A gamma ray log run across a sand–shale sequence recorded maximum and minimum values of $70$ API and $30$ API, respectively. A bed in this sequence has a gamma log value of $50$ API. Assuming a linear relationship between shale index and shale volume, the volume fraction of shale in the bed is ............. (rounded to one decimal place).
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Solution and Explanation
$I_{GR}=\dfrac{GR- GR_{\min}}{GR_{\max}-GR_{\min}} =\dfrac{50-30}{70-30}=\dfrac{20}{40}=0.5.$
Step 2: Convert to shale volume.
With a linear model, $V_{sh}=I_{GR}\Rightarrow V_{sh}=0.5$ (to one decimal place).
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