Shale Volume LAMBDAs

The linear gamma-ray shale index. It places a reading between the clean-sand and shale picks on a 0 to 1 scale. It is the input the Larionov shale-volume equations expect, and it is the shale volume itself only when the index is taken as linear. IGR = (GR − GRclean) / (GRshale − GRclean). Readings outside the two picks fall outside 0–1; the index is not clipped.

Shale volume for unconsolidated Tertiary rocks from the Larionov equation. Young rocks need less shale volume than a linear index implies at the same gamma ray, because the curve bows down. Vsh = 0.083 (2^(3.7 IGR) − 1). IGR is the linear gamma-ray index, a fraction. At 0 and at 1 the result is 0 and about 1.

Shale volume for older, consolidated rocks from the Larionov equation. The curve sits above the Tertiary one: the same gamma-ray index means more shale. Vsh = 0.33 (2^(2 IGR) − 1). IGR is the linear gamma-ray index, a fraction.

Three shale indices from a spectral gamma ray log, returned as one row: thorium, potassium, then the uranium-free curve. Each index is the linear pick between the clean and shale responses of that curve. Thorium and potassium avoid uranium that is not in the clay, which is why the total gamma ray on its own misleads in a radioactive sand. I_Th = (Th_log − Th_min) / (Th_shale − Th_min), and the same shape for potassium and for the uranium-free gamma ray. The three numbers are not averaged and not reduced to a minimum; that choice is left to the sheet.