Dictionary:Delta

{{#category_index:D|delta}} $\delta ^{*}$ 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 c_ij 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 :

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