Investigation of Causal Relationships of the Cross‐Scale Wave Coupling Through Information Theoretical Approach

Abstract On 2015 October 2, MMS spacecraft observed an electron micro‐injection event near the southern hemispheric high‐altitude cusp, coinciding with intense wave activity across several frequency bands. We investigated the MMS magnetic field and plasma during this event to explore cross‐scale coupling among the wave modes. Employing the Hilbert‐Huang transform, we perform an empirical mode decomposition to extract frequencies and amplitudes of the intrinsic mode functions (IMFs). In this analysis, we establish both linear and nonlinear relationships and examine the information transfer between the IMFs. Notably, the transfer entropy suggests that high frequency ion cyclotron waves may be driven by the mirror mode structures. Our case study effectively demonstrates the utility of the information theory based tools for studying cross‐scale wave coupling phenomena.