Velocity anisotropy is present at a point in a medium if the seismic velocity in one direction in general differs from that in another direction. The problems associated with the determination of subsurface velocity in anisotropic media by the use of surface seismic reflection data are analyzed. Previous studies of anisotropy in exploration seismology required bore-hole data as well as surface data to detect the presence of velocity anisotropy. Three special types of wave propagation are of interest in reflection seismology, in addition to the general case. The theory of isotropic media is commonly utilized in exploration seismology. Elliptical anisotropy has been the method for handling anisotropic media in the past. The theory of transversely isotropic media is studied in detail since this is a reasonable anisotropy model for exploration use. Layered periodic isotropic structures are considered because of the relationships between the elastic coefficients that yield transverse isotropy in the limiting case for which the isotropic lavers are thin in comparison to the wavelength of a propagating disturbance. Synthetic common-depth-point reflection seismic traces were generated for a uniformly anisotropic halfspace, a model with seismic velocity increasing linearly with depth, velocity increasing stepwise with depth, a buried anisotropic interval in an otherwise isotropic section, and models characterized by the dip varying continuously with depth. Correlation methods (velocity analysis) are developed for the determination of rms velocity vs. two-way reflection time for both isotropic and anisotropic (transversely isotropic) media. These methods are applied to the models discussed above for varying amounts of anisotropy for each model. When the surfaces defined by the velocity analysis correlation matrices are integrated to determine the volume under the surface, it is possible to determine within about one percent the degree of anisotropy in a uniformly anisotropic medium. In a medium of varying anisotropy, it does not appear possible to obtain the same degree of accuracy as for the uniform case. Two isotropic dipping layer models were studied to determine the effects of dip on velocity analysis. The effects of dip are such that the analysis methods yield erroneous results for dips in excess of about 10-12 degrees for the models studied. Random noise degrades the velocity analysis (i.e., the magnitudes of the correlation peaks), but does not affect the accuracy of the results. Lateral velocity gradients appear to have no discernible effects on a velocity analysis for the models studied. Results of this study indicate that the compressional wave data normally used in reflection seismic work may not be useful for the detection of velocity anisotropy. Shear wave (SV) data, on the other hand, are ideally suited to this purpose. Hmvever, the necessity of shear wave data for the detection of anisotropy may limit these methods strictly to land use. This study indicates that the probability of detecting anisotropy by using surface methods is sufficiently high to warrant field testing. / Ph. D.