# Dictionary:delta

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$\delta ^{*}$ is one of the Thomsen anisotropic parameters (q.v.):

$\delta ^{*}={\frac {1}{2(c_{33})^{2}}}\left[2(c_{13}+c_{44})^{2}-(c_{33}-c_{44})(c_{11}+c_{33}-2c_{44})\right]$ where cij indicate elements in the elastic constants matrix . Another Thomsen anisotropic parameter is $\varepsilon$ , and with weak anisotropy, $\delta$ , which is independent of $\varepsilon$ , is generally used instead of $\delta ^{*}$ it is the most critical factor for transverse isotropy:

$\delta ={\frac {1}{2}}\left[{\frac {\varepsilon +\delta ^{*}}{1-{\frac {\beta ^{2}}{\alpha ^{2}}}}}\right]={\frac {1}{2}}{\frac {(c_{13}+c_{44})^{2}-(c_{33}-c_{44})^{2}}{c_{33}(c_{33}-c_{44})}}$ Several seismic expressions involve $\delta$ , such as the short-offset moveout correction to the vertical velocity,

$V_{NMO}=\alpha _{\parallel }(1+\delta )$ For long offsets, another anisotropy parameter, $\eta$ (eta) captures the deviation of long-offset P-wave moveout from what it would have been for isotropicity :

$\eta ={\frac {\varepsilon -\delta }{1+2\delta }}$ 