Amplitude versus offset

The situation becomes much more complicated in the case of non-normal incidence, due to mode conversion between P-waves and S-waves, and is described by the Zoeppritz equations.

[2] These equations have 4 unknowns and can be solved but they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved.

This form of the equations allows one to see the effects of density and P- or S- wave velocity variations on the reflection amplitudes.

[5] Ostrander was the first to introduce a practical application of the AVO effect, showing that a gas sand underlying a shale exhibited amplitude variation with offset.

[6] Shuey further modified the equations by assuming – as Ostrander had – that Poisson's ratio was the elastic property most directly related to the angular dependence of the reflection coefficient.

This equation can be further simplified by assuming that the angle of incidence is less than 30 degrees (i.e. the offset is relatively small), so the third term will tend to zero.

This is the case in most seismic surveys and gives the "Shuey Approximation": This was the final development needed before AVO analysis could become a commercial tool for the oil industry.

This allows a geophysicist to construct a group of traces with a range of offsets that all sample the same subsurface location in order to perform AVO analysis.

Plotting P (or R(0)) against G for every time sample in every CMP gather produces an AVO crossplot and can be interpreted in a number of ways.

An AVO anomaly can also include examples where amplitude with offset falls at a lower rate than the surrounding reflective events.

Most major companies use AVO routinely as a tool to "de-risk" exploration targets and to better define the extent and the composition of existing hydrocarbon reservoirs.

An important caveat is that the existence of abnormally rising or falling amplitudes can sometimes be caused by other factors, such as alternative lithologies and residual hydrocarbons in a breached gas column.