# Difference between revisions of "AVO intercept and gradient"

AVO Intercept and Gradient refer either to terms in the linearized AVO equations or to the equivalent measurements from seismic data. Wiggins et al (1983) rearranged the Aki & Richards (1980) linearization of the Zoeppritz equations to obtain;

${\displaystyle R(\theta )\approx A+B\sin ^{2}\theta +C\sin ^{2}\theta \tan ^{2}\theta }$

where

${\displaystyle A={\frac {1}{2}}({\frac {\Delta V_{P}}{V_{P}}}+{\frac {\Delta \rho }{\rho }})\,\,\,\,\,\,\,\,B={\frac {\Delta V_{P}}{2V_{P}}}-4k({\frac {\Delta V_{S}}{V_{S}}})-2k({\frac {\Delta \rho }{\rho }})\,\,\,\,\,\,\,\,C={\frac {\Delta V_{P}}{2V_{P}}}}$

A is referred to as the intercept, B the gradient and C the curvature term. k = (Vs/Vp) squared[1][2]

Intercept and gradient can be estimated from seismic data by least squares regression applied to constant time slices of moveout corrected common reflection point gathers. Care must be taken when estimating the gradient to avoid bias caused by the curvature term either by excluding large angles, typically above 30⁰, or by using a 3-term fit and discarding the third term (the curvature measurement is usually unreliable).

When this process is applied to an entire gather it results in an intercept and a gradient trace and when applied to an entire 3D dataset it will result in intercept and gradient volumes.

## References

1. Aki, K., and Richards, P., 2002, Quantitative seismology: University Science Books, Sausalito, Califonia, USA, 2nd edition.
2. Wiggins, R., Kenny, G. S. and C. D. McClure, 1983, A method for determining and displaying the shear-velocity reflectivities of a geologic formation, 1983, European Patent Application 0113944.