These steps have been used both on data for which we design the spatial filtering (LOI instrument), and on data for which we did not design the filtering (GONG). As a matter of fact these diagnostics are so powerful that a theoretical knowledge of the various matrices is not always necessary to understand the data. Very often these diagnostics can also be used to find bugs in the data analysis routines. Nevertheless, it is advisable to know to the first order the leakage and ratio matrices for speeding up the analysis process.
Last but not least, the knowledge of the leakage matrices can be used for cleaning the data from m leaks and from undesired aliasing degrees. This cleaning can be performed either when the pixel time series are available (MDI data, Toutain et al. 1998) or more simply when only the Fourier spectra are available (LOI, GONG). The cleaning has very useful application for the GONG velocity data for removing aliasing degrees from l=1, 6 and 9 for instance, and for inferring better l=1 splittings (Rabello-Soares & Appourchaux 1998, in preparation). The cleaning is somewhat easier with Fourier spectra as one does not need to reduce large amount of image time series. It is advisable that, in the near future, this cleaning technique be used for higher degree modes. This will hopefully provide helioseismology with frequency and splitting data having much less systematic errors than before.
Acknowledgements
SOHO is a mission of international collaboration between ESA and NASA. This work utilizes data obtained by the Global Oscillation Network Group (GONG) project managed by the National Solar Observatory, a Division of the National Optical Astronomy Observatories, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. The GONG data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísico de Canarias and Cerro Tololo Interamerican Observatory. Many thanks to Takashi Sekii for constructive comments on the manuscript, and for extensive cyberspace chatting. I am grateful Mihir Desai for proofreading the English. Last but not least, many thanks to my wife for her patience during the painful writing of these 2 articles.
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