This study demonstrates the feasibility of dating by the K-Ar method an eruptive sequence of silicic volcanic rocks with ages close to the limits of conventional 14C dating. Forty-six conventional K-Ar analyses of sanidine and glass from rhyolites of the Sierra La Primavera, Mexico, yielded dates of 5 to 150 Ka (thousand years). One-sigma errors range from 3 to 39 Ka. Although the samples contain small amounts of extraneous argon, most of the dates are consistent with relative ages determined in the field. The exceptions are dates on immediately postcaldera eruptive units, which are older than the dates for the caldera-producing ash-flow tuff. A similar result has been obtained on dating tuffs and lavas of some other Pleistocene calderas. This effect is attributed to incomplete outgassing of the larger amount of extraneous argon dissolved in magma that occupied a position deeper in the chamber than the ash-flow tuff magma and that erupted immediately after caldera collapse.
We present two new error equations: One, a simple extension of the commonly used equation, demonstrates the importance of including a term for the uncertainty in the spectrometer mass-discrimination factor in the error equation. The second equation is a more rigorous formulation of the propagation of errors in the calculation of the age. It yields meaningful error estimates for all proportions of radiogenic 40Ar, and, because it expresses the error in absolute rather than relative terms, it can be used to put an upper limit on the age of a sample when no radiogenic 40Ar has been resolved.