Some twenty years ago it was suggested that the average angle, Θ =(Θ 1 +Θ 2 )/2, in the Aki-Richards approximation could itself be approximated by the angle of incidence, 1 Θ . The newly updated CREWES Reflectivity Explorer is a useful tool for exploring such questions. Using this tool, some numerical observations are described which suggest that approximating Θ by Θ 1 actually increases the accuracy of the theory at low angles (although the Θ formulation is still superior near the critical angle). A theoretical study is outlined which is successful in explaining this interesting result. The theoretical study also suggests a means by which the strengths of both the Θ and Θ 1 formulations may be combined into one theory. This new theory is given, and is shown to be accurate over a wider range of angles than the Θ 1 formulation. It is therefore promising for use with pre-critical AVO studies. The same approach can be applied to various derivatives of the Aki-Richards approximation, such as the Fatti and Smith-Gidlow approximations.
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