Shuey’s two-term approximation of the reflectivity equation is:
Another source of uncertainty is the fact that we are using a linear approximation to calculate the gradient from the near and far, instead of using a least squares calculation.
In Geoteric, we can use the Parser to create the Gradient and Intercept volumes based on two angle stacks, normally near and far. The Parser can be found in Processes & Workflows > Processes > Volume Maths > Parser.
To calculate the Gradient volume we can use the expression:
Where im1=near stack reflectivity, im2=far stack reflectivity. θf and θn need to be replaced by the central angle of the far and near stacks.
If the output volume is clipped (check the histogram using Opacity), you may need to re-run the parser applying a scale factor to keep the data within your dynamic range:
The intercept volume can be calculated using the expression:
If the gradient volume was scaled to avoid clipping, the intercept volume expression will need to be scaled using the same factor:
The scatterplot available within the IFC+ tool can be used to crossplot sample areas on a gradient and intercept crossplot and identify potential fluid anomalies.
Gradient vs Intercept scatterplot showing a background area (red class) and a class III anomaly area (blue class)