Time-distance inversion methods and results - (Invited review)

The current interpretations of the travel-time measurements in quiet and active regions on the Sun are discussed. These interpretations are based on various approximations to the 3-D wave equation such as the Fermat principle for acoustic rays and the Born approximation. The ray approximation and its modifications have provided the first view of the 3-D structures and flows in the solar interior. However, more accurate and computationally efficient approximations describing the relation between the wave travel times and the internal properties are required to study the structures and flows in detail. Inversion of the large three-dimensional datasets is efficiently carried out by regularized iterative methods. Some results of time-distance inversions for emerging active regions, sunspots, meridional flows and supergranulation are presented. An active region which emerged on the solar disk in January 1998, was studied from SOHO/MDI for eight days, both before and after its emergence at the surface. The results show a complicated structure of the emerging region in the interior, and suggest that the emerging flux ropes travel very quickly through the depth range of our observations. The estimated speed of emergence is about 1.3 km s(-1). Tomographic images of a large sunspot reveal sunspot 'fingers' - long narrow structures at a depth of about 4 Mm, which connect the sunspot with surrounding pores of the same polarity.