A double power-law memory kernel for magnetic fluctuations in the magnetosphere–ionosphere system observed close to the geomagnetic equator

We present a method for studying dynamic correlations in the magnetosphere-ionosphere system. This method solves the Generalized Langevin equation using a memory kernel derived from the experimental autocorrelation function of the random fluctuating force that drives electric currents near Earth’s geomagnetic equator. Our results show that the correlations exhibit a double power-law decay that depends on Earth’s geomagnetic activity level. This approach accurately describes statistical observables observed close to the geomagnetic equator, such as the mean squared fluctuation of the magnetosphere, without relying on specific interparticle interactions. The long-term memory effect identified in our study could have significant implications for monitoring Earth’s space weather. • The magnetospheric mean squared fluctuation (MMSF) is a reliable statistical observable that allows us to study dynamic correlations in the Earth’s magnetosphere-ionosphere (MI) system locally. • The MMSF shows anomalous diffusion and varies in relaxation time depending on Earth’s geomagnetic activity. • The MMSF can be accurately described by integrating a phenomenological kernel into the Generalized Langevin Equation. • Long-time memory effects in the MI system are characterized by a memory kernel that follows a double power-law behavior close to the geomagnetic equator.