Solar Equatorial Rotation Rate Inferred From Inversion of Frequency Splitting of High-Degree Modes

The equatorial rotation rate has been inferred as a function of depth through the outer 16 Mm of the Sun from observations of high-degree five-minute oscillations. An optimal averaging inversion procedure due to Backus \& Gilbert (1970) has been applied to frequency splittings measured from power spectra obtained using Doppler data spanning three and five consecutive days. The resulting rotation curves have proven to be much more stable than the curves obtained from data sets of single days. The results imply that the solar rotation rate increases with depth by 0.023 /$\mu$Hz reaching a maximum at about 2 Mm below the surface, then decreases by 0.037 /$\mu$Hz down to 16 Mm.