A method to determine the characteristic lengths of anisotropic two-dimensional random media is developed which is based on the linear theory of Aki and Chouet (1975) and Sato (1982). The correlation lengths of an equivalent anisotropic Gaussian medium are extracted from the spectrum of the codas. It is proved that for Gaussian correlation functions and weak velocity fluctuations the geometric anisotropy of the velocity distribution does not induce any propagation anisotropy. The spectral power of codas for Boolean media is also analyzed. ¿ American Geophysical Union 1992