HELIOSEISMIC LINE-SHAPE ESTIMATION GIVEN STOCHASTIC EXCITATION

Spectral parameter estimation for physical systems with complicated temporal forcing functions is poorly developed. Yet, to discern the effect of large-scale convection on helioseismic line widths (cf. Lavely & Ritzwoller; Ritzwoller & Kelly, we require a method to retrieve line shape information in the presence of a stochastic source spectrum. We consider the properties of two estimators, each designed to deal with the effects of a complicated source spectrum differently. We show that one of the estimators (eqs. [10], [20]-[24]), based on a Monte Carlo model of the source spectrum, accurately estimates input line-width and amplitude trends and their errors in an idealized, but realistic, simulation of helioseismic data. The success of this method requires its application not to individual spectral lines, but to the estimation of smooth trends over a large number of spectral lines, for example, along a helioseismic dispersion branch. On average, additive noise amplifies and broadens spectral lines and tends to mimic the line-broadening effect of convection. This biasing is shown to have a relatively small effect on the line width variation within each multiplet, but can severely bias modal average amplitude and line width. Cross talk due to incomplete spatial sampling biases line widths more significantly, but a technique exists that may correct for its most significant components. Finally, line width measurement accuracy degrades as the duration of the time series length shortens, but accurate measurements of realistic line widths can be achieved with time series lengths as short as 1 month.