Conventional elastic impedance (EI) is defined as a function of the reflection angle, theta. Although EI based on the conventional 2-term AVO equation is only valid as a model to predict recorded prestack seismic data over the 0-30 degree angle range, it is defined mathematically over a 0-90 degree angle range which corresponds to a sin^2(theta) range of 0-1. Whitcombe et al (2002) recognized that outside of the 0-30° angle range, although EI is not valid for predicting prestack seismic data it may correspond with rock physics or petrophysical properties of interest. Whitcombe et al (2002) therefore extended conventional EI so that it is defined for all values of sin2? between positive and negative infinity. This is achieved by replacing sin^2(theta) with a new function tan(Chi), such that

This results in bounds on the angle Chi of -90 to +90 degrees. The seismic data corresponding to EEI at a given Chi angle can be constructed by performing a sample-by-sample linear projection of the recorded prestack amplitudes in sin^2(theta).

A more detailed discussion of EEI can be found in the EEI Theory Technical Note