Shale-Trend Normal Amplitude

Intuitively now, we have developed an understanding for where on the A-C plane to expect prospective events and a little about what a location on the plane indicates about the rocks. The perpendicular distance away from the shale trend explained above is what truly quantifies an AVA anomaly. Therefore, if we can define a unit vector that accurately describes the shale trend, the cross-product with a vector containing the values of A and C for any point in the subsurface will interpret whether that point is anomalous or not. This quantity I will call the Shale-normal Amplitude. Simply stated, defining the reflection coefficient vector

$$\vec{RFC}\;=\;(A,C)\;\;$$

and the shale trend background vector

$$\vec{S}\;=\;(cos\theta,sin\theta)\,$$

the Shale-Normal Amplitude is  

$${SNA}\;=\frac{\vert \vec{RFC} \times \vec{S}\vert}{\vert\ve... ...\vert}\;=\frac{A sin\theta\,-\,C cos\theta}{\vert\vec{S}\vert}.$$ (4)