Up: The art of fitting
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.
Up: The art of fitting
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