A simple approximation to the P‐wave reflection coefficient and its implication in the inversion of amplitude variation with offset data
I derive an approximate formula for the plane P‐wave reflection coefficient as a function of ray‐parameter. The approximation shows that the behavior of the P‐wave reflection coefficient at nonnormal angles of incidence is mainly controlled by two parameters: (1) [Formula: see text], the fluid‐fluid reflection coefficient (i.e., the reflection coefficient when the S‐wave velocities in both media are set to zero) and (2) Δμ/ρ, the ratio of the contrast in shear moduli to the average bulk density. I also show that the other formulas for the P‐wave reflection coefficient given by R. Bortfeld and R. Shuey can be approximately derived from my formula. I give numerical examples to demonstrate the accuracy of the formula. Using a least‐squares inversion of theoretical values for the reflection coefficients, I demonstrate that, in a linear inversion of amplitude versus offset data, Δμ/ρ is better estimated than the contrast in Poisson’s ratio, Δσ. Finally, comparing the exact reflection coefficient with Shuey’s approximation for typical shale and Class 1 gas‐sand models, I show that Shuey’s approximation under‐estimates the value of |Δσ| for such reflections.