Spatial gradients from irregular, multiple-point spacecraft configurations

We present a generalized multipoint analysis of physical quantities, such as magnetic field and plasma flow, based on spatial gradient properties, where the multipoint data may be taken by irregular (distorted) configurations of any number of spacecraft. The methodology is modified from a previous, fully 3-D gradient analysis technique, designed to apply strictly to 4-point measurements and to be stable for regular spacecraft configurations. Here, we adapt the method to be tolerant against distorted configurations and to return a partial result when fewer spacecraft measurements are available. We apply the method to a variety of important physical quantities, such as the electric current density and the vorticity of plasma flows based on Cluster and THEMIS multiple-point measurements. The method may also have valuable applications on the coming Swarm mission.