A method for estimating a lithotype of an earth formation, the method includes: obtaining at least two different energy spectra of radiation received from the earth formation using the logging tool, each energy spectrum having at least one of a natural gamma-ray spectrum, a fast neutron-induced inelastic spectrum, and a thermal neutron induced capture spectrum; establishing at least one geochemically-based constraint related to elemental spectral yields to be determined; determining the elemental spectral yields from the at least two different energy spectra by decomposing the at least two different energy spectra over weighted sum of monoelemental standards wherein at least one weight is constrained by the at least one geochemically-based constraint and each weight represents a proportion of one monoelemental standard; converting the elemental spectral yields to elemental concentrations; and using a classifier to receive the elemental concentrations as input and to provide a lithotype as output.