Natural fractures are essential elements which can be commonly observed in reservoirs. The saying that "All reservoirs should be considered fractured until proven otherwise. (Narr et al., 2006)" is the best portrayal of its universality. The study of fracture systems is of great importance since it has been proven to have a strong impact on reservoir characteristics. The goal of this thesis is to figure out the relationship between seismic signatures and vertically fractured media.In this thesis, first the effective VTI medium is obtained from well log data by using Backus averaging theory. Then, the effective ORT medium is constructed based on Schoenberg-Helbig model by embedding one vertical fracture set into VTI host medium. By comparing the anisotropy parameters, it is possible to detect one single fracture set between the host and effective media.The combination of more vertical fracture sets (not parallel) and VTI background medium is supposed to provide effective MONO medium. However, two perpendicular fracture sets result in effective ORT medium. When summing up uniformly distributed vertical fractures within azimuthal angle [−90◦, 90◦], the effective VTI medium is provided.Numerical tests are performed to simulate more realistic fracture distributions by using Gaussian functions. The results show that it is very hard to distinguish between different fracture distributions through seismic signatures. However, for models in this study, certain geophysical methods can be applied to detect different distributions. This is very model-dependent. Therefore, in the future, more work should be done to obtain further correlation between seismic signatures and fracture systems.