DISPERSION IN TIME-DISTANCE HELIOSEISMOLOGY

In time-distance helioseismology, travel time is the time taken by a w ave packet to travel between two spatially separated locations on the surface of the Sun. It is computed by cross-correlating oscillation si gnals at the two locations and identifying the position of the envelop e peak of the cross-correlation function, or the position of one of it s phase peaks, as the travel time. The wave packet spectrum is a subse t of the signal spectra. Adding more frequencies to the wave packet sp ectrum is shown to not necessarily narrow the width of the envelope of the cross-correlation function. ''Dispersion'' in the travel time acr oss the spectrum restricts the minimum width of the cross-correlation function and shifts the position of the envelope and phase peaks as a function of the central frequency and width of the wave packet spectru m. Wave packets at the surface of polytropes show no dispersion in tra vel time; hence, Gaussian spectra yield Gaussian envelopes, and envelo pe widths at constant central frequency go to zero with increasing spe ctral width, showing no shift in the envelope peak or phase peaks. In the Sun, however, dispersion is inherent: Envelope and phase peaks are functions of the central frequency and width of the spectrum, and Gau ssian spectra do not yield Gaussian envelopes and can even conspire to resemble a sum of two or more Gaussians.