Inversion of gamma‐ray data for element abundances

Abstract

The conversion of airborne spectrometer data to abundances of K, U, and Th on the ground poses several problems concerning gamma‐ray interpretation. We show that the solution of the associated matrix equation Ax = c for x (the unknown abundances), where the elements of A form the empirical spectra (or calibration constants), is very dependent upon the selection of spectrometer channels or windows included in the count vector c. Assuming the matrix A is known for a particular source and detector system (here provided by the South African Geological Survey), the matrix inversion shows (1) cosmic background abundance apparently can vary within the time of a few seconds along a flight line, (2) a full‐spectrum multichannel solution is necessary to solve accurately for x, and (3) some hitherto largely ignored low energy peaks (0.94 MeV for Th and 1.12 MeV for U) should be seriously considered for the most accurate abundance estimation with a small number of channels.