The application of a shift theorem analysis technique to multipoint measurements

A Fourier domain technique has been proposed previously which, in principle, quanti®es the extent to which multipoint in-situ measurements can identify whether or not an observed structure is time stationary in its rest frame. Once a structure, sampled for example by four spacecraft, is shown to be quasistationary in its rest frame, the structure's velocity vector can be determined with respect to the sampling spacecraft. We investigate the properties of this technique, which we will refer to as a stationarity test, by applying it to two point measurements of a simulated boundary layer. The boundary layer was evolved using a PIC (particle in cell) electromagnetic code. Initial and boundary conditions were chosen such, that two cases could be considered, i.e. a spacecraft pair moving through (1) a time stationary boundary structure and (2) a boundary structure which is evolving (expanding) in time. The code also introduces noise in the simulated data time series which is uncorrelated between the two spacecraft. We demonstrate that, provided that the time series is Hanning windowed, the test is e€ective in determining the relative velocity between the boundary layer and spacecraft and in determining the range of frequencies over which the data can be treated as time stationary or time evolving. This work presents a ®rst step towards understanding the e€ectiveness of this technique, as required in order for it to be applied to multispacecraft data.