Dividing equation 1 by equation 2,






(3)


(4)


(5)


By definition:



By definition:












By definition, Poisson's ratio:




(6)

Equation 6 is the same as equation 3

References

  1. Sheriff, Robert E. (2002). Encyclopedic Dictionary of Exploration Geophysics (4th ed.). Society of Exploration Geophysicists, SEG Geophysical Reference Series No. 13. ISBN 978-1-56080-118-4. DOI: http://dx.doi.org/10.1190/1.9781560802969

See also

External links

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