Three‐dimensional Inversion of Time‐Distance Helioseismology Data: Ray‐Path and Fresnel‐Zone Approximations

Abstract

Time-distance helioseismology has provided important new insight into the subphotospheric structure and dynamics of sunspots, active regions, supergranular cells, and large-scale flows. These inferences have been made by using either the ray-path or Fresnel-zone approximations. We present inversion results of travel-time perturbations of wavepackets propagating inside the Sun, using both ray-path and Fresnel-zone kernels for real and artificial data. The ray approximation was the first approximation used in time-distance helioseismology for deriving the sensitivity of travel times to perturbations in the solar interior. However, new types of sensitivity kernels are being developed to take into account finite-wavelength effects (such as kernels based on a Fresnel-zone approximation) and thus improve the resolution and accuracy of the inversions. Since many results have been obtained with the ray-path approximation, it is important to compare them with the new Fresnel-zone inversions to quantify their accuracy. We have applied the two approximations to artificial and real data and concluded that both approximations provide similar results for structures lying within the scope of the kernels. Nonetheless, the vertical structure can be inferred at greater depth with the Fresnel-zone kernels than with the ray-path ones, using the same travel-time data. Applying Fresnel-zone inversion to the MDI time-distance data of 1998 June 20 we confirm the two-part structure of the sunspots previously derived with the ray approximation.