Measurements from many logging instruments such as Gamma ray counts from a pulsed neutron instrument, and amplitudes of spin-echo signals from a NMR instrument, typically have a spectrum that contains a plurality of exponentially decaying components. The slowest decaying component is obtained by fitting a single exponential over the tail end of the data and selecting a beginning for the fitting window that minimizes the product of the chi-square and the standard error of the fit. The single determined component may be subtracted from the data and the process repeated to give additional components. The determined components are indicative of thermal neutron capture cross-sections (in the case of a pulsed neutron instrument) and of the distribution of relaxation times and fluids within the pores of a rock in the case of a NMR instrument.