Equivalence between Duvall’s Law and the Time-Distance Curve

Abstract

Duvall's law is shown to be equivalent to the phase time-distance curve. The two are connected through a simple transformation. Thus, like Duvall's law, the phase time-distance curve can be analytically inverted to obtain the radial sound speed. The use of the phase information of the time-distance technique makes the inversion of the time-distance Duvall law particularly advantageous over the traditional inversion of Duvall's law. The radial sound speed can also be obtained numerically through the radial limit of the global or local tomography of the Sun. With global tomography, one can take advantage of the higher order skips of wave packets to obtain local tomograms of any section of the Sun, including the interior of the farside, that currently cannot be directly observed.