On some problems of the lead isotope method and its application in geology

Some new trends in the mathematical modelling of the lead isotope evolution in connection with the dynamic development of the earth's crust and with the exchange of materials between the crust and the mantle are discussed. The mathematical modelling of the derivatives with respect to time of U/Pb and Th/Pb ratios (dμ/dt and dW/dt) instead of μ and W provides the possibility of describing a wider variety in change of μ and W with less unknown parameters. It is possible to determine the two model ages (uranogenic and thorogenic) and a model parameter from the isotopic ratios of the lead in a sample. The values of this parameter indicate the time of enrichment (ancient or younger) in U/Pb, which is an extremely important index for identifying the lead source-type. The differences in the uranogenic and the thorogenic model ages, due to different geochemical behaviour and migration abilities of U and Th in metamorphic processes, provide additional information about the genesis of ores and the source-type of the lead. (author)