Fluid Inclusion Gas Analysis Using Weighted Non-linear Least Squares of Error

We crushed minerals in vacuum and analyzed fluid inclusion gas using three quadrupoles. We analyzed for H2, He, CH4, H2O, CO, N2, O2, H2S, Ar, CO2, C2H4, C2H6, SO2, C3H6, C3H8, C4H8, C4H10, cyclopentane (C5H10), pentane (C5H12), benzene, and toluene. Common problems in this analysis are overlapping mass peaks produced by fragmentation of gases, gas adsorption on the wall of vacuum chamber, and differences in gas signals and gas sensitivity between quadrupoles. Especially, overlapping mass peaks limit the analysis of organic gases because organic gases produce large number of fragments, contributing to the mass peak of other organic gases. To evaluate individual gas components, we either subtract this contribution by evaluating the contribution from other organic gases or multiply inverse gas sensitivity matrix by the measured masses. Unfortunately, simple subtraction accumulates the error in each step and is not suitable for complex fragmentation produced by organic gases. Matrix inversion is more suitable for this but analysis errors are not optimally distributed between gases. As a result, both methods often result in large residual errors and could produce negative gas concentrations. To overcome this limitation, we utilized weighted non-linear least squares of errors with positive constraints for gas concentrations. This method adjusts modeled mass signals to the measured mass signals for least squares of residual errors. To prevent the least squares of errors is dominated by major gas components; we set a higher weight for minor gas components than major components. Thus, all the errors are evenly distributed among gas components. We are able to obtain consistent results with Hansonburg fluorite (Socorro, NM) and using this method instead of matrix inversion substantially reduces residual errors.