A model for the degassing of Xe, Ar, and He from the Earth has been constructed. The Earth is divided into three idealized reservoirs in terms of their noble gas inventories: undegassed mantle, degassed mantle or mid-ocean ridge basalt (MORB) mantle, and atmosphere plus continental crust. Degassing is assumed to occur via the partitioning of gases between a vapor phase and basaltic melt, in accord with He-Ar isotope systematics which require that 3He be degassed at a slower rate than 36Ar on average. A total inversion technique is used to handle the large uncertainties associated with the input parameters. The model successfully reconciles presently available isotope ratios of 129Xe/130Xe, 40Ar/36Ar, and 4He/3He in the different Earth reservoirs, and accurately predicts the present degassing rates of He and Ar. This is the first time that noble gas isotope data have been shown to be consistent with a single degassng model. The success of this model demonstrates the feasibility of a solubility-controlled degassing mechanism, and shows that there is a relationship between noble gas isotope ratios and the melt-vapor partition coefficients of those gases, which has been obscured by the complicated radiogenic growth and degassing equations. The 129Xe/130Xe ratios in MORB are shown to be consistent with the low solubility of Xe in silicate melts, which resulted in a faster degassing rate for Xe than for other gases in the context of this model. Therefore, the mean degassing time derived from Xe is not directly applicable to other gases. The degassing mantle, our end-member degassed mantle reservoir, is found to be almost completely degassed for the noble gases, while the exact degree of degassing depends on the species under consideration, as well as the choice of isotope ratios to characterize this mantle segment.

If extreme isotope ratios are used, the degree of degassing for the degassed mantle is: 99.92% for 130Xe, 99.7% for 36Ar, 97.5% for 3He, 82% for 40Ar and 88% for 4He. The mean time of degassing, measured from the formation of Earth, is 21¿7 Ma for 130Xe, 56¿19 Ma for 36Ar, 310¿120 Ma for 3He, ~1.5 Ga for 40Ar, and ~0.8 Ga 4He. Because the degassing is likely to be solubility controlled at some level, study of noble gases alone does not fully constrain the evolution of the atmosphere. However, the model can be extended to major gaseous species in the Earth's primary atmosphere if the relevant solubilities are known. Similarities between the solubilities of CO2, CO, and He, and between N2 and Ar, suggest a mean age for the total atmosphere on the order of 4.4 to 4.3 Ga. The formation of the oceans was a much later event because of the much higher solubility of H2O in silicate melt. If H2O has been the primary outgassing species for ocean water, the oceans have a mean age on the order of 2.7 Ga, suggesting that the volume ratio of continental crust to the oceans might have remained relatively constant during Earth history. ¿ American Geophysical Union 1989