We measure apparent teleseismic shear wave splitting parameters at several stations of the Berkeley Digital Seismic Network (BDSN) and three temporary broadband stations of the University of California at Santa Cruz located near the San Andreas fault system in northern and central California. Previously proposed anisotropic models for the region include a two-layered structure and a structure with a constant degree of anisotropy and a horizontal fast axis that gradually rotates as a function of depth. We significantly increase the number of observations and confirm the existence of depth-dependent anisotropy beneath the San Andreas fault system. We also investigate the extent to which the enhanced data set can constrain the details of the depth-dependence. Using theoretical expressions, we determine a suite of two-layer models that fit our observations and result in practically indistinguishable apparent splitting parameters. The wide range of acceptable models indicates that apparent splitting parameters alone cannot constrain all four parameters that specify the two anisotropic layers (upper and lower fast polarization directions and delay times). Synthetic seismograms for three very different two-layer models chosen from our suite of acceptable models and a model with a gradually rotating fast axis show subtle waveform variations, and apparent, splitting parameters measured from these records do not overlap. Hence we conclude that waveforms indeed contain additional information about the anisotropic structure. We incorporate waveform data by searching for the four splitting parameters of two-layer models that minimize the splitting of several records at each station simultaneously. The resulting models largely overlap with the models obtained using the theoretical expressions, which indicates that the addition of waveform data is not sufficient to uniquely determine all four parameters of a two-layer model. Constraining the upper fast polarization direction to be parallel to the relative motion vector of the Pacific and North American plates, N35 ¿W, allows the values of the other three model parameters to be uniquely determined. The lower layer fast polarization direction beneath all stations is approximately E-W and the delay times vary from 0.85 to 1.70 s. The delay times in the upper layer are smaller and they vary between 0.50 and 1.25 s. Shear within the uppermost mantle due to the relative plate motion is a satisfactory explanation for the shallow anisotropic signature. The sublithospheric E-W fast directions may be caused by small-scale convection within a slabless window, or by motions of the lithosphere relative to the deeper mantle. ¿ 2001 American Geophysical Union