These plots are also self-checking and are useful for dating old rocks with complex histories.The plots can still produce valuable and accurate data using rocks that have been subjected to heating and metamorphic events (Dalrymple 20).Houtermans calculated the time required for lead composition of primordial lead samples to decay to the lead composition of young ores.
In order to be used as a natural clock to calculate the age of the earth, the processes generating lead isotopes must meet the four conditions of a natural clock: an irreversible process, a uniform rate, an initial condition, and a final condition.
The use of lead isotope ratios makes this isochron self-checking.
A large scattering of measurements would indicate the sample is multi-stage rather than single-stage, making the isochron unreliable.
An example isochron from Dalrymple (2004) is shown in Figure 4.8 below. Unlike other isochrons, the slope of the Pb-Pb isochron decreases with increasing age.
This is because Pb, causing the isochron to decrease in slope with increasing age.