Regression and hypothesis tests for multivariate GNSS state time series

A satellite based observation system can continuously or repeatedly generate a user state vector time series that may contain useful information. One typical example is the collection of International GNSS Services (IGS) station daily and weekly combined solutions. Another example is the epoch-by-epoch kinematic position time series of a receiver derived by a GPS real time kinematic (RTK) technique. Although some multivariate analysis techniques have been adopted to assess the noise characteristics of multivariate state time series, statistic testings are limited to univariate time series. After review of frequently used hypotheses test statistics in univariate analysis of GNSS state time series, the paper presents a number of T-squared multivariate analysis statistics for use in the analysis of multivariate GNSS state time series. These T-squared test statistics have taken the correlation between coordinate components into account, which is neglected in univariate analysis. Numerical analysis was conducted with the multi-year time series of an IGS station to schematically demonstrate the results from the multivariate hypothesis testing in comparison with the univariate hypothesis testing results. The results have demonstrated that, in general, the testing for multivariate mean shifts and outliers tends to reject less data samples than the testing for univariate mean shifts and outliers under the same confidence level. It is noted that neither univariate nor multivariate data analysis methods are intended to replace physical analysis. Instead, these should be treated as complementary statistical methods for a prior or posteriori investigations. Physical analysis is necessary subsequently to refine and interpret the results

Rare Helium-Bearing Compound FeO2He Stabilized at Deep-Earth Conditions

There is compelling geochemical evidence for primordial helium trapped in Earth’s lower mantle, but the origin and nature of the helium source remain elusive due to scarce knowledge on viable helium-bearing compounds that are extremely rare. Here we explore materials physics underlying this prominent challenge. Our structure searches in conjunction with first-principles energetic and thermodynamic calculations uncover a remarkable helium-bearing compound FeO2He at high pressure-temperature conditions relevant to the core-mantle boundary. Calculated sound velocities consistent with seismic data validate FeO2He as a feasible constituent in ultralow velocity zones at the lowermost mantle. These mutually corroborating findings establish the first and hitherto only helium-bearing compound viable at pertinent geophysical conditions, thus providing vital physics mechanisms and materials insights for elucidating the enigmatic helium reservoir in deep Earth