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This 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 radioactive nuclei of potassium (K) and the thorium (Th) and uranium-radium (U) series. 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 using only the observed counting rates at the same depth. 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 a Kalman filter based on a dynamical model of the (Th,U,K) vertical variations can produce real-time estimates that are readily usable on a quantitative basis. The paper focuses on the usual critical issues in applying Kalman filtering to real data, namely modeling, adaptivity, and computational aspects.