Question

Gamma-ray (GR) log values for clean sandstone and shale are 15 API and 115 API, respectively. If GR records 35 API for shaly-sandstone, then the GR index is _____________ (rounded off to one decimal place).

Hint:

GR index = (measured GR − clean-sand GR) / (shale GR − clean-sand GR); it is a simple linear normalisation between the two end-member log readings.

Answer 1

Correct Answer: 0.2

Alternative framing — think of \(GR_{min}\) and \(GR_{max}\) as the 0% and 100% shale markers on a linear scale spanning a total of \(115-15=100\) API units.

The measured value of 35 API sits \(35-15=20\) API units above the clean-sand marker, i.e. 20 units out of the total 100-unit span:

\[ \text{Fractional position on the GR scale}=\dfrac{20}{100}=0.20=20\% \]

So \(I_{GR}=0.2\), exactly matching the direct-formula route. (In practice this linear GR index is often further passed through a non-linear correction, such as the Larionov or Steiber relation, to get the actual shale volume \(V_{sh}\); but the question only asks for the linear GR index itself, which is exactly 0.2.)