The plane one-dimensional photon transport equation is solved for the scattered γ-radiation flux in the case of two adjacent media. One medium represents a natural ground with uniformly distributed potassium, uranium, and thorium γ-ray emitters. The other medium is air with no radioactive contaminants. The solution method is the double-P1 approximation with equidistant lethargy mesh. By this approach, which is discussed in some detail, it is possible to calculate the complete terrestrial γ-radiation field in an economical way. Calculated ground-level γ-ray exposure rates for igneous rocks with effective atomic numbers in the range 13.1 to 15.5 are presented.
Kirkegaard, P., & Løvborg, L. (1980). Transport of Terrestrial gamma-Radiation in Plane Semi-Infinite Geometry. Journal of Computational Physics, 36(1), 20-34. https://doi.org/10.1016/0021-9991(80)90172-2