Extended elastic impedance

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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. 

The table shows the relative weightings of the intercept and gradient in terms of k to optimize correlation with a range of elastic properties. The right hand column shows the equivalent chi angle for a k of 0.25 (after Ball et al, 2014).[2]
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


  1. 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. 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

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Extended elastic impedance
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