This paper is concerned with anisotropic effects on seismic data and signal analysis for transversely isotropic rock media with vertical anisotropy. It is understood that these effects are significant in many practical applications, e.g. earthquake forecasting, materials exploration inside the Earth’s crust, as well as various practical works in oil industry. Under the framework of the most accepted anisotropic media model (i.e. VTI media, transverse isotropy with a vertical axis symmetry), with applications of a set of available anisotropic rock parameters for sandstone and shale, we have performed numerical calculations of the anisotropic effects. We show that for rocks with strong anisotropy, the induced relative depth error can be significantly large. Nevertheless, with an improved understanding of the seismic-signal propagation and proper data processing, the error can be reduced, which in turn may enhance the probability of forecasting accurately the various wave propagations inside the Earth’s crust, e.g. correctly forecasting the incoming earthquakes from the center of the Earth.