APPENDIX B

The hole size correction of total gamma ray is based on environmental parameter t (Schlumberger, 1994), which takes into account hole and tool geometry and mud weight, as follows:

t = (W_mud/8.345) x [(2.54 x d_hole/2) – (2.54 x d_tool/2)], (1)

where

W_mud = mud weight (lb·m),

d_hole = borehole tool diameter (in), and

d_tool = logging tool diameter (in).

For the holes drilled to moderate depths (up to 5000 m) and filled with seawater, equation 1 can be simplified to:

t = 1.316 x d_hole – 3.5. (2)

The total gamma ray (gAPI) value computed from the MGT data should be multiplied by a correction factor, CF, to account for the hole conditions described by parameter t.

The correction factor to gAPI units for the MGT tool, centered in a borehole, is

CF = 0.82 – (1.31 x 10^–3)t + (5.59 x 10^–3)t²

– (2.45 x 10^–4)t³ + (4.7 x 10^–6)t⁴. (3)

For the eccentered MGT tool, CF can be calculated by:

CF = 0.812 + (2.44 x 10^–2)t + (1.36 x 10^–4)t² – (8.22 x 10^–6)t³. (4)

To compute corrected values for U, K, Th values from the MGT, the correction factors are determined by equations 5, 6, and 7, respectively:

CF_U = 0.6 + (2.37 x 10^–2)D + (2.17 x 10^–3)D², (5)

CF_K = 0.6 + (2.19 x 10^–2)D + (2.44 x 10^–3)D², and (6)

CF_T = 0.61 + (2.6 x 10^–2)D + (1.68 x 10^–3)D², (7)

where D = borehole diameter (in).

These equations are based on experimental data in a model environment (Mathis et al., 1984) and the MGT calibration results presented in Table AT2. The MGT data for K, U, and Th values should each be multiplied by their corresponding CF value. The K, U, and Th correction factors are calculated for a centered MGT tool in a water-filled borehole. If the borehole conditions differ from this case, equations 5, 6, and 7 represent only an approximation of the environmental correction.