Cosmogenic nuclides contained in the annual layers of natural materials record temporal variations in the galactic cosmic ray flux. C-14 in tree rings and Be-10 in ice cores from polar regions are often used to retrieve accurate histories of galactic cosmic rays. However, the variation in C-14 produced in the atmosphere is strongly attenuated in the carbon cycle and the amplitude of decadal scale variations in tree rings is approximately 0.2 parts per thousand. In the case of Be-10 in ice cores, the variation remains at a relatively large amplitude; however, the records are accompanied by dating uncertainties. Another material that contains Be-10 is sediment in continental areas. Terrestrial carbonate deposits sometimes form clear annual layers; however, detailed analyses on such deposits have not yet been widely conducted. Therefore, we evaluate the possibility of retrieving information concerning the galactic cosmic ray flux from the terrestrial carbonate deposits. In this paper, we report our preliminary results obtained from the measurements of Be-10 in travertine and tufa samples from South China. We find that the Be-10 flux obtained from the travertines is comparable to the level produced by galactic cosmic rays and that travertines might have potential as a tool for investigating past cosmic-ray variations with annual resolution.