The fractal dimension of variations of the solar magnetic field

Extract

Analysis of time series of the solar magnetic field energy (SMFE) at various solar latitudes ($\varphi = -75^{\circ}\div +75^{\circ}$) has been done. Higuchi's technique Higuchi(1988) to measure the fractal dimension (FD) of time series has been chosen and the daily values $B(\varphi,t)$ of the solar magnetic field on the source surface for 1960-1999 have been used. These values had been computed in IZMIRAN using method by Obridko et al. (1994) As a matter of fact, Higuchi's measurements of the FD of time series $X_t$ comes to calculation of the length of the curve $l(k)\sim<\mid X_{t+k}-X_t\mid >k^{-2}$ and estimate of the coefficient $D$ in equation $\lg {l(k)}=A-D\lg k$ for considered range of $k$. The dimensions $D(\varphi,K)$ of the time series $B(\varphi,t)^2$ have been computed for various time scales $0<k<K$ $([k]=[t]=1^d)$. It has been found that at $k>10-27$ the time series of SMFE form fractal with $D\approx1.9$.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html