AVO Slope and Intercept Attributes
Three linear approximations of Zoeppritz’s equation (Fig. 6.A.1) are commonly applied in AVO modeling. They have similar if not identical information content. However, the arrangement of terms in each equation emphasizes different AVO attributes as a function of incident angle. By making a few approximations, the interrelationship of the three equations is easy to visualize, and interpretational insight is gained.
The Shuey equation in Fig. 6.A.1 was discussed earlier. In 1987 Smith and Gidlow (and Gidlow et al, in 1992) introduced the linear-approximation equation shown in the middle of the figure. With this arrangement, Smith and Gidlow proposed a new attribute called the fluid factor that enhanced the visibility of hydrocarbon-saturated rocks. The lower equation is the more conventional one seen in the literature (Wiggins et al., 1983).
If the rock properties in Fig. 6.A.1 are replaced with the normal-incident reflection coefficient NIP, the variable B, and the last term in each equation is designated as a higher-order (H.O.) term, then the equations in Fig. 6.A.2 result. The similarity between the equations now becomes more obvious. The first term of each equation contains the normal-incident reflectivity modified by a different power of cosine-squared. The second term contains rock properties identified as the B reflectivities, which are modified by sine-squared. It should be noted that, unlike the other two, Shuey’s equation already has the assumption that background α/β = 2. This was necessary to obtain the cosine-squared term.