# Seismic AVO/AVA concepts

I have a basic question concerning AVO, AVA, and reflections. What is the difference between AVO/AVA and obliquity factors from a given reflection from a point in the subsurface? If there is a technical difference, how is it accounted for during processing and amplitude conditioning?

While the terms are rarely used rigorously, AVO and AVA refer to slightly different versions of the same type of analysis.

The amplitude (and phase) of a seismic reflection varies with the offset distance between the source and receiver. Hence 'amplitude variation with offset', or AVO.

Strictly speaking, however, the variation — which is given by the Zoeppritz equations — is with the incidence or offset angle, often called $\theta$. That is, the reflectivity is a function of angle, not of distance. So 'amplitude variation with angle' (AVA) is arguably a better name for the phenomenon.

It turns out that the reflectivity varies linearly with respect to $\sin^2\theta$, so we often use that relationship instead, e.g. via the 2-term Shuey approximation:

$$R(\theta) = R(0) + G\sin^2\theta$$

where R is the reflectivity and $G$ is a function of P-wave velocity $V_\mathrm{P}$, S-wave velocity $V_\mathrm{S}$, and density $\rho$.

If we're being strict about the language, the practical difference in seismic analysis is that you'd perform AVO analysis on offset gathers or partial offset stacks (such as you might get directly from processing), and AVA analysis on angle gathers or partial angle stacks (which would require you to interpolate the offset-based data using a velocity model and ray-tracing).