Gapfilling interrupted helioseismic data with the EM algorithm

Helioseismic data are often interrupted by gaps, which diminish the quality of the data. In the frequency domain, these gaps lead to systematical effects with misleading interpretation of the power spectra. We propose a gap filling method that is based on modeling solar oscillation data with a statistical process, i.e., the stochastic nature of a single oscillation is taken into account by regarding it as realization of an autoregressive (AR) processes of second order. From the whole oscillation time series given as the superposition of the realization of many excited modes, the process parameters are estimated via the expectation maximization (EM) algorithm. Then the estimated model is used to predict the further course of the oscillatory process during occurring gaps. We demonstrate the applicability of this procedure on the basis of both simulations and data obtained with the DIFOS satellite experiment suffering from gaps of 30 min duration occurring regularly every 90 min due to the orbit around the Earth.