An application of Kalman filtering in nuclear well logging

The paper describes an application of (adaptive) Kalman filtering to a geophysical subsurface estimation problem. The NGT is a sonde designed to detect the natural gamma rays of various energies emitted from a formation by the thorium (Th), uranium (U) and potassium (K). Using a minicomputer at the surface, the (Th, U, K) concentrations along the borehole have to be estimated on-line from the detection of the gamma rays in five energy windows. The standard technique in the logging industry has been to compute the elemental concentrations at a given depth from the corresponding observed counting rates. The resulting estimates have fairly large statistical errors which have limited the application of the NGT in computer reservoir evaluation. In this paper, it is shown that much better estimates can be obtained from a Kalman filter based on a dynamical model of the (Th, U, K) vertical variations.