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1 Introduction

The physics of the solar interior is known from inversion of solar p-mode frequencies and splittings. These measurements are derived from fitting p-mode Fourier spectra. Schou (1992) was the first one to assume a multi-normal distribution for p-mode Fourier spectra and using a real leakage matrix. Following this pioneering work, Appourchaux et al. (1997) (hereafter Part I), generalized the theoretical background for fitting p-mode Fourier spectra to complex leakage matrix, and included explicitly the correlation of the noise between the Fourier spectra. Using Monte-Carlo simulations, we showed that our fitted parameters were unbiased. We also studied systematic errors due to an imperfect knowledge of the leakage covariance matrix. Unfortunately, a theoretical knowledge of fitting data is not enough as only real data will teach us if our approach is correct. Contrary to fitting p-mode power spectra, the process of fitting the Fourier spectra as described in Part I is rather difficult to understand and visualize. Schou (1992) gave a few diagnostics for understanding how the Fourier spectra are fitted but without showing an easy way to visualize the covariance matrices.

In this paper, we show how one can easily visualize the mode and noise correlation matrices, and then derive the mode leakage matrix. In the first section, we describe 4 new diagrams that have various diagnostics power. In the second section, we describe how we use those diagrams for inferring the leakage and noise covariance matrices for the data of the Luminosity Oscillations Imager (LOI) on board the Solar and Heliospheric Observatory (SOHO) data (Appourchaux et al. 1997), and for the data of the Global Oscillations Network Group (GONG) (Hill et al. 1996). The LOI time series starts on 27 March 1996 and ends on 27 March 1997 with a duty cycle greater than 99%. The GONG time series starts on 27 August 1995 and ends on 22 August 1996 with a 75% duty cycle. In the last section we conclude by emphasizing the usefulness of these diagrams.


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Up: The art of fitting

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