Determining paleotemperature and other variables by using an error-weighted, nonlinear inversion of noble gas concentrations in water

Abstract

We present an error-weighted, nonlinear inverse technique appropriate for using noble gas concentrations in water to resolve recharge paleotemperature and up to two other variables. This method gives an estimate of the precision of the fitted variables and enables us to assess the confidence of the conceptual models used to invert the data. We illustrate the utility of this method with comprehensive data sets from the Pannonian basin, San Juan basin, and tropical Brazil (Stute and Deak, 1989; Stute et al., 1995a, b). Solving for temperature and excess air, we demonstrate that the inverse method reproduces iterative techniques but with a bias relative to the latter of up to 0.6°C. This is due to error weighting in the inverse technique placing more emphasis on the heavy noble gas concentrations in the temperature determination. The Σχ 2 of the Pannonian and San Juan data set is high and suggests that the measured noble gas concentrations are controlled by more than temperature and excess air at recharge. Solving for either recharge salinity or altitude as a third variable, synthetic data sets reproduce input values. Literature data, however, produce an average negative offset from known recharge salinity and altitude. This offset in natural systems points to a significant noble gas fractionation effect in all of the aquifer systems investigated. We also solve for fractionation by diffusive gas loss at recharge (Stute et al., 1995b). The tropical Brazil data set reproduces independently derived literature fractionation constants. Although this improves the data fit, a simple statistical test shows that diffusive fractionation alone cannot account for the sample noble gas abundance pattern observed in the tropical Brazil samples. Our derived errors of between ±1.5 and ±5.6°C (1σ) are significantly higher than the quoted literature error of ±0.8°C. This is due to both the inclusion of the third variable and the poor fit of the sample data to the conceptual model. When solving for fractionation in the Pannonian basin and San Juan data, we demonstrate that optimal recharge salinity for the combined data is now within error of meteoric water. Paleotemperature errors range between ±0.3 and ±2.4°C and ±0.8°C and ±2.3°C, respectively. In both cases, the data show a significant degree of improvement in the fit of the data to the model, the conceptual model is statistically consistent with both data sets, young samples are within error of the present day recharge temperatures, and samples previously considered outliers now agree with samples in the same age bracket. Despite the incomplete fit to the tropical Brazil data, it would appear that diffusive gas loss provides a necessary and reasonable proxy to a seemingly ubiquitous aquifer fractionation process. This must be considered when interpreting the noble gas paleotemperature in meteoric aquifer systems.