# Extended elastic impedance

Extended elastic impedance , is an effective impedance dependent on the coordinate rotation angle in the AVO intercept/gradient domain. It is therefore the impedance equivalent of ;

where is the intercept, the gradient. If is the value above an interface and the value below then the standard impedance/reflectivity relationship applies;

It also follows that *EEI(0) = AI*. *EEI(90)* is referred to as Gradient Impedance, *GI*, and is the impedance equivalent of the AVO gradient term (or ). *EEI* can be used as the basis for well-ties, inversion and rock property analysis of chi angle stacks in the same way as *EI* does for theta angle stacks.

The formula for *EEI* can be derived from the above two equations;^{[1]}

where and , , and are normalisation constants. As with elastic impedance, the value of the background velocity ratio *k* must be kept constant for an EEI series.

*EEI* Can also be expressed as a combination of *AI* and *GI*;

*EEI* curves at various chi angles typically exhibit high correlation with a number of elastic properties. Ball et al (2014) show that the optimum chi angles depend only on the value of *k* (see table).^{[2]}

Extended elastic impedance has similar advantages to elastic impedance but applied to the intercept/gradient crossplot domain. AIGI crossplots can form the basis of a seismic rock property study by showing what facies can be separated in 2-term AVO analysis and at what chi angles.

Chi (k=0.25) | |||
---|---|---|---|

P-impedance | 1 | 0 | 0 |

S-impedance | 0.5 | -45 | |

Mu-rho | 1 | -45 | |

K-rho | 10 | ||

Lambda-rho | 18 | ||

E-rho | -24 | ||

Poisson's ratio | 45 | ||

Gradient | 0 | 1 | 90 |

## References

- ↑ Whitcombe, D. N., P. A. Connolly, R. L. Reagan, and T. C. Redshaw, 2002, Extended elastic impedance for fluid and lithology prediction: GEOPHYSICS, 67, 63–67, http://dx.doi.org/10.1190/1.1451337.
- ↑
^{2.0}^{2.1}Ball, V., L. Tenorio, J.P. Blangy, M. Thomas & C. Schiott, 2014, Uncertainty Quantification of Two-term Relative Elastic Inversion, presented at the Second EAGE Integrated Reservoir Modelling Conference