Vclay from GR (Linear Index)

Summary

The linear method takes the Gamma ray index directly as the Clay volume. It is the simplest gamma ray method and the starting point for every non-linear transform. It is usually a maximum estimate of clay volume, so use it as an upper bound or when nothing better is justified.

Inputs and outputs

Equations

The gamma ray index scales the log between the clean and clay values and is clamped to the interval 0 to 1:

The clay volume is the index itself:

Single-value calculator

Behavior

Clay volume rises in a straight line from 0 at the clean pick to 1 at the clay pick. The plot shows three clay picks with the same clean pick. Moving the clay pick from 100 to 180 gAPI changes the clay volume at a gamma ray of 80 from about 0.75 to about 0.38, which shows how much the answer depends on the picks.

Parameter guidance

The method has no parameters of its own. The result depends on the two gamma ray picks, Clean gamma ray and Clay gamma ray, which every gamma-ray-based method shares. How to pick them, and why to pick them per zone, is covered on the Clay Volume page under shared parameter picking.

Worked example

A reading of 65 gAPI, with a clean pick of 20 gAPI and a clay pick of 120 gAPI:

gr, gr_clean, gr_clay = 65.0, 20.0, 120.0
igr = min(1.0, max(0.0, (gr - gr_clean) / (gr_clay - gr_clean)))
print(f"IGR = ({gr:g} - {gr_clean:g}) / ({gr_clay:g} - {gr_clean:g}) = {igr:.3f}")
print(f"Vcl = IGR = {igr:.3f}")

Output

IGR = (65 - 20) / (120 - 20) = 0.450
Vcl = IGR = 0.450

Assumptions and limitations

• The gamma ray responds only to clay. Radioactive feldspars, micas, glauconite, uranium-rich organic matter and heavy-mineral sands raise the gamma ray without adding clay, so clay volume is overestimated.
• One pair of clean and clay picks applies across the zone. If clay mineralogy or the clean-sand response changes with depth, the picks must change too.
• The gamma ray is environmentally corrected and normalized across wells, as covered in Stage 1.
• Clay volume is linear in gamma ray response. In most rocks it is not, which is why the linear index tends to overestimate clay.

QC checks

• The result is between 0 and 1, equal to 0 at the clean pick and close to 1 at the clay pick.
• A visibly clean sand reads close to zero, not a few percent.
• Compare with an independent clay indicator such as neutron-density in a clean and a shaly interval. If the gamma-ray result is consistently higher, suspect a radioactive mineral.
• Compare with the other gamma ray transforms. The ordering at a given index must be the same at every depth.

Going Deeper

The linear index is the standard first step because it is model-free: it only interpolates between two observations. The non-linear methods (Larionov, Clavier, Stieber) are all functions of this same index. Where core or XRD clay content is available, a cross-plot of core clay volume against the index shows directly how far the linear assumption is from the data and which transform, if any, fits the formation.

References

References will be added once verified.

Python reference implementation

Related methods

• Vclay from GR (Larionov, Tertiary)
• Vclay from GR (Larionov, Older Rocks)
• Vclay from GR (Clavier)
• Vclay from GR (Stieber)