Empirical mode decomposition analysis of random processes in the solar atmosphere

Context. Coloured noisy components with a power law spectral energy distribution are often shown to appear in solar signals of various types. Such a frequency-dependent noise may indicate the operation of various randomly distributed dynamical processes in the solar atmosphere. Aims. We develop a recipe for the correct usage of the empirical mode decomposition (EMD) technique in the presence of coloured noise, allowing for clear distinguishing between quasi-periodic oscillatory phenomena in the solar atmosphere and superimposed random background processes. For illustration, we statistically investigate extreme ultraviolet (EUV) emission intensity variations observed with SDO/AIA in the coronal (171 angstrom), chromospheric (304 angstrom), and upper photospheric (1600 angstrom) layers of the solar atmosphere, from a quiet sun and a sunspot umbrae region. Methods. EMD has been used for analysis because of its adaptive nature and essential applicability to the processing non-stationary and amplitude-modulated time series. For the comparison of the results obtained with EMD, we use the Fourier transform technique as an etalon. Results. We empirically revealed statistical properties of synthetic coloured noises in EMD, and suggested a scheme that allows for the detection of noisy components among the intrinsic modes obtained with EMD in real signals. Application of the method to the solar EUV signals showed that they indeed behave randomly and could be represented as a combination of different coloured noises characterised by a specific value of the power law indices in their spectral energy distributions. On the other hand, 3-min oscillations in the analysed sunspot were detected to have energies significantly above the corresponding noise level. Conclusions. The correct accounting for the background frequency-dependent random processes is essential when using EMD for analysis of oscillations in the solar atmosphere. For the quiet sun region the power law index was found to increase with height above the photosphere, indicating that the higher frequency processes are trapped deeper in the quiet sun atmosphere. In contrast, lower levels of the sunspot umbrae were found to be characterised by higher values of the power law index, meaning the domination of lower frequencies deep inside the sunspot atmosphere. Comparison of the EMD results with those obtained with the Fourier transform showed good consistency, justifying the applicability of EMD.