Detecting geomagnetic field nonlinearities by bispectral analysis and a phase coupling nonlinear technique

Abstract

The Earth's magnetic field varies over a wide range of characteristic times, say, from years to centuries, and more. In order to detect some nonlinear features of the geomagnetic field evolution we first apply a nonlinear spectral technique, i.e. bispectral analysis, to the secular variation of Hartland Geomagnetic Observatory (U.K.). Then, due to difficulties of bispectral analysis inherent in the shortness of data, we introduce a simpler, but more efficient, technique called Spectral Phase Analysis for Quadratic Coupling Estimation (SPAQCE). Both nonlinear spectral methods here applied are based on the presence of a phase (sum and difference) coupling in case of quadratic interactions between two constituent components of the physical system underlying the generation of the geomagnetic field. The application of SPAQCE to annual means of a UK combined geomagnetic time series allows us to discriminate nonlinear interactions between couples of characteristic times (specifically 5-6, 5-8 and 2-26 years) of the field generated in the outer core.