Shuey equation

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.


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

where


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

and


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

and


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

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