In many cases, acoustical traveltime tomography is applied by assuming isotropy of media. Indeed, isotropy makes the tomographic problem to be treated more simply. It should be admitted that some tomographic results are successfully achieved with the assumption of isotropy. Nevertheless, the simplification of isotropy is of inherent limitation. In fact, most of materials, such as rocks, composites, and biological tissues are of velocity anisotropy in varying degrees. Therefore in recent years, the investigations on anisotropic tomography attracted much attention, which not only can remove the unavoidable discrepancy produced by isotropic assumption, but also provide very useful information on the internal distribution of the physical properties in the materials being investigated.