The effect of the age of lead loss on t1

 

The t1 determined by the discordance correction algoritm is dependent on the age of lead loss (t2). The bias introduced by an erroneous choice of t2 is independent of the amount of common lead removed by the correction algoritm, but is quite strongly dependent on the amount of lead lost at t2 (see Fig. 3 in Andersen 2002). In general, an underestimate of the age of lead loss (t2(true)-t2(assumed)>0) will cause an underestimate of t1 (t1(true)-t1(estimated)>0). As long as the amount of lead lost at t2 is small (< 5% of the total amount of lead in the case of a mid-Proterozoic zircon having lost lead in the Phanerozoic), the estimated t1 may be expected to deviate from the true t1 by less than 2σt1, even when t2 is underestimated by as much as 500 Ma. For zircons which are more strongly discordant, the systematic error increases dramatically with the amount of lead lost. The bias is not symmetrical around the true t2 value, an overestimate of t2 will lead to a rapidly increasing overestimate of t1, which is also increasing more rapidly with increasing discordance of the zircon. It should be noted that there is an upper limit for t2, beyond which the method cannot work. This limit is defined by a t2 for which the point C2 at the 3D concordia  is situated so that the common lead correction line from A' can no longer intersect the chord C1C2 . Assuming a t2 near this limit may lead to very strongly biased upper intercept ages, or to a situation where equation 7 cannot be solved for t1.

 

When the age of lead loss cannot be constrained by independent data, the relationship between systematic errors in t1 and t2 suggests that t2 should be chosen so that the risk of a significant overestimate is minimized. Whereas using t2=0 may give meaningful t1 values for zircons which have lost lead in the early Paleozoic (at least for fl<5%), the converse is not true: Assuming a Paleozoic t2 for zircons which have suffered recent lead loss coould cause a significant overestimate of t1 even for fl=1 - 2 %. In any case, zircons, which after correction for common lead, appear to have lost more than a few percent of their lead, should be regarded as potentially biased 'in t1. The relationship between discordance and systematic error may offer a possible control on the choice of t2: If a population of zircons with variable fl is corrected at a number of possible t2, the value likely to cause least systematic error in t1 will be the one which gives the least systematic change of t1 with increasing discordance.