a practical application of the AVO effect, showing that a gas sand underlying a shale exhibited amplitude variation with offset. Shuey (1985) 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 gives the 3-term Shuey Equation: where and ; where =angle of incidence; = P-wave velocity in medium; = P-wave velocity contrast across interface; = S-wave velocity in medium; = S-wave velocity contrast across interface; = density in medium; = density contrast across interface; In the Shuey equation, R(0) is the reflection coefficient at normal incidence and is controlled by the contrast in acoustic impedances. G, often referred to as the AVO gradient, describes the variation of reflection amplitudes at intermediate offsets and the third term, F, describes the behaviour at large angles/far offsets that are close to the critical angle. 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. Use Modern seismic reflection surveys are designed and acquired in such a way that the same point on the subsurface is sampled multiple times, with each sample having a different source and receiver location. The seismic data is then carefully processed to preserve seismic amplitudes and accurately determine the spatial coordinates of each sample. 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. This is known as a Common Midpoint Gather (a midpoint being the area of the subsurface that a seismic wave reflects off before returning to the receiver) and in a typical seismic reflection processing workflow, the average amplitude would be calculated along the time sample, in a process known as "stacking". This process significantly reduces random noise but loses all information that could be used for AVO analysis. AVO crossplots A CMP gather is constructed, the traces are conditioned so that they reference the same two-way travel time, sorted in order of increasing offset and the amplitude of each trace at a