Transfer Functions for Predicting Borehole Gamma-Ray Logs

摘要

If the gamma-ray emission rate of rocks varies only with depth, the intensity recorded in a vertical borehole is mathematically predictable. The Fourier transforms of these two functions of depth relate multiplicatively via transfer functions expressible as infinite series whose terms depend on Bessel functions. The results encode readily as programs with imperceptible run times that sample the transfers regularly for use with digitized data. Separate transfers treat non-directional and directional detectors, both supposed of negligible size and located on the borehole axis. Predicting the log from a synthetic test bed confirms and illustrates the theory.