Some conclusions

Schoenberg-Muir averaging offers a clean, straightforward method of calculating bulk properties of layered and fractured media. It is tempting to apply the method to arbitrary stacks of layers, oblique layers, and fractures, even though these cases are not really covered by the theory.

We have shown that oblique layers, at least, seem to work pretty well anyway. Work remains to be done to quantify how long the layers need to be relative to their width before the ``infinite layer'' approximation breaks down. (In the limit of ``layers'' consisting of single gridpoints, we know that the result of averaging a set of isotropic media must be isotropic.) Our results also indicate that the sensitivity of the S&M approximations to layer thickness depends on the contrast between the layers. More work also remains to quantify this effect.