A simple way to improve AVO approximations

Charles P. Ursenbach

Some twenty years ago it was suggested that the average angle, =(1+2)/2, in the Aki-Richards approximation could itself be approximated by the angle of incidence, 1 . 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 by 1 actually increases the accuracy of the theory at low angles (although the 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 and 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 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.