Optimal Gaussian Phase-Speed Filters in Time-Distance Helioseismology

Gaussian phase-speed filters are widely used in time-distance helioseismology to select specific wave packets whose travel times are then measured at the solar surface. This filtering increases the signal-to-noise (S/N) ratio of the temporal cross-covariances that are fitted to derive the travel times. The central phase speeds of these Gaussian filters are prescribed by a solar model; their widths are typically chosen empirically. No systematic study has been published on the effect of this filter width on the S/N ratio of the travel times. Such an analysis requires the ability to generate both noise and signal travel-time perturbations, this is now possible due to the recent introduction of a noise model and Born-approximation sensitivity kernels. These kernels allow for a derivation of travel-time perturbations as functions of a given sound-speed perturbation and are dependent on the phase-speed filters applied to the data, unlike simpler kernels. In this paper, we show that there is indeed an optimum value of the filter width that results in a maximum S/N ratio for the travel-time maps. Narrower filters exclude too much signal to produce useful travel-time perturbation maps, while broader filters are not selective enough.