Some sort of interpolation is called for, but what works best for elastic tensors? Schoenburg-Muir (hereafter S&M) theory tells us how to average a stack of flat elastic layers of arbitrary anisotropy exactly, and so suggests a good starting point.
We apply this method to the gridding problem in a straightforward way: lay the model grid down on the geological model as before, but this time look inside each square grid cell to find a stack of layers to be averaged using S&M theory.
Our model results show that this S&M averaging method works quite well, and works significantly better than simply averaging the elastic stiffness constants. The price we pay is an increase in model complexity. For example, although the geological model itself may be everywhere isotropic, interpolated grid cells at dipping layer boundaries will have transverse isotropic symmetry with the symmetry axis tilted normally to the dipping lithologic boundary.