The Zoeppritz equations consist of four equations with four unknowns
RP, RS, TP, and TS, are the reflected P, reflected S, transmitted P, and transmitted S-wave amplitude coefficients, respectively, =angle of incidence, =angle of the transmitted P-wave, =angle of reflected S-wave and =angle of the transmitted S-wave. Inverting the matrix form of the Zoeppritz equations give the coefficients as a function of angle.
Although the four equations can be solved for the four unknowns, they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved (density, velocity etc.).[3] Several attempts have been made to develop approximations to the Zoeppritz equations, such as Bortfeld's (1961) and Aki & Richards’ (1980),[4] but the most successful of these is the Shuey's, which assumes Poisson's ratio to be the elastic property most directly related to the angular dependence of the reflection coefficient.