Modeling and simulation of the horizontal component of the geomagnetic field by fractional stochastic differential equations in conjunction with empirical mode decomposition

Abstract

In this paper, we investigate the characteristics and develop a stochastic model for the horizontal component B x of the magnetic field at 22 stations of the global near‐real‐time magnetic observatory network INTERMAGNET. The model is in the form of a fractional stochastic differential equation. A method to estimate the parameters on the basis of observed data and to simulate the data using the model is given. The degree of fractional differentiation and the alpha‐stability exponent of the process are employed to cluster the stations. The B x time series possess pronounced local trends, which must be removed before modeling and simulation can be performed. This trend removal is carried out by an empirical mode decomposition. An outcome is an efficient method to simulate the B x time series by empirical mode decomposition and fractional stochastic differential equation. The numerical results indicate the existence of two distinct clusters of the INTERMAGNET: one in the mid‐ and low latitudes consistent with the D st index, and the other above geomagnetic latitude 60°N consistent with the AE index. This clustering corresponds to the inner magnetosphere and the outer magnetosphere, respectively.