Vclay from GR (Larionov, Tertiary)

Summary

The Larionov relation for Tertiary rocks converts the Gamma ray index to Clay volume with an exponential curve that reduces the linear index strongly. It is intended for younger, less consolidated rocks. Use it when only a gamma ray is available and the formation is Tertiary.

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 Larionov relation for Tertiary rocks then gives the clay volume:

Single-value calculator

Behavior

The curve is convex, so it removes most of the clay volume at low index values and converges toward 1 only near the clay pick. At an index of 0.5 it gives about 0.22, compared with 0.33 for the older-rock relation and 0.50 for the linear index. At an index of 1 it gives 0.996, not exactly 1, which is a property of the published constants.

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. The constants 0.083 and 3.7 are part of the published relation and are not normally changed.

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)))
vcl = 0.083 * (2 ** (3.7 * igr) - 1)
print(f"IGR = {igr:.3f}")
print(f"Vcl = 0.083 x (2^(3.7 x {igr:.3f}) - 1) = {vcl:.3f}")
print(f"Vcl at IGR = 1: {0.083 * (2 ** 3.7 - 1):.3f}")

Output

IGR = 0.450
Vcl = 0.083 x (2^(3.7 x 0.450) - 1) = 0.180
Vcl at IGR = 1: 0.996

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.
• The formation is Tertiary or similarly young and unconsolidated. Applying it to older, consolidated rock will under-predict clay volume.

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.
• The result at an index of 1 is slightly below 1. If a clay volume of exactly 1 is needed in shales, clamp the output.

Going Deeper

Larionov published two curves, one for Tertiary rocks and one for older rocks, from empirical comparison of the gamma ray index with independent clay estimates. The split by age is a proxy for compaction and consolidation rather than a physical boundary, so a Tertiary label is a starting point, not a guarantee. The strong reduction relative to the linear index means the method is sensitive to the clean pick: an overestimated clean value removes real clay.

References

1. Larionov, V.V., 1969. Borehole Radiometry (Radiometriya skvazhin). Nedra, Moscow (in Russian).

Python reference implementation

Related methods

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