The P and S impedance contrasts at each subsurface position were then estimated by applying a least squares elastic parameter inversion method Lumley and Beydoun (1991); Lumley (1993) to the preprocessed CMP gathers. This technique fits the observed AVO curves of the reflectors at each pseudo-depth and surface position to the theoretical P and S impedance curves (Figure ) which are based on linearized Zoeppritz equations.
For a unit perturbation in relative P impedance contrast, the P impedance inversion curve dominates at small angles of incidence and increases with increasing angles of incidence. For a unit perturbation in relative S impedance contrast, the S impedance inversion curve is zero at normal incidence, and is increasingly negative with increasing offset. Over the conventional range of surface reflection data acquisition geometry illumination, which is typically 0 to 35, the density inversion curve is not significant, as most of the density contrast contributes to the reflection AVO through the impedance contrasts alone. As the reflection amplitudes are mostly a combination of the P and S impedance contrast inversion curves, reflectors with P and S impedance contrasts of the same polarity and magnitude are expected to show approximately constant amplitudes versus offset. On the other hand, reflectors with P and S impedance contrasts of opposite polarities, indicating a transition zone of changing rock pore fluid properties, should show either increasing positive or increasing negative amplitude versus offset. The least-squares impedance inversion results of the preprocessed CMP gathers are shown in Figures and .