A Note on Helioseismic Tomography

Abstract

Helioseismic tomography is a form of the tomographic techniques adapted to image the interior of the Sun from observations of the acoustic oscillations at the surface. The important adaptation is the computation of travel time. Phase travel time, a measure of the time a wave packet takes to travel between two spatially separated surface locations, is computed by cross-correlating the oscillation signals and identifying a zero-crossing of the correlation function. To improve the signal-to-noise ratio, the oscillation signals, or individual correlation functions, are spatially averaged. It is tacitly assumed that the travel time of the averaged signal, or correlation function, is the average of the individual travel times. In general, this assumption is false; the phase travel time of the average signal is a solution to a nonlinear equation and depends on the amplitudes of the individual correlation functions. This demands suitable modifications of the computation of travel times and the tomographic equations.