The accuracy of the Born and ray approximations in time-distance helioseismology

Time-distance helioseismology measures the time for acoustic wave packets t o travel, through the solar interior, from one location on the solar surfac e to another. Interpretation of travel times requires an understanding of t heir dependence on subsurface inhomogeneities. Traditionally, time-distance measurements have been modeled in the ray approximation. Recent efforts ha ve focused on the Born approximation, which includes finite-wavelength effe cts. In order to understand the limitations and ranges of validity of the r ay and Born approximations, we apply them to a simple problem-adiabatic aco ustic waves in a uniform medium with a spherical inclusion-for which a nume rical solution to the wave equation is computationally feasible. We show th at, for perturbations with length scales large compared to the size of the first Fresnel zone, both the Born and first-order ray approximations yield the same result and that the fractional error in the travel time shift, com puted by either approximation, is proportional to the fractional strength o f the sound speed perturbation. Furthermore, we demonstrate that for pertur bations with length scales smaller than the first Fresnel zone the ray appr oximation can substantially overestimate travel time perturbations while th e Born approximation gives the correct order of magnitude. The main cause o f the inaccuracy of the Born approximation travel times is the appearance o f a diffracted wave. This wave, however, has not yet been observed in the s olar data.