# Shuey equation

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An approximation to the Aki–Richards equation, making an even simpler approximation to the full angular reflectivity solution given by the Zoeppritz equations. This formulation is given by Avseth et al.[1]

${\displaystyle R(\theta )=R(0)+G\sin ^{2}\theta +F(\tan ^{2}\theta -\sin ^{2}\theta )\ }$

where

${\displaystyle R(0)={\frac {1}{2}}\left({\frac {\Delta V_{\mathrm {P} }}{V_{\mathrm {P} }}}+{\frac {\Delta \rho }{\rho }}\right)}$

and

${\displaystyle G={\frac {1}{2}}{\frac {\Delta V_{\mathrm {P} }}{V_{\mathrm {P} }}}-2{\frac {V_{\mathrm {S} }^{2}}{V_{\mathrm {P} }^{2}}}\left({\frac {\Delta \rho }{\rho }}+2{\frac {\Delta V_{\mathrm {S} }}{V_{\mathrm {S} }}}\right)}$

and

${\displaystyle F={\frac {1}{2}}{\frac {\Delta V_{\mathrm {P} }}{V_{\mathrm {P} }}}}$

For short and medium offsets, the 2-term Shuey approximation is often used.