Determination of Specific Time Variations in the Energy of the Earth’s Magnetic Potential Field from the IGRF Model

Abstract

A method is proposed for the analysis of time series based on a logarithmic derivative or a specific variation. As compared to conventional analyses based on the Fourier transform, the advantage of the analysis of such variations is that it allows a rough estimate of the characteristic times exceeding the length of the series. The main disadvantages are the incomplete determination of the statistical weight of each considered variation, its initial discreteness, the absence of periodicity, and the impossibility of transformation into orthogonal functions. As a simple statistical hypothesis, it is assumed that each specific variation provides an equally probable contribution to its manifestation within a considered series, and the possibility for its manifestation outward is the same as within. The proposed method of analysis is determined and tested on the series of values of the Earth’s magnetic potential field energy from the IGRF model of 1900–2020. The median value is 1/(1995 years) for all specific variations, 1/(1942 years) for the positive values, and –1/(1628 years) for the dominant negative ones. These values are in good agreement with the geodynamo theory, observations, and generally accepted observation estimates of the western drift. The least probable values extreme in moduli –1/(128 years) and –1/(19 013 years) are related to MHD advection and magnetic diffusion, which make it possible to estimate the average flow velocity and the value of the Earth’s core conductivity, respectively. The large ratio of extreme specific variations indicates that the geodynamo has a strongly nonlinear and turbulent geodynamo character . The arithmetic mean and mean square specific variations are also analyzed with respect to the geodynamo theory and observations.