Parametric representation of helioseismic data I. A method for estimation of mode correlation

This paper describes a parametric method aimed at the estimation of correla tion in the excitation of solar p modes. Unlike previous work which investi gated the correlation ill the statistical properties of the mode's power, r ather we study the excitation signal itself. In this approach. each mode is represented as a second-order autoregressive process and the correlation o f 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 th e denominator of the ARMA process resulting front the sum of the different modes, their 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 l = 1 mode is modified by the existence of correla tion in the excitation when the modes overlap. This leads to an incorrect e stimation of the rotational splitting when assuming independence of the com ponents. We checked the ability of our method to recover the correlation of the excitation and the true frequencies. We also applied the method to rea l data. The results have been compared to the traditional Lorentz fitting. For the l = 1 modes, a good agreement on the parameters of the modes has be en found, although no constraints have been imposed on the amplitudes and w idths. In the present paper, we develop the mathematics of the method, and present the results obtained on simulations, as well as an application to t he GOLF data. The results about correlation in the excitation of solar p mo des will be reported in a forthcoming paper.