There are many geologic settings where anisotropic migration is necessary to obtain accurate seismic images. While this is well known, stable anisotropic parameter estimation has posed a serious challenge. Seismic data, though extensive in coverage, cannot constrain the anisotropy parameters alone (Tsvankin and Thomsen, 1995). The set of parameters is better constrained by integrating the seismic information with certain types of well data. However, the well data are generally sparse, so the parameters are only constrained at a few locations. Nonuniqueness is obviously a fundamental issue in our estimation problem.