Parametric representation of helioseismic data

I. A method for estimation of mode correlation

¹ UMR 6525 Astrophysique, Université de Nice-Sophia-Antipolis, F-06108 Nice Cedex 2, France
² I3S UPRES-A 6070, Université de Nice-Sophia-Antipolis, F-06560 Valbonne, France

Send offprint request to: F.-X. Schmider

Received: 16 June 1998
Accepted: 12 March 1999

Abstract

This paper describes a parametric method aimed at the estimation of correlation in the excitation of solar p modes. Unlike previous work which investigated the correlation in the statistical properties of the mode's power, rather we study the excitation signal itself. In this approach, each mode is represented as a second-order autoregressive process and the correlation of the modes is modeled by the covariance of the excitation inputs. We have developed an algorithm to estimate in two steps the dynamical parameters of the modes and the covariance matrix of the excitation. We first extract the denominator of the ARMA process resulting from the sum of the different modes, then estimate iteratively the covariance matrix of the excitation. The method has been first validated on simulated signals. We verified that the power spectrum of an mode is modified by the existence of correlation in the excitation when the modes overlap. This leads to an incorrect estimation of the rotational splitting when assuming independence of the components. We checked the ability of our method to recover the correlation of the excitation and the true frequencies. We also applied the method to real data. The results have been compared to the traditional Lorentz fitting. For the modes, a good agreement on the parameters of the modes has been found, although no constraints have been imposed on the amplitudes and widths. In the present paper, we develop the mathematics of the method, and present the results obtained on simulations, as well as an application to the GOLF data. The results about correlation in the excitation of solar p modes will be reported in a forthcoming paper.