Interconversion formulae for two-parameter AVO methods

Charles P. Ursenbach

Most AVO studies use two-parameter inversion methods. These each yield a pair of estimated paramters, such as P-wave and S-wave velocity rectivities, or intercept and gradient quantities. These methods are all approximations to a more general three-parameter method based on the Aki-Richards approximation. In addition to the pairs of parameters generated above, three-parameter inversion also yields a quantity related to density, but this inversion is often plagued by numerical instability.

For both theoretical and practical reasons, it is of value to understand the relationships between the various two-parameter methods. To this end, formal expressions are derived for the inversion errors of each method. Using these expressions, interconversion formulae are obtained, which allow one to convert the results of any two-parameter method to those of any other two-parameter method. The analysis demonstrates that the only requirement is that the maximum angle of incidence be at least a few degrees below any critical angle. The error expressions obtained also suggest the formulation of additional AVO tools that may be of use to industry.