Standard two-parameter inversion methods are analyzed and shown to be equivalent to each other below the critical point. New two-parameter methods are derived which are modifications of the method of Fatti et al. and which yield different estimates of the shear impedance reflectivity. The first is linear and its results can also be obtained by appropriate combination of the results of Fatti et al. The second is non-linear, containing a term quadratic in the shear impedance reflectivity, but it can be solved non-iteratively. Inversions of synthetic data are carried which show that these methods can improve on the Fatti method for large density and shear impedance reflectivities. Finally we demonstrate how to incorporate the quadratic term into estimation of shear impedance reflectivity from the intercept and gradient obtained from Shuey's two-term equation, and illustrate this with calculations on synthetic data.
View full article as PDF (0.38 Mb)