Seismic anisotropy has been widely studied this last decade, particularly by measuring splitting of vertically propagating core shear waves. The main interest in this technique is to characterize upper mantle flow beneath seismic stations. On the other hand, the major restriction in this method is that a single station gives a single anisotropy measurement. Alternative methods have been developed in order to avoid this restriction. An accurate determination of upper mantle seismic anisotropy beneath a seismic station may allow one, by doing anisotropy correction, to characterize remote or deeper anisotropy. The Geoscope network is ideal for this purpose because it is composed of a large set (about 26) of high-quality, broadband seismometers globally distributed and because some of these stations have run for more than 10 years and most of them for more than 5 years. We selected about 100 events at each site, generally of magnitude (mb) > 6.0, and we performed systematic measurements of the splitting parameters (fast polarization direction ϕ and delay time δt) on SKS, SKKS, and PKS phases. Splitting on oceanic islands has been difficult to observe owing to the low quality of the signal but also perhaps owing to complex upper mantle structures beneath the stations. Station KIP (Kipapa, Hawaii) in the Pacific is the only oceanic Geoscope station with a clear anisotropy. We determined well-constrained splitting parameters for 10 of the 17 continental stations that may be explained by a single anisotropic layer. The poor correlation between fast polarization directions and the absolute plate motion together with the apparent incoherence between the plate velocities and the observed delay times suggest that a simple drag-induced asthenospheric flow alone fails to explain most of the observations. For some stations located on or near major lithospheric structures (TAM, Tamanrasset, Algeria, for instance), we observe a good correlation between fast polarization directions and regional structures. At station SCZ (Santa Cruz, California), we found clear variations of the splitting parameters as a function of the event backazimuth, compatible with two layers of anisotropy. Three stations (CAN (Canberra), HYB (Hyderabad, India) and SSB (Saint Sauveur Badole, France)) seem to be devoid of detectable anisotropy.