Accuracy of the Born and Ray Approximations for Time-Distance Helioseismology of Flows

Time-distance helioseismology has been used extensively to study mass flows (for example, flows associated with supergranulation), active regions, and sunspots. In nearly all of these studies the sensitivity of travel times to subsurface flows has been modeled using the first-order ray approximation. The Born approximation has been proposed as a more accurate alternative. In this paper we study the accuracy of the ray and Born approximations by comparison with numerical simulations of acoustic wave propagation through simple flows in two dimensions. The numerical experiments show that the Born approximation captures the basic behavior of the travel times except when the flow is strong enough that a significant reflected wave is seen. As expected, the first-order ray approximation fails to capture scattering effects.