Authors: Xuanye Ma (ERAU), Katariina Nykyri (ERAU), Simon Wing (JHU/APL), Katherine Holland (ERAU)

The solar wind propagates at supersonic speed in the interplanetary medium. Therefore, one would expect that the upstream measurement of the solar wind (e.g., at Sun-Earth’s Lagrange point 1 (L1)) can be the cause (driver) of the downstream measurement (e.g., MMS and THEMIS). The cross-correlation provides a good measurement for the linear relation between the upstream and downstream measurements. Nevertheless, the relation between the upstream and downstream measurements can be nonlinear, which can be examined by the mutual information from the information theory. Furthermore, the information theory also provides a useful tool–transfer entropy to help identify the causality between two variables. However, one should keep in mind, the mutual information and transfer entropy provide a measure of information propagation in the system, rather than the propagation of some physical quantity. To better interpret and understand the results from the information theory, it is important to examine the relationship between the information and the real physical quantities in some simple conditions. Thus, we tested the information theory in some solar-wind-like MHD simulations (i.e., supersonic background). It shows that for the single point source the information propagates at the conical shock wave speed instead of the bulk velocity. This indicates that if the Earth’s magnetosphere is away from the cone of influence of the solar wind at L1, then the measurement of the solar wind at L1 has nothing to do with the space weather impacting the Earth.  Furthermore, we also compared the results from cross-correlation and information theory to examine whether the upstream and downstream relation is linear or nonlinear. A more complicated condition will also be discussed.