Empirical Mode Decomposition and Hilbert Analysis Applied to Rotation Residuals of the Solar Convection Zone

Abstract

We apply empirical mode decomposition (EMD) and Hilbert analysis to time series of rotation residuals at all latitudes and at all depths in the convection zone derived from 49 Global Oscillation Network Group data sets covering the period 1995 May 7 to 2000 May 15. Hilbert analysis combined with EMD is a tool to analyze nonlinear and nonstationary signals and is used to localize events in time-frequency space. We calculate Hilbert power spectra, power as a function of time and frequency, for each time series in order to determine whether the rotation rate in the convection zone shows any other systematic temporal variation besides the so-called torsional oscillation pattern in the upper convection zone and the periodicity of 1.3 yr near the base of the convection zone. In other regions of the convection zone, the temporal variations of the rotation residuals are compatible with a noise signal except near about 0.86 Rsolar in radius, where we find indications of a long-term period of about 6 yr. However, it is uncertain whether this signal is of solar origin, since the available data set is too short to rule out the possibility of an artifact. In addition, we calculate the amount of power contained in the torsional oscillation signal as a function of time, latitude, and radius to study the variation of the torsional oscillation pattern. The depth to which the pattern extends apparently changes with time. For example, at midlatitudes the pattern extends to deeper layers with increasing time. The degree of stationarity doubles from the surface to about 0.92 Rsolar in radius, which indicates that the torsional oscillation pattern disappears with increasing depth in agreement with previous results.