Multispacecraft missions such as Cluster, Themis, Swarm, and MMS contribute to the exploration of geospace with their capability to produce gradient and curl estimates from sets of spatially distributed in situ measurements. This paper combines all existing estimators of the reciprocal vector family for spatial derivatives and their errors. The resulting framework proves to be robust and adaptive in the sense that it works reliably for arrays with arbitrary numbers of spacecraft and possibly degenerate geometries. The analysis procedure is illustrated using synthetic data as well as magnetic measurements from the Cluster and Swarm missions. An implementation of the core algorithm in Python is shown to be compact and computationally efficient so that it can be easily integrated in the various free and open source packages for the Space Physics and Heliophysics community.

In the presented work, the spectral emissivity of basaltic melts at magmatic temperatures was retrieved in a laboratory-controlled experiment by measuring their spectral radiance. Granulated bombs of Etnean basalts were melted and the radiant energy from the melting surface was recorded by a portable spectroradiometer in the short wavelength infrared (SWIR) spectral range between 1500 and 2500 nm. The Draping algorithm, an improved algorithm for temperature and emissivity separation, was applied for the first time to SWIR hyperspectral data in order to take into account the non-uniform temperature distribution of the melt surface and, at the same time, solving the two temperatures and the spectral emissivity. The results have been validated by comparing our results with the emissivity measured at a "lava simulator". Basalt spectral emissivity does not vary significantly at magmatic temperature, but shows an absorption feature in the range 2180–2290 nm, an atmospheric window pivotal for the IR remote sensing of active volcanoes.