AVO - Shuey's Approximation

From Mavko (2000) we have, P-wave reflectivity versus angle:

$$R(\theta)\approx R_{0}+[ER_{0}+\frac{\Delta v}{(1-v)^{2}}]\s... ...1}{2} \frac{\Delta V_{p}}{V_{p}}[\tan^{2}\theta-\sin^{2}\theta]$$ (10)

$$R_{0}\approx \frac{1}{2} (\frac{\Delta V_{p}}{V_{p}} + \frac{\Delta \rho}{\rho})$$ (11)

$$E=F-2(1+F)\frac{1-2v}{1-v}$$ (12)

$$F=\frac{\frac{\Delta V_{p}}{V_{p}}}{\frac{\Delta V_{p}}{V_{p}}+\frac{\Delta \rho}{\rho}}$$ (13)

Empirical relations for estimating V_s from V_p Mavko (2000)

1|c|Lithology 1|c|a_i2 1|c|a_i1 1|c|a_i0

Sandstone 0.80416 -0.85588

Limestone -0.05508 1.01677 -1.03049

Dolomite 0.58321 -0.07775

Shale 0.76969 -0.86735

Castagna et al. (1992) relation used in this work is

V_s=a_i2V_p²+a_i1V_p+a_i0