Constant angle projections of seismic sections can be designed to provide maximum discrimination between fluids or lithologies. The optimum projection for a noise-free, isotropic environment can be obtained using an extension to the elastic impedance concept, which itself is an extension of acoustic impedance (AI) to nonzero angles of incidence. To achieve this, we modify the definition of elastic impedance (EI) beyond the range of physically meaningful angles by substituting tanχ for sin2θ in the two-term reflectivity equation. The primary variable now becomes χ rather than θ. We allow it to vary between −90° and +90°, which gives an extension of EI for any combination of intercept and gradient. We refer to this form of elastic impedance as extended elastic impedance (EEI).
In this paper we demonstrate that EEI can be tuned using different χ values to be approximately proportional to a number of elastic parameters, and we give EEI expressions for shear impedance (SI), bulk modulus, shear modulus, Lamé's parameter, and Vp/Vs. This leads to the identification of different areas of EEI space that tend to be optimum for fluid and lithology imaging. Having identified an appropriate χ value, the equivalent seismic section can be obtained from combinations of intercept and gradient stacks from routine AVO processing.