The Born approximation in time-distance helioseismology

Physics

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Time-Distance Helioseismology, Local Helioseismology, Born Approximation

Scientific paper

Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, for example meridional flow, that are not accessible by standard global helioseismology. The interpretation of travel times has typically been done in the ray approximation. The interaction of acoustic waves with features smaller than their wavelength, such as in active regions or in the tachocline, is not expected to be well represented by ray theory. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and allows a single scattering between the source and receiver of the acoustic wave. We show that in the case of spherically symmetric perturbations the Born approximation can be easily related to normal mode perturbation theory. The Born approximation agrees with ray theory when applied to large scale perturbations, and performs better than ray theory when applied to perturbations with small spatial scale. We show, via an example OLA inversion of artificial data, that reasonable averaging kernels can be built from Born approximation kernels.

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