TY - JOUR
T1 - The art of fitting p-mode spectra. II. Leakage and noise covariance matrices
AU - Appourchaux, T.
AU - Rabello-Soares, M. C.
AU - Gizon, L.
PY - 1998/10/1
Y1 - 1998/10/1
N2 - In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using "Maximum Likelihood Estimators". In this article, hereafter Part II, we show how to use the theory developed in Part I for fitting real data. We introduce 4 new diagnostics in helioseismology: the (m, v) echelle diagram, the cross echelle diagram, the inter echelle diagram, and the cross spectrum ratio. These diagnostics are extremely powerful to visualize and understand the covariance matrices of the Fourier spectra, and also to find bugs in the data analysis code. The diagrams are used to verify the computation of the leakage matrices, and also to measure quantitatively these matrices. Cross spectrum ratios are used to obtain quantitative information on the noise covariance matrices. Numerous examples using the LOI/SOHO and GONG data are given.
AB - In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using "Maximum Likelihood Estimators". In this article, hereafter Part II, we show how to use the theory developed in Part I for fitting real data. We introduce 4 new diagnostics in helioseismology: the (m, v) echelle diagram, the cross echelle diagram, the inter echelle diagram, and the cross spectrum ratio. These diagnostics are extremely powerful to visualize and understand the covariance matrices of the Fourier spectra, and also to find bugs in the data analysis code. The diagrams are used to verify the computation of the leakage matrices, and also to measure quantitatively these matrices. Cross spectrum ratios are used to obtain quantitative information on the noise covariance matrices. Numerous examples using the LOI/SOHO and GONG data are given.
KW - Methods: data analysis
KW - Observational
KW - Statistical
KW - Sun: oscillations
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U2 - 10.1051/aas:1998440
DO - 10.1051/aas:1998440
M3 - Article
AN - SCOPUS:0001657199
SN - 0365-0138
VL - 132
SP - 121
EP - 132
JO - Astronomy and Astrophysics Supplement Series
JF - Astronomy and Astrophysics Supplement Series
IS - 1
ER -