  The solar tachocline at the bottom of the convection zone is an important
region for the dynamics of the Sun and the solar dynamo. In this region, the
sound speed inferred by global helioseismology exhibits a bump of approximately
0.4% relative to the standard solar model. Global helioseismology does not
provide any information on possible latitudinal variations or asymmetries
between the Northern and Southern hemisphere. Here, we develop a time-distance
helioseismology technique, including surface- and deep-focusing measurement
schemes and a combination of both, for two-dimensional tomographic imaging of
the solar tachocline that infers radial and latitudinal variations in the sound
speed. We test the technique using artificial solar oscillation data obtained
from numerical simulations. The technique successfully recovers major features
of the simplified tachocline models. The technique is then applied to SOHO/MDI
medium-l data and provides for the first time a full two-dimensional
sound-speed perturbation image of the solar tachocline. The one-dimensional
radial profile obtained by latitudinal averaging of the image is in good
agreement with the previous global helioseismology result. It is found that the
amplitude of the sound-speed perturbation at the tachocline varies with
latitude, but it is not clear whether this is in part or fully an effect of
instrumental distortion. Our initial results demonstrate that time-distance
helioseismology can be used to probe the deep interior structure of the Sun,
including the solar tachocline.
