Direct measurement of-travel-time kernels for helioseismology

Solar f-modes are surface gravity waves that propagate horizontally in a thin layer near the photosphere with a dispersion relation approximately that of deep water waves. At the power maximum near frequency ω/2π = 3 mHz, the wavelength of 5 Mm is large enough for various wave scattering properties to be observable. Gizon & Birch have calculated spatial kernels for scattering in the Born approximation. In this paper, using isolated small magnetic features as approximate point scatterers, a linear-response kernel has been measured. In addition, the kernel has been estimated by deconvolving the magnetograms from the travel-time maps. The observed kernel is similar to the theoretical kernel for wave damping computed by Gizon & Birch: it includes elliptical and hyperbolic features. This is the first observational evidence to suggest that it is appropriate to use the Born approximation to compute kernels (as opposed to the ray approximation). Furthermore, the observed hyperbolic features confirm that it is important to take into account scattering of the waves coming from distant source locations (as opposed to the single-source approximation). The observed kernel is due to a superposition of the direct and indirect effects of the magnetic field. A simple model that includes both monopole and dipole scattering compares favorably with the data. This new technique appears to be promising to study how seismic waves interact with magnetic flux tubes.